%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG140+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n024.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 18:30:13 EDT 2022 % Result : Unsatisfiable 9.94s 10.18s % Output : Proof 10.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : ALG140+1 : TPTP v8.1.0. Released v2.7.0. % 0.10/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n024.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Wed Jun 8 17:19:19 EDT 2022 % 0.13/0.33 % CPUTime : % 9.94/10.18 (* PROOF-FOUND *) % 9.94/10.18 % SZS status Unsatisfiable % 9.94/10.18 (* BEGIN-PROOF *) % 9.94/10.18 % SZS output start Proof % 9.94/10.18 Theorem zenon_thm : False. % 9.94/10.18 Proof. % 9.94/10.18 assert (zenon_L1_ : (~((e1) = (e1))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H1d. % 9.94/10.18 apply zenon_H1d. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L1_ *) % 9.94/10.18 assert (zenon_L2_ : (~((e0) = (e1))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e0)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H1e zenon_H1f zenon_H20. % 9.94/10.18 cut (((op (e0) (e0)) = (e1)) = ((e0) = (e1))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H1e. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H1f. % 9.94/10.18 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 9.94/10.18 cut (((op (e0) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H21 zenon_H20). % 9.94/10.18 apply zenon_H1d. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L2_ *) % 9.94/10.18 assert (zenon_L3_ : (~((e2) = (e2))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H22. % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L3_ *) % 9.94/10.18 assert (zenon_L4_ : (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H23 zenon_H24 zenon_H20. % 9.94/10.18 cut (((op (e0) (e0)) = (e2)) = ((e0) = (e2))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H23. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H24. % 9.94/10.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.18 cut (((op (e0) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H21 zenon_H20). % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L4_ *) % 9.94/10.18 assert (zenon_L5_ : (~((e1) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H25 zenon_H26 zenon_H27. % 9.94/10.18 cut (((op (e1) (e1)) = (e2)) = ((e1) = (e2))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H25. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H26. % 9.94/10.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.18 cut (((op (e1) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H28 zenon_H27). % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L5_ *) % 9.94/10.18 assert (zenon_L6_ : (~((e3) = (e3))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H29. % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L6_ *) % 9.94/10.18 assert (zenon_L7_ : (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e0)) = (e0)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H2a zenon_H2b zenon_H20. % 9.94/10.18 cut (((op (e0) (e0)) = (e3)) = ((e0) = (e3))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H2a. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H2b. % 9.94/10.18 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.18 cut (((op (e0) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H21 zenon_H20). % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L7_ *) % 9.94/10.18 assert (zenon_L8_ : (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H2c zenon_H2d zenon_H27. % 9.94/10.18 cut (((op (e1) (e1)) = (e3)) = ((e1) = (e3))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H2c. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H2d. % 9.94/10.18 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.18 cut (((op (e1) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H28 zenon_H27). % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L8_ *) % 9.94/10.18 assert (zenon_L9_ : ((op (e2) (e2)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H2e zenon_H2f zenon_H30. % 9.94/10.18 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 9.94/10.18 cut (((e3) = (e3)) = ((e2) = (e3))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H30. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H31. % 9.94/10.18 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.18 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e2) (e2)) = (e2)) = ((e3) = (e2))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H32. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H2e. % 9.94/10.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.18 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H33 zenon_H2f). % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L9_ *) % 9.94/10.18 assert (zenon_L10_ : (~((e0) = (e0))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H34. % 9.94/10.18 apply zenon_H34. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L10_ *) % 9.94/10.18 assert (zenon_L11_ : ((~((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 (e0) (e0)) = (e0)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H35 zenon_H20. % 9.94/10.18 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 9.94/10.18 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (op (e0) (e0))) = (e0))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H37. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H20. % 9.94/10.18 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 9.94/10.18 cut (((op (e0) (e0)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 9.94/10.18 congruence. % 9.94/10.18 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H39 | zenon_intro zenon_H3a ]. % 9.94/10.18 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e0)) = (op (e0) (op (e0) (e0))))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H38. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H39. % 9.94/10.18 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 9.94/10.18 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e0) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 9.94/10.18 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_H34. apply refl_equal. % 9.94/10.18 exact (zenon_H21 zenon_H20). % 9.94/10.18 apply zenon_H3a. apply refl_equal. % 9.94/10.18 apply zenon_H3a. apply refl_equal. % 9.94/10.18 apply zenon_H34. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L11_ *) % 9.94/10.18 assert (zenon_L12_ : (~((op (e1) (op (e1) (e1))) = (e1))) -> ((op (e1) (e1)) = (e1)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H3c zenon_H27. % 9.94/10.18 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (op (e1) (e1))) = (e1))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H3c. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H27. % 9.94/10.18 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 9.94/10.18 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 9.94/10.18 congruence. % 9.94/10.18 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_H3e | zenon_intro zenon_H3f ]. % 9.94/10.18 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e1)) = (op (e1) (op (e1) (e1))))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H3d. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H3e. % 9.94/10.18 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 9.94/10.18 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e1) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 9.94/10.18 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_H1d. apply refl_equal. % 9.94/10.18 exact (zenon_H28 zenon_H27). % 9.94/10.18 apply zenon_H3f. apply refl_equal. % 9.94/10.18 apply zenon_H3f. apply refl_equal. % 9.94/10.18 apply zenon_H1d. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L12_ *) % 9.94/10.18 assert (zenon_L13_ : ((~((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). % 9.94/10.18 do 0 intro. intros zenon_H41 zenon_H27. % 9.94/10.18 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 9.94/10.18 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H3c. zenon_intro zenon_H44. % 9.94/10.18 apply (zenon_L12_); trivial. % 9.94/10.18 (* end of lemma zenon_L13_ *) % 9.94/10.18 assert (zenon_L14_ : (~((op (e2) (op (e2) (e2))) = (e2))) -> ((op (e2) (e2)) = (e2)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H45 zenon_H2e. % 9.94/10.18 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (op (e2) (e2))) = (e2))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H45. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H2e. % 9.94/10.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.18 cut (((op (e2) (e2)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 9.94/10.18 congruence. % 9.94/10.18 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H47 | zenon_intro zenon_H48 ]. % 9.94/10.18 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e2)) = (op (e2) (op (e2) (e2))))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H46. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H47. % 9.94/10.18 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 9.94/10.18 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e2) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 9.94/10.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 exact (zenon_H4a zenon_H2e). % 9.94/10.18 apply zenon_H48. apply refl_equal. % 9.94/10.18 apply zenon_H48. apply refl_equal. % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L14_ *) % 9.94/10.18 assert (zenon_L15_ : ((~((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). % 9.94/10.18 do 0 intro. intros zenon_H4b zenon_H2e. % 9.94/10.18 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 9.94/10.18 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 9.94/10.18 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 9.94/10.18 apply (zenon_L14_); trivial. % 9.94/10.18 (* end of lemma zenon_L15_ *) % 9.94/10.18 assert (zenon_L16_ : (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H51 zenon_H52. % 9.94/10.18 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (op (e3) (e3))) = (e3))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H51. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H52. % 9.94/10.18 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.18 cut (((op (e3) (e3)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 9.94/10.18 congruence. % 9.94/10.18 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H54 | zenon_intro zenon_H55 ]. % 9.94/10.18 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e3)) = (op (e3) (op (e3) (e3))))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H53. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H54. % 9.94/10.18 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 9.94/10.18 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e3) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 9.94/10.18 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 exact (zenon_H57 zenon_H52). % 9.94/10.18 apply zenon_H55. apply refl_equal. % 9.94/10.18 apply zenon_H55. apply refl_equal. % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L16_ *) % 9.94/10.18 assert (zenon_L17_ : ((~((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). % 9.94/10.18 do 0 intro. intros zenon_H58 zenon_H52. % 9.94/10.18 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 9.94/10.18 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 9.94/10.18 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H51. % 9.94/10.18 apply (zenon_L16_); trivial. % 9.94/10.18 (* end of lemma zenon_L17_ *) % 9.94/10.18 assert (zenon_L18_ : ((op (e1) (e1)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H27 zenon_H5e zenon_H5f. % 9.94/10.18 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H60 | zenon_intro zenon_H61 ]. % 9.94/10.18 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H5f. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H60. % 9.94/10.18 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.18 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H62. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H27. % 9.94/10.18 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 9.94/10.18 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_H61. apply refl_equal. % 9.94/10.18 apply zenon_H63. apply sym_equal. exact zenon_H5e. % 9.94/10.18 apply zenon_H61. apply refl_equal. % 9.94/10.18 apply zenon_H61. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L18_ *) % 9.94/10.18 assert (zenon_L19_ : (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H64 zenon_H24 zenon_H65. % 9.94/10.18 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e0) (e1)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H64. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H24. % 9.94/10.18 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 9.94/10.18 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_H67. apply refl_equal. % 9.94/10.18 apply zenon_H66. apply sym_equal. exact zenon_H65. % 9.94/10.18 (* end of lemma zenon_L19_ *) % 9.94/10.18 assert (zenon_L20_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H68 zenon_H69 zenon_H25. % 9.94/10.18 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H6a | zenon_intro zenon_H22 ]. % 9.94/10.18 cut (((e2) = (e2)) = ((e1) = (e2))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H25. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H6a. % 9.94/10.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.18 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e1) (e0)) = (e1)) = ((e2) = (e1))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H6b. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H68. % 9.94/10.18 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 9.94/10.18 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H6c zenon_H69). % 9.94/10.18 apply zenon_H1d. apply refl_equal. % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L20_ *) % 9.94/10.18 assert (zenon_L21_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H6d zenon_H2a zenon_H2b. % 9.94/10.18 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H20. zenon_intro zenon_H6e. % 9.94/10.18 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H20. zenon_intro zenon_H6f. % 9.94/10.18 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H20. zenon_intro zenon_H20. % 9.94/10.18 apply (zenon_L7_); trivial. % 9.94/10.18 (* end of lemma zenon_L21_ *) % 9.94/10.18 assert (zenon_L22_ : (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H64 zenon_H2b zenon_H70. % 9.94/10.18 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e0) (e1)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H64. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H2b. % 9.94/10.18 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 9.94/10.18 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_H67. apply refl_equal. % 9.94/10.18 apply zenon_H71. apply sym_equal. exact zenon_H70. % 9.94/10.18 (* end of lemma zenon_L22_ *) % 9.94/10.18 assert (zenon_L23_ : ((op (e3) (e0)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H72 zenon_H73 zenon_H74. % 9.94/10.18 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ]. % 9.94/10.18 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e1) (e0)) = (op (e3) (e0)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H74. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H75. % 9.94/10.18 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 9.94/10.18 cut (((op (e3) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H77]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e1) (e0)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H77. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H72. % 9.94/10.18 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 9.94/10.18 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_H76. apply refl_equal. % 9.94/10.18 apply zenon_H78. apply sym_equal. exact zenon_H73. % 9.94/10.18 apply zenon_H76. apply refl_equal. % 9.94/10.18 apply zenon_H76. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L23_ *) % 9.94/10.18 assert (zenon_L24_ : ((op (e3) (e1)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H79 zenon_H70 zenon_H7a. % 9.94/10.18 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H7b | zenon_intro zenon_H7c ]. % 9.94/10.18 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e0) (e1)) = (op (e3) (e1)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H7a. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H7b. % 9.94/10.18 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 9.94/10.18 cut (((op (e3) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e0) (e1)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H7d. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H79. % 9.94/10.18 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 9.94/10.18 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_H7c. apply refl_equal. % 9.94/10.18 apply zenon_H71. apply sym_equal. exact zenon_H70. % 9.94/10.18 apply zenon_H7c. apply refl_equal. % 9.94/10.18 apply zenon_H7c. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L24_ *) % 9.94/10.18 assert (zenon_L25_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H7e zenon_H2f zenon_H7f. % 9.94/10.18 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H7e. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H2f. % 9.94/10.18 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 9.94/10.18 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_H81. apply refl_equal. % 9.94/10.18 apply zenon_H80. apply sym_equal. exact zenon_H7f. % 9.94/10.18 (* end of lemma zenon_L25_ *) % 9.94/10.18 assert (zenon_L26_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H82 zenon_H52 zenon_H30. % 9.94/10.18 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 9.94/10.18 cut (((e3) = (e3)) = ((e2) = (e3))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H30. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H31. % 9.94/10.18 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.18 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e3) (e3)) = (e2)) = ((e3) = (e2))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H32. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H82. % 9.94/10.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.18 cut (((op (e3) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H57 zenon_H52). % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L26_ *) % 9.94/10.18 assert (zenon_L27_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H83 zenon_H74 zenon_H73 zenon_H7a zenon_H70 zenon_H2f zenon_H7e zenon_H82 zenon_H30. % 9.94/10.18 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 9.94/10.18 apply (zenon_L23_); trivial. % 9.94/10.18 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 9.94/10.18 apply (zenon_L24_); trivial. % 9.94/10.18 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 9.94/10.18 apply (zenon_L25_); trivial. % 9.94/10.18 apply (zenon_L26_); trivial. % 9.94/10.18 (* end of lemma zenon_L27_ *) % 9.94/10.18 assert (zenon_L28_ : ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H86 zenon_H87 zenon_H30. % 9.94/10.18 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 9.94/10.18 cut (((e3) = (e3)) = ((e2) = (e3))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H30. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H31. % 9.94/10.18 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.18 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e2) (e0)) = (e2)) = ((e3) = (e2))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H32. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H86. % 9.94/10.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.18 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H88 zenon_H87). % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L28_ *) % 9.94/10.18 assert (zenon_L29_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H89 zenon_H65 zenon_H23. % 9.94/10.18 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H6a | zenon_intro zenon_H22 ]. % 9.94/10.18 cut (((e2) = (e2)) = ((e0) = (e2))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H23. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H6a. % 9.94/10.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.18 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e0) (e1)) = (e0)) = ((e2) = (e0))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H8a. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H89. % 9.94/10.18 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 9.94/10.18 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H8b zenon_H65). % 9.94/10.18 apply zenon_H34. apply refl_equal. % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L29_ *) % 9.94/10.18 assert (zenon_L30_ : (~((e1) = (e2))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H25 zenon_H24 zenon_H1f. % 9.94/10.18 cut (((op (e0) (e0)) = (e2)) = ((e1) = (e2))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H25. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H24. % 9.94/10.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.18 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H8c zenon_H1f). % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L30_ *) % 9.94/10.18 assert (zenon_L31_ : (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H23 zenon_H26 zenon_H8d. % 9.94/10.18 cut (((op (e1) (e1)) = (e2)) = ((e0) = (e2))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H23. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H26. % 9.94/10.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.18 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H8e zenon_H8d). % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L31_ *) % 9.94/10.18 assert (zenon_L32_ : (~((e1) = (e3))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H2c zenon_H2b zenon_H1f. % 9.94/10.18 cut (((op (e0) (e0)) = (e3)) = ((e1) = (e3))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H2c. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H2b. % 9.94/10.18 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.18 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H8c zenon_H1f). % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L32_ *) % 9.94/10.18 assert (zenon_L33_ : (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H2a zenon_H2d zenon_H8d. % 9.94/10.18 cut (((op (e1) (e1)) = (e3)) = ((e0) = (e3))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H2a. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H2d. % 9.94/10.18 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.18 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H8e zenon_H8d). % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L33_ *) % 9.94/10.18 assert (zenon_L34_ : ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H8d zenon_H89 zenon_H5f. % 9.94/10.18 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H60 | zenon_intro zenon_H61 ]. % 9.94/10.18 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H5f. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H60. % 9.94/10.18 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.18 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H62. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H8d. % 9.94/10.18 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 9.94/10.18 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_H61. apply refl_equal. % 9.94/10.18 apply zenon_H8f. apply sym_equal. exact zenon_H89. % 9.94/10.18 apply zenon_H61. apply refl_equal. % 9.94/10.18 apply zenon_H61. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L34_ *) % 9.94/10.18 assert (zenon_L35_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H90 zenon_H91 zenon_H23. % 9.94/10.18 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H6a | zenon_intro zenon_H22 ]. % 9.94/10.18 cut (((e2) = (e2)) = ((e0) = (e2))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H23. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H6a. % 9.94/10.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.18 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e3) (e0)) = (e0)) = ((e2) = (e0))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H8a. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H90. % 9.94/10.18 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 9.94/10.18 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H92]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H92 zenon_H91). % 9.94/10.18 apply zenon_H34. apply refl_equal. % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L35_ *) % 9.94/10.18 assert (zenon_L36_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H93 zenon_H8d zenon_H94. % 9.94/10.18 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H93. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H8d. % 9.94/10.18 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H95]. % 9.94/10.18 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_H61. apply refl_equal. % 9.94/10.18 apply zenon_H95. apply sym_equal. exact zenon_H94. % 9.94/10.18 (* end of lemma zenon_L36_ *) % 9.94/10.18 assert (zenon_L37_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H96 zenon_H97 zenon_H98. % 9.94/10.18 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H96. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H97. % 9.94/10.18 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 9.94/10.18 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_H9a. apply refl_equal. % 9.94/10.18 apply zenon_H99. apply sym_equal. exact zenon_H98. % 9.94/10.18 (* end of lemma zenon_L37_ *) % 9.94/10.18 assert (zenon_L38_ : ((op (e1) (e1)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 9.94/10.18 do 0 intro. intros zenon_H26 zenon_H2d zenon_H30. % 9.94/10.18 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 9.94/10.18 cut (((e3) = (e3)) = ((e2) = (e3))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H30. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H31. % 9.94/10.18 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.18 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e1) (e1)) = (e2)) = ((e3) = (e2))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H32. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H26. % 9.94/10.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.18 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_H9b zenon_H2d). % 9.94/10.18 apply zenon_H22. apply refl_equal. % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L38_ *) % 9.94/10.18 assert (zenon_L39_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e1)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H6d zenon_H1e zenon_H1f. % 9.94/10.18 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H20. zenon_intro zenon_H6e. % 9.94/10.18 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H20. zenon_intro zenon_H6f. % 9.94/10.18 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H20. zenon_intro zenon_H20. % 9.94/10.18 apply (zenon_L2_); trivial. % 9.94/10.18 (* end of lemma zenon_L39_ *) % 9.94/10.18 assert (zenon_L40_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H9c zenon_H9d zenon_H9e. % 9.94/10.18 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e2) (e0)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H9c. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H9d. % 9.94/10.18 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 9.94/10.18 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_Ha0. apply refl_equal. % 9.94/10.18 apply zenon_H9f. apply sym_equal. exact zenon_H9e. % 9.94/10.18 (* end of lemma zenon_L40_ *) % 9.94/10.18 assert (zenon_L41_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 9.94/10.18 do 0 intro. intros zenon_Ha1 zenon_H89 zenon_Ha2. % 9.94/10.18 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_Ha1. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H89. % 9.94/10.18 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 9.94/10.18 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_Ha4. apply refl_equal. % 9.94/10.18 apply zenon_Ha3. apply sym_equal. exact zenon_Ha2. % 9.94/10.18 (* end of lemma zenon_L41_ *) % 9.94/10.18 assert (zenon_L42_ : (~((e0) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> False). % 9.94/10.18 do 0 intro. intros zenon_H2a zenon_H2f zenon_Ha5. % 9.94/10.18 cut (((op (e2) (e2)) = (e3)) = ((e0) = (e3))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_H2a. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_H2f. % 9.94/10.18 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.18 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 9.94/10.18 congruence. % 9.94/10.18 exact (zenon_Ha6 zenon_Ha5). % 9.94/10.18 apply zenon_H29. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L42_ *) % 9.94/10.18 assert (zenon_L43_ : ((op (e3) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 9.94/10.18 do 0 intro. intros zenon_Ha7 zenon_Ha8 zenon_Ha9. % 9.94/10.18 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 9.94/10.18 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_Ha9. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_Haa. % 9.94/10.18 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 9.94/10.18 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_Hac. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_Ha7. % 9.94/10.18 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 9.94/10.18 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_Hab. apply refl_equal. % 9.94/10.18 apply zenon_Had. apply sym_equal. exact zenon_Ha8. % 9.94/10.18 apply zenon_Hab. apply refl_equal. % 9.94/10.18 apply zenon_Hab. apply refl_equal. % 9.94/10.18 (* end of lemma zenon_L43_ *) % 9.94/10.18 assert (zenon_L44_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 9.94/10.18 do 0 intro. intros zenon_Hae zenon_H9d zenon_H9c zenon_H89 zenon_Ha1 zenon_H2f zenon_H2a zenon_Ha7 zenon_Ha9. % 9.94/10.18 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 9.94/10.18 apply (zenon_L40_); trivial. % 9.94/10.18 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 9.94/10.18 apply (zenon_L41_); trivial. % 9.94/10.18 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 9.94/10.18 apply (zenon_L42_); trivial. % 9.94/10.18 apply (zenon_L43_); trivial. % 9.94/10.18 (* end of lemma zenon_L44_ *) % 9.94/10.18 assert (zenon_L45_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 9.94/10.18 do 0 intro. intros zenon_Hb1 zenon_Hae zenon_H9c zenon_Ha1 zenon_H2f zenon_H2a zenon_Ha7 zenon_Ha9. % 9.94/10.18 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_H20. zenon_intro zenon_Hb2. % 9.94/10.18 apply (zenon_and_s _ _ zenon_Hb2). zenon_intro zenon_H20. zenon_intro zenon_Hb3. % 9.94/10.18 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 9.94/10.18 apply (zenon_L44_); trivial. % 9.94/10.18 (* end of lemma zenon_L45_ *) % 9.94/10.18 assert (zenon_L46_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e1)) -> False). % 9.94/10.18 do 0 intro. intros zenon_Hb4 zenon_H1e zenon_H1f. % 9.94/10.18 apply (zenon_and_s _ _ zenon_Hb4). zenon_intro zenon_H20. zenon_intro zenon_Hb5. % 9.94/10.18 apply (zenon_and_s _ _ zenon_Hb5). zenon_intro zenon_H20. zenon_intro zenon_Hb6. % 9.94/10.18 apply (zenon_L2_); trivial. % 9.94/10.18 (* end of lemma zenon_L46_ *) % 9.94/10.18 assert (zenon_L47_ : ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 9.94/10.18 do 0 intro. intros zenon_Ha7 zenon_Hb7 zenon_Hb8. % 9.94/10.18 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 9.94/10.18 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_Hb8. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_Haa. % 9.94/10.18 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 9.94/10.18 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 9.94/10.18 congruence. % 9.94/10.18 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 9.94/10.18 intro zenon_D_pnotp. % 9.94/10.18 apply zenon_Hb9. % 9.94/10.18 rewrite <- zenon_D_pnotp. % 9.94/10.18 exact zenon_Ha7. % 9.94/10.18 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 9.94/10.18 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 9.94/10.18 congruence. % 9.94/10.18 apply zenon_Hab. apply refl_equal. % 9.94/10.18 apply zenon_Hba. apply sym_equal. exact zenon_Hb7. % 9.94/10.18 apply zenon_Hab. apply refl_equal. % 9.94/10.18 apply zenon_Hab. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L47_ *) % 9.94/10.19 assert (zenon_L48_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hbb zenon_Ha7 zenon_Hb8. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hbb). zenon_intro zenon_H20. zenon_intro zenon_Hbc. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_H20. zenon_intro zenon_Hbd. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 9.94/10.19 apply (zenon_L47_); trivial. % 9.94/10.19 (* end of lemma zenon_L48_ *) % 9.94/10.19 assert (zenon_L49_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hbe zenon_H1f zenon_H68. % 9.94/10.19 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hbe. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H1f. % 9.94/10.19 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 9.94/10.19 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H67. apply refl_equal. % 9.94/10.19 apply zenon_Hbf. apply sym_equal. exact zenon_H68. % 9.94/10.19 (* end of lemma zenon_L49_ *) % 9.94/10.19 assert (zenon_L50_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e1)) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hc0 zenon_Hbe zenon_H1f. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_H89. zenon_intro zenon_Hc1. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H9d. zenon_intro zenon_Hc2. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 9.94/10.19 apply (zenon_L49_); trivial. % 9.94/10.19 (* end of lemma zenon_L50_ *) % 9.94/10.19 assert (zenon_L51_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hc3 zenon_H25 zenon_H26. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_H89. zenon_intro zenon_Hc4. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_H9d. zenon_intro zenon_Hc5. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 9.94/10.19 apply (zenon_L5_); trivial. % 9.94/10.19 (* end of lemma zenon_L51_ *) % 9.94/10.19 assert (zenon_L52_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hc6 zenon_Hae zenon_H9c zenon_Ha1 zenon_H2f zenon_H2a zenon_Ha7 zenon_Ha9. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_H89. zenon_intro zenon_Hc7. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_H9d. zenon_intro zenon_Hc8. % 9.94/10.19 apply (zenon_L44_); trivial. % 9.94/10.19 (* end of lemma zenon_L52_ *) % 9.94/10.19 assert (zenon_L53_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hc9 zenon_Hae zenon_H9c zenon_Ha1 zenon_H2f zenon_H2a zenon_Ha7 zenon_Ha9. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H89. zenon_intro zenon_Hca. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_H9d. zenon_intro zenon_Hcb. % 9.94/10.19 apply (zenon_L44_); trivial. % 9.94/10.19 (* end of lemma zenon_L53_ *) % 9.94/10.19 assert (zenon_L54_ : (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H23 zenon_H86 zenon_H9e. % 9.94/10.19 cut (((op (e2) (e0)) = (e2)) = ((e0) = (e2))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H23. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H86. % 9.94/10.19 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.19 cut (((op (e2) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 9.94/10.19 congruence. % 9.94/10.19 exact (zenon_Hcc zenon_H9e). % 9.94/10.19 apply zenon_H22. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L54_ *) % 9.94/10.19 assert (zenon_L55_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((e0) = (e2))) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hcd zenon_H23. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hcd). zenon_intro zenon_H97. zenon_intro zenon_Hce. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_H9e. zenon_intro zenon_Hcf. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd0. zenon_intro zenon_H86. % 9.94/10.19 apply (zenon_L54_); trivial. % 9.94/10.19 (* end of lemma zenon_L55_ *) % 9.94/10.19 assert (zenon_L56_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hd1 zenon_H26 zenon_Hd2. % 9.94/10.19 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hd1. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H26. % 9.94/10.19 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H61. apply refl_equal. % 9.94/10.19 apply zenon_Hd3. apply sym_equal. exact zenon_Hd2. % 9.94/10.19 (* end of lemma zenon_L56_ *) % 9.94/10.19 assert (zenon_L57_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hd4 zenon_Hd1 zenon_H26. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_H97. zenon_intro zenon_Hd5. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_H9e. zenon_intro zenon_Hd6. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 9.94/10.19 apply (zenon_L56_); trivial. % 9.94/10.19 (* end of lemma zenon_L57_ *) % 9.94/10.19 assert (zenon_L58_ : (~((op (e0) (op (e0) (e1))) = (e1))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hd8 zenon_H1f zenon_H89. % 9.94/10.19 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (op (e0) (e1))) = (e1))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hd8. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H1f. % 9.94/10.19 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 9.94/10.19 cut (((op (e0) (e0)) = (op (e0) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 9.94/10.19 congruence. % 9.94/10.19 elim (classic ((op (e0) (op (e0) (e1))) = (op (e0) (op (e0) (e1))))); [ zenon_intro zenon_Hda | zenon_intro zenon_Hdb ]. % 9.94/10.19 cut (((op (e0) (op (e0) (e1))) = (op (e0) (op (e0) (e1)))) = ((op (e0) (e0)) = (op (e0) (op (e0) (e1))))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hd9. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Hda. % 9.94/10.19 cut (((op (e0) (op (e0) (e1))) = (op (e0) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 9.94/10.19 cut (((op (e0) (op (e0) (e1))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hdc]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e0) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 9.94/10.19 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H34. apply refl_equal. % 9.94/10.19 exact (zenon_Hdd zenon_H89). % 9.94/10.19 apply zenon_Hdb. apply refl_equal. % 9.94/10.19 apply zenon_Hdb. apply refl_equal. % 9.94/10.19 apply zenon_H1d. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L58_ *) % 9.94/10.19 assert (zenon_L59_ : ((op (e1) (e1)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H2d zenon_H70 zenon_H5f. % 9.94/10.19 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H60 | zenon_intro zenon_H61 ]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H5f. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H60. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H62. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H2d. % 9.94/10.19 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H61. apply refl_equal. % 9.94/10.19 apply zenon_H71. apply sym_equal. exact zenon_H70. % 9.94/10.19 apply zenon_H61. apply refl_equal. % 9.94/10.19 apply zenon_H61. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L59_ *) % 9.94/10.19 assert (zenon_L60_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H97 zenon_Hde zenon_H2a. % 9.94/10.19 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 9.94/10.19 cut (((e3) = (e3)) = ((e0) = (e3))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H2a. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H31. % 9.94/10.19 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.19 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e0) (e2)) = (e0)) = ((e3) = (e0))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hdf. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H97. % 9.94/10.19 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 9.94/10.19 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_He0]. % 9.94/10.19 congruence. % 9.94/10.19 exact (zenon_He0 zenon_Hde). % 9.94/10.19 apply zenon_H34. apply refl_equal. % 9.94/10.19 apply zenon_H29. apply refl_equal. % 9.94/10.19 apply zenon_H29. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L60_ *) % 9.94/10.19 assert (zenon_L61_ : (~((op (e0) (op (e0) (e3))) = (e3))) -> ((op (e0) (e3)) = (e3)) -> False). % 9.94/10.19 do 0 intro. intros zenon_He1 zenon_He2. % 9.94/10.19 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (op (e0) (e3))) = (e3))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_He1. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_He2. % 9.94/10.19 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.19 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_He3]. % 9.94/10.19 congruence. % 9.94/10.19 elim (classic ((op (e0) (op (e0) (e3))) = (op (e0) (op (e0) (e3))))); [ zenon_intro zenon_He4 | zenon_intro zenon_He5 ]. % 9.94/10.19 cut (((op (e0) (op (e0) (e3))) = (op (e0) (op (e0) (e3)))) = ((op (e0) (e3)) = (op (e0) (op (e0) (e3))))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_He3. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_He4. % 9.94/10.19 cut (((op (e0) (op (e0) (e3))) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 9.94/10.19 cut (((op (e0) (op (e0) (e3))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 9.94/10.19 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H34. apply refl_equal. % 9.94/10.19 exact (zenon_He7 zenon_He2). % 9.94/10.19 apply zenon_He5. apply refl_equal. % 9.94/10.19 apply zenon_He5. apply refl_equal. % 9.94/10.19 apply zenon_H29. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L61_ *) % 9.94/10.19 assert (zenon_L62_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (op (e0) (e3))) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_He8 zenon_H1f zenon_H2c zenon_H5f zenon_H2d zenon_H2a zenon_H97 zenon_He1. % 9.94/10.19 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 9.94/10.19 apply (zenon_L32_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 9.94/10.19 apply (zenon_L59_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 9.94/10.19 apply (zenon_L60_); trivial. % 9.94/10.19 apply (zenon_L61_); trivial. % 9.94/10.19 (* end of lemma zenon_L62_ *) % 9.94/10.19 assert (zenon_L63_ : ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H2e zenon_Hd0 zenon_Heb. % 9.94/10.19 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hec | zenon_intro zenon_H81 ]. % 9.94/10.19 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Heb. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Hec. % 9.94/10.19 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 9.94/10.19 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hed]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hed. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H2e. % 9.94/10.19 cut (((e2) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hee]. % 9.94/10.19 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H81. apply refl_equal. % 9.94/10.19 apply zenon_Hee. apply sym_equal. exact zenon_Hd0. % 9.94/10.19 apply zenon_H81. apply refl_equal. % 9.94/10.19 apply zenon_H81. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L63_ *) % 9.94/10.19 assert (zenon_L64_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hef zenon_H2b zenon_Hde. % 9.94/10.19 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e0) (e2)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hef. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H2b. % 9.94/10.19 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 9.94/10.19 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H67. apply refl_equal. % 9.94/10.19 apply zenon_Hf0. apply sym_equal. exact zenon_Hde. % 9.94/10.19 (* end of lemma zenon_L64_ *) % 9.94/10.19 assert (zenon_L65_ : ((op (e1) (e1)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H2d zenon_H73 zenon_Hf1. % 9.94/10.19 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H60 | zenon_intro zenon_H61 ]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (e0)) = (op (e1) (e1)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hf1. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H60. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e1) (e0)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hf2. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H2d. % 9.94/10.19 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H61. apply refl_equal. % 9.94/10.19 apply zenon_H78. apply sym_equal. exact zenon_H73. % 9.94/10.19 apply zenon_H61. apply refl_equal. % 9.94/10.19 apply zenon_H61. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L65_ *) % 9.94/10.19 assert (zenon_L66_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hf3 zenon_Hf4 zenon_H25. % 9.94/10.19 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H6a | zenon_intro zenon_H22 ]. % 9.94/10.19 cut (((e2) = (e2)) = ((e1) = (e2))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H25. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H6a. % 9.94/10.19 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.19 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e0) (e3)) = (e1)) = ((e2) = (e1))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H6b. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Hf3. % 9.94/10.19 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 9.94/10.19 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 9.94/10.19 congruence. % 9.94/10.19 exact (zenon_Hf5 zenon_Hf4). % 9.94/10.19 apply zenon_H1d. apply refl_equal. % 9.94/10.19 apply zenon_H22. apply refl_equal. % 9.94/10.19 apply zenon_H22. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L66_ *) % 9.94/10.19 assert (zenon_L67_ : (~((op (e1) (op (e1) (e3))) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hf6 zenon_H2d zenon_Hf7. % 9.94/10.19 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (op (e1) (e3))) = (e3))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hf6. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H2d. % 9.94/10.19 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 9.94/10.19 congruence. % 9.94/10.19 elim (classic ((op (e1) (op (e1) (e3))) = (op (e1) (op (e1) (e3))))); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hfa ]. % 9.94/10.19 cut (((op (e1) (op (e1) (e3))) = (op (e1) (op (e1) (e3)))) = ((op (e1) (e1)) = (op (e1) (op (e1) (e3))))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hf8. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Hf9. % 9.94/10.19 cut (((op (e1) (op (e1) (e3))) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 9.94/10.19 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e1) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 9.94/10.19 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H1d. apply refl_equal. % 9.94/10.19 exact (zenon_Hfc zenon_Hf7). % 9.94/10.19 apply zenon_Hfa. apply refl_equal. % 9.94/10.19 apply zenon_Hfa. apply refl_equal. % 9.94/10.19 apply zenon_H29. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L67_ *) % 9.94/10.19 assert (zenon_L68_ : ((op (e3) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_Ha7 zenon_Hfd zenon_Hfe. % 9.94/10.19 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 9.94/10.19 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hfe. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Haa. % 9.94/10.19 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 9.94/10.19 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hff. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Ha7. % 9.94/10.19 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 9.94/10.19 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_Hab. apply refl_equal. % 9.94/10.19 apply zenon_H100. apply sym_equal. exact zenon_Hfd. % 9.94/10.19 apply zenon_Hab. apply refl_equal. % 9.94/10.19 apply zenon_Hab. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L68_ *) % 9.94/10.19 assert (zenon_L69_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H101 zenon_Hf7 zenon_H102. % 9.94/10.19 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H101. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Hf7. % 9.94/10.19 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 9.94/10.19 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H104. apply refl_equal. % 9.94/10.19 apply zenon_H103. apply sym_equal. exact zenon_H102. % 9.94/10.19 (* end of lemma zenon_L69_ *) % 9.94/10.19 assert (zenon_L70_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H105 zenon_Hf4 zenon_H106. % 9.94/10.19 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H105. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Hf4. % 9.94/10.19 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 9.94/10.19 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H108. apply refl_equal. % 9.94/10.19 apply zenon_H107. apply sym_equal. exact zenon_H106. % 9.94/10.19 (* end of lemma zenon_L70_ *) % 9.94/10.19 assert (zenon_L71_ : ((op (e1) (e3)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H109 zenon_He2 zenon_H105. % 9.94/10.19 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H10a | zenon_intro zenon_H104 ]. % 9.94/10.19 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e0) (e3)) = (op (e1) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H105. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H10a. % 9.94/10.19 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 9.94/10.19 cut (((op (e1) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10b]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (e3)) = (op (e0) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H10b. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H109. % 9.94/10.19 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 9.94/10.19 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H104. apply refl_equal. % 9.94/10.19 apply zenon_H10c. apply sym_equal. exact zenon_He2. % 9.94/10.19 apply zenon_H104. apply refl_equal. % 9.94/10.19 apply zenon_H104. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L71_ *) % 9.94/10.19 assert (zenon_L72_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H10d zenon_Hfe zenon_Ha7 zenon_H102 zenon_H101 zenon_Hf4 zenon_He2 zenon_H105. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hfd | zenon_intro zenon_H10e ]. % 9.94/10.19 apply (zenon_L68_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H10f ]. % 9.94/10.19 apply (zenon_L69_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H106 | zenon_intro zenon_H109 ]. % 9.94/10.19 apply (zenon_L70_); trivial. % 9.94/10.19 apply (zenon_L71_); trivial. % 9.94/10.19 (* end of lemma zenon_L72_ *) % 9.94/10.19 assert (zenon_L73_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H110 zenon_H2d zenon_H109. % 9.94/10.19 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e1) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H110. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H2d. % 9.94/10.19 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H61. apply refl_equal. % 9.94/10.19 apply zenon_H111. apply sym_equal. exact zenon_H109. % 9.94/10.19 (* end of lemma zenon_L73_ *) % 9.94/10.19 assert (zenon_L74_ : ((op (e2) (e3)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H112 zenon_H87 zenon_H113. % 9.94/10.19 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ]. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e0)) = (op (e2) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H113. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H114. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (e3)) = (op (e2) (e0)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H116. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H112. % 9.94/10.19 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H115. apply refl_equal. % 9.94/10.19 apply zenon_H117. apply sym_equal. exact zenon_H87. % 9.94/10.19 apply zenon_H115. apply refl_equal. % 9.94/10.19 apply zenon_H115. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L74_ *) % 9.94/10.19 assert (zenon_L75_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_Ha7 zenon_H52 zenon_H2a. % 9.94/10.19 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 9.94/10.19 cut (((e3) = (e3)) = ((e0) = (e3))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H2a. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H31. % 9.94/10.19 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.19 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e3) (e3)) = (e0)) = ((e3) = (e0))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hdf. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Ha7. % 9.94/10.19 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 9.94/10.19 cut (((op (e3) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 9.94/10.19 congruence. % 9.94/10.19 exact (zenon_H57 zenon_H52). % 9.94/10.19 apply zenon_H34. apply refl_equal. % 9.94/10.19 apply zenon_H29. apply refl_equal. % 9.94/10.19 apply zenon_H29. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L75_ *) % 9.94/10.19 assert (zenon_L76_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H118 zenon_H105 zenon_Hf4 zenon_H101 zenon_H102 zenon_Hfe zenon_H10d zenon_H2d zenon_H110 zenon_H113 zenon_H87 zenon_Ha7 zenon_H2a. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_He2 | zenon_intro zenon_H119 ]. % 9.94/10.19 apply (zenon_L72_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H109 | zenon_intro zenon_H11a ]. % 9.94/10.19 apply (zenon_L73_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H112 | zenon_intro zenon_H52 ]. % 9.94/10.19 apply (zenon_L74_); trivial. % 9.94/10.19 apply (zenon_L75_); trivial. % 9.94/10.19 (* end of lemma zenon_L76_ *) % 9.94/10.19 assert (zenon_L77_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 9.94/10.19 do 0 intro. intros zenon_Ha7 zenon_H11b zenon_H1e. % 9.94/10.19 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H11c | zenon_intro zenon_H1d ]. % 9.94/10.19 cut (((e1) = (e1)) = ((e0) = (e1))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H1e. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H11c. % 9.94/10.19 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 9.94/10.19 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e3) (e3)) = (e0)) = ((e1) = (e0))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H11d. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Ha7. % 9.94/10.19 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 9.94/10.19 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 9.94/10.19 congruence. % 9.94/10.19 exact (zenon_H11e zenon_H11b). % 9.94/10.19 apply zenon_H34. apply refl_equal. % 9.94/10.19 apply zenon_H1d. apply refl_equal. % 9.94/10.19 apply zenon_H1d. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L77_ *) % 9.94/10.19 assert (zenon_L78_ : ((op (e3) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H72 zenon_H87 zenon_H11f. % 9.94/10.19 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ]. % 9.94/10.19 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e2) (e0)) = (op (e3) (e0)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H11f. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H75. % 9.94/10.19 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 9.94/10.19 cut (((op (e3) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e2) (e0)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H120. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H72. % 9.94/10.19 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 9.94/10.19 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H76. apply refl_equal. % 9.94/10.19 apply zenon_H117. apply sym_equal. exact zenon_H87. % 9.94/10.19 apply zenon_H76. apply refl_equal. % 9.94/10.19 apply zenon_H76. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L78_ *) % 9.94/10.19 assert (zenon_L79_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hd1 zenon_H2d zenon_H121. % 9.94/10.19 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hd1. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H2d. % 9.94/10.19 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H61. apply refl_equal. % 9.94/10.19 apply zenon_H122. apply sym_equal. exact zenon_H121. % 9.94/10.19 (* end of lemma zenon_L79_ *) % 9.94/10.19 assert (zenon_L80_ : ((op (e2) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H112 zenon_H109 zenon_H101. % 9.94/10.19 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ]. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e1) (e3)) = (op (e2) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H101. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H114. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (e3)) = (op (e1) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H123. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H112. % 9.94/10.19 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H115. apply refl_equal. % 9.94/10.19 apply zenon_H111. apply sym_equal. exact zenon_H109. % 9.94/10.19 apply zenon_H115. apply refl_equal. % 9.94/10.19 apply zenon_H115. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L80_ *) % 9.94/10.19 assert (zenon_L81_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H10d zenon_Hfe zenon_Ha7 zenon_H102 zenon_Hf4 zenon_H105 zenon_H112 zenon_H101. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hfd | zenon_intro zenon_H10e ]. % 9.94/10.19 apply (zenon_L68_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H10f ]. % 9.94/10.19 apply (zenon_L69_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H106 | zenon_intro zenon_H109 ]. % 9.94/10.19 apply (zenon_L70_); trivial. % 9.94/10.19 apply (zenon_L80_); trivial. % 9.94/10.19 (* end of lemma zenon_L81_ *) % 9.94/10.19 assert (zenon_L82_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H124 zenon_H25 zenon_H2d zenon_Hf6 zenon_H101 zenon_H112 zenon_H105 zenon_Hf4 zenon_Hfe zenon_H10d zenon_Ha7 zenon_H1e. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 9.94/10.19 apply (zenon_L66_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 9.94/10.19 apply (zenon_L67_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 9.94/10.19 apply (zenon_L81_); trivial. % 9.94/10.19 apply (zenon_L77_); trivial. % 9.94/10.19 (* end of lemma zenon_L82_ *) % 9.94/10.19 assert (zenon_L83_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H127 zenon_H2e zenon_H128. % 9.94/10.19 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H127. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H2e. % 9.94/10.19 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H129]. % 9.94/10.19 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H81. apply refl_equal. % 9.94/10.19 apply zenon_H129. apply sym_equal. exact zenon_H128. % 9.94/10.19 (* end of lemma zenon_L83_ *) % 9.94/10.19 assert (zenon_L84_ : ((op (e2) (e3)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H112 zenon_He2 zenon_H12a. % 9.94/10.19 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ]. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e0) (e3)) = (op (e2) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H12a. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H114. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (e3)) = (op (e0) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H12b. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H112. % 9.94/10.19 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H115. apply refl_equal. % 9.94/10.19 apply zenon_H10c. apply sym_equal. exact zenon_He2. % 9.94/10.19 apply zenon_H115. apply refl_equal. % 9.94/10.19 apply zenon_H115. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L84_ *) % 9.94/10.19 assert (zenon_L85_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H12c zenon_Ha9 zenon_Ha7 zenon_Hf7 zenon_H101 zenon_H2e zenon_H127 zenon_He2 zenon_H12a. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 9.94/10.19 apply (zenon_L43_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 9.94/10.19 apply (zenon_L69_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 9.94/10.19 apply (zenon_L83_); trivial. % 9.94/10.19 apply (zenon_L84_); trivial. % 9.94/10.19 (* end of lemma zenon_L85_ *) % 9.94/10.19 assert (zenon_L86_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H124 zenon_H25 zenon_H12a zenon_H127 zenon_H2e zenon_Ha9 zenon_H12c zenon_H105 zenon_He2 zenon_Hf4 zenon_H101 zenon_Hfe zenon_H10d zenon_Ha7 zenon_H1e. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 9.94/10.19 apply (zenon_L66_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 9.94/10.19 apply (zenon_L85_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 9.94/10.19 apply (zenon_L72_); trivial. % 9.94/10.19 apply (zenon_L77_); trivial. % 9.94/10.19 (* end of lemma zenon_L86_ *) % 9.94/10.19 assert (zenon_L87_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 9.94/10.19 do 0 intro. intros zenon_He8 zenon_H1f zenon_H2c zenon_H5f zenon_Hf6 zenon_H2d zenon_H30 zenon_Hd1 zenon_H11f zenon_H12f zenon_H2a zenon_H113 zenon_H110 zenon_H118 zenon_Hf1 zenon_Hef zenon_H130 zenon_H124 zenon_H25 zenon_H12a zenon_H127 zenon_H2e zenon_Ha9 zenon_H12c zenon_H105 zenon_Hf4 zenon_H101 zenon_Hfe zenon_H10d zenon_Ha7 zenon_H1e. % 9.94/10.19 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 9.94/10.19 apply (zenon_L32_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 9.94/10.19 apply (zenon_L59_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 9.94/10.19 apply (zenon_L64_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 9.94/10.19 apply (zenon_L65_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 9.94/10.19 apply (zenon_L66_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 9.94/10.19 apply (zenon_L67_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 9.94/10.19 apply (zenon_L76_); trivial. % 9.94/10.19 apply (zenon_L77_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 9.94/10.19 apply (zenon_L78_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 9.94/10.19 apply (zenon_L79_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 9.94/10.19 apply (zenon_L9_); trivial. % 9.94/10.19 apply (zenon_L82_); trivial. % 9.94/10.19 apply (zenon_L86_); trivial. % 9.94/10.19 (* end of lemma zenon_L87_ *) % 9.94/10.19 assert (zenon_L88_ : (~((op (e1) (op (e1) (e0))) = (e0))) -> ((op (e1) (e0)) = (e0)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H43 zenon_H9d. % 9.94/10.19 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (op (e1) (e0))) = (e0))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H43. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H9d. % 9.94/10.19 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 9.94/10.19 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 9.94/10.19 congruence. % 9.94/10.19 elim (classic ((op (e1) (op (e1) (e0))) = (op (e1) (op (e1) (e0))))); [ zenon_intro zenon_H136 | zenon_intro zenon_H137 ]. % 9.94/10.19 cut (((op (e1) (op (e1) (e0))) = (op (e1) (op (e1) (e0)))) = ((op (e1) (e0)) = (op (e1) (op (e1) (e0))))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H135. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H136. % 9.94/10.19 cut (((op (e1) (op (e1) (e0))) = (op (e1) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 9.94/10.19 cut (((op (e1) (op (e1) (e0))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H138]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e1) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 9.94/10.19 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H1d. apply refl_equal. % 9.94/10.19 exact (zenon_H139 zenon_H9d). % 9.94/10.19 apply zenon_H137. apply refl_equal. % 9.94/10.19 apply zenon_H137. apply refl_equal. % 9.94/10.19 apply zenon_H34. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L88_ *) % 9.94/10.19 assert (zenon_L89_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H13a zenon_H97 zenon_H13b. % 9.94/10.19 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H13a. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H97. % 9.94/10.19 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H13c]. % 9.94/10.19 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H9a. apply refl_equal. % 9.94/10.19 apply zenon_H13c. apply sym_equal. exact zenon_H13b. % 9.94/10.19 (* end of lemma zenon_L89_ *) % 9.94/10.19 assert (zenon_L90_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H13d zenon_H43 zenon_H2d zenon_H2a zenon_H97 zenon_H13a zenon_Ha7 zenon_Hfe. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 9.94/10.19 apply (zenon_L88_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 9.94/10.19 apply (zenon_L33_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 9.94/10.19 apply (zenon_L89_); trivial. % 9.94/10.19 apply (zenon_L68_); trivial. % 9.94/10.19 (* end of lemma zenon_L90_ *) % 9.94/10.19 assert (zenon_L91_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H93 zenon_H2d zenon_H79. % 9.94/10.19 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H93. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H2d. % 9.94/10.19 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H61. apply refl_equal. % 9.94/10.19 apply zenon_H140. apply sym_equal. exact zenon_H79. % 9.94/10.19 (* end of lemma zenon_L91_ *) % 9.94/10.19 assert (zenon_L92_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_Ha7 zenon_H94 zenon_H141. % 9.94/10.19 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 9.94/10.19 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H141. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Haa. % 9.94/10.19 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 9.94/10.19 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H142]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H142. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Ha7. % 9.94/10.19 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H95]. % 9.94/10.19 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_Hab. apply refl_equal. % 9.94/10.19 apply zenon_H95. apply sym_equal. exact zenon_H94. % 9.94/10.19 apply zenon_Hab. apply refl_equal. % 9.94/10.19 apply zenon_Hab. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L92_ *) % 9.94/10.19 assert (zenon_L93_ : (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e3) (e1)) = (e1)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H5c zenon_H143. % 9.94/10.19 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (op (e3) (e1))) = (e1))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H5c. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H143. % 9.94/10.19 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 9.94/10.19 cut (((op (e3) (e1)) = (op (e3) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H144]. % 9.94/10.19 congruence. % 9.94/10.19 elim (classic ((op (e3) (op (e3) (e1))) = (op (e3) (op (e3) (e1))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 9.94/10.19 cut (((op (e3) (op (e3) (e1))) = (op (e3) (op (e3) (e1)))) = ((op (e3) (e1)) = (op (e3) (op (e3) (e1))))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H144. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H145. % 9.94/10.19 cut (((op (e3) (op (e3) (e1))) = (op (e3) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 9.94/10.19 cut (((op (e3) (op (e3) (e1))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H147]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e3) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H148]. % 9.94/10.19 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H29. apply refl_equal. % 9.94/10.19 exact (zenon_H148 zenon_H143). % 9.94/10.19 apply zenon_H146. apply refl_equal. % 9.94/10.19 apply zenon_H146. apply refl_equal. % 9.94/10.19 apply zenon_H1d. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L93_ *) % 9.94/10.19 assert (zenon_L94_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H7a zenon_H65 zenon_H149. % 9.94/10.19 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H7a. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H65. % 9.94/10.19 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 9.94/10.19 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_Ha4. apply refl_equal. % 9.94/10.19 apply zenon_H14a. apply sym_equal. exact zenon_H149. % 9.94/10.19 (* end of lemma zenon_L94_ *) % 9.94/10.19 assert (zenon_L95_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H14b zenon_H79 zenon_H7f. % 9.94/10.19 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H14b. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H79. % 9.94/10.19 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 9.94/10.19 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H7c. apply refl_equal. % 9.94/10.19 apply zenon_H80. apply sym_equal. exact zenon_H7f. % 9.94/10.19 (* end of lemma zenon_L95_ *) % 9.94/10.19 assert (zenon_L96_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H14c zenon_H141 zenon_Ha7 zenon_H5c zenon_H65 zenon_H7a zenon_H14b zenon_H7f. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H94 | zenon_intro zenon_H14d ]. % 9.94/10.19 apply (zenon_L92_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 9.94/10.19 apply (zenon_L93_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H149 | zenon_intro zenon_H79 ]. % 9.94/10.19 apply (zenon_L94_); trivial. % 9.94/10.19 apply (zenon_L95_); trivial. % 9.94/10.19 (* end of lemma zenon_L96_ *) % 9.94/10.19 assert (zenon_L97_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H83 zenon_H11f zenon_H87 zenon_H2d zenon_H93 zenon_H14b zenon_H7a zenon_H65 zenon_H5c zenon_H141 zenon_H14c zenon_Ha7 zenon_H2a. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 9.94/10.19 apply (zenon_L78_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 9.94/10.19 apply (zenon_L91_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 9.94/10.19 apply (zenon_L96_); trivial. % 9.94/10.19 apply (zenon_L75_); trivial. % 9.94/10.19 (* end of lemma zenon_L97_ *) % 9.94/10.19 assert (zenon_L98_ : (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H5a zenon_Ha7 zenon_H72. % 9.94/10.19 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (op (e3) (e0))) = (e0))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H5a. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Ha7. % 9.94/10.19 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 9.94/10.19 cut (((op (e3) (e3)) = (op (e3) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 9.94/10.19 congruence. % 9.94/10.19 elim (classic ((op (e3) (op (e3) (e0))) = (op (e3) (op (e3) (e0))))); [ zenon_intro zenon_H150 | zenon_intro zenon_H151 ]. % 9.94/10.19 cut (((op (e3) (op (e3) (e0))) = (op (e3) (op (e3) (e0)))) = ((op (e3) (e3)) = (op (e3) (op (e3) (e0))))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H14f. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H150. % 9.94/10.19 cut (((op (e3) (op (e3) (e0))) = (op (e3) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 9.94/10.19 cut (((op (e3) (op (e3) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H152]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e3) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 9.94/10.19 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H29. apply refl_equal. % 9.94/10.19 exact (zenon_H153 zenon_H72). % 9.94/10.19 apply zenon_H151. apply refl_equal. % 9.94/10.19 apply zenon_H151. apply refl_equal. % 9.94/10.19 apply zenon_H34. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L98_ *) % 9.94/10.19 assert (zenon_L99_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e3) (e3)) = (e0)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H130 zenon_Hde zenon_Hef zenon_Hf1 zenon_H2d zenon_H113 zenon_H112 zenon_H5a zenon_Ha7. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 9.94/10.19 apply (zenon_L64_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 9.94/10.19 apply (zenon_L65_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 9.94/10.19 apply (zenon_L74_); trivial. % 9.94/10.19 apply (zenon_L98_); trivial. % 9.94/10.19 (* end of lemma zenon_L99_ *) % 9.94/10.19 assert (zenon_L100_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H118 zenon_H12a zenon_H127 zenon_H2e zenon_H101 zenon_Hf7 zenon_Ha9 zenon_H12c zenon_H110 zenon_H5a zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_Hde zenon_H130 zenon_Ha7 zenon_H2a. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_He2 | zenon_intro zenon_H119 ]. % 9.94/10.19 apply (zenon_L85_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H109 | zenon_intro zenon_H11a ]. % 9.94/10.19 apply (zenon_L73_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H112 | zenon_intro zenon_H52 ]. % 9.94/10.19 apply (zenon_L99_); trivial. % 9.94/10.19 apply (zenon_L75_); trivial. % 9.94/10.19 (* end of lemma zenon_L100_ *) % 9.94/10.19 assert (zenon_L101_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (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))))))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H154 zenon_H1e zenon_H10d zenon_Hfe zenon_H101 zenon_H105 zenon_H12c zenon_Ha9 zenon_H127 zenon_H12a zenon_H25 zenon_H124 zenon_H118 zenon_H110 zenon_H113 zenon_Hf1 zenon_Hef zenon_H130 zenon_H5f zenon_H2c zenon_H1f zenon_He8 zenon_Heb zenon_H14c zenon_H141 zenon_H7a zenon_H14b zenon_H93 zenon_H11f zenon_H83 zenon_H155 zenon_H156 zenon_H12f zenon_Hd1 zenon_H23 zenon_H13a zenon_H13d zenon_Hb8 zenon_H157 zenon_H30 zenon_H2e zenon_Ha7 zenon_H2a. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 9.94/10.19 apply (zenon_L32_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_Hd8. zenon_intro zenon_H15b. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_H15c. zenon_intro zenon_He1. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 9.94/10.19 apply (zenon_L2_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 9.94/10.19 apply (zenon_L58_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 9.94/10.19 apply (zenon_L62_); trivial. % 9.94/10.19 apply (zenon_L47_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H3c. zenon_intro zenon_H44. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H160. zenon_intro zenon_Hf6. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 9.94/10.19 apply (zenon_L2_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 9.94/10.19 apply (zenon_L30_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 9.94/10.19 apply (zenon_L29_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 9.94/10.19 apply (zenon_L63_); trivial. % 9.94/10.19 apply (zenon_L87_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 9.94/10.19 apply (zenon_L90_); trivial. % 9.94/10.19 apply (zenon_L47_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 9.94/10.19 apply (zenon_L15_); trivial. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 9.94/10.19 apply (zenon_L30_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 9.94/10.19 apply (zenon_L32_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 9.94/10.19 apply (zenon_L65_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 9.94/10.19 apply (zenon_L97_); trivial. % 9.94/10.19 apply (zenon_L98_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 9.94/10.19 apply (zenon_L63_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 9.94/10.19 apply (zenon_L32_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 9.94/10.19 apply (zenon_L59_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 9.94/10.19 apply (zenon_L64_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 9.94/10.19 apply (zenon_L65_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 9.94/10.19 apply (zenon_L66_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 9.94/10.19 apply (zenon_L100_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 9.94/10.19 apply (zenon_L76_); trivial. % 9.94/10.19 apply (zenon_L77_); trivial. % 9.94/10.19 apply (zenon_L98_); trivial. % 9.94/10.19 apply (zenon_L86_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 9.94/10.19 apply (zenon_L9_); trivial. % 9.94/10.19 apply (zenon_L75_); trivial. % 9.94/10.19 (* end of lemma zenon_L101_ *) % 9.94/10.19 assert (zenon_L102_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (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))))))))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H163 zenon_H154 zenon_H1e zenon_H10d zenon_Hfe zenon_H101 zenon_H105 zenon_H12c zenon_Ha9 zenon_H127 zenon_H12a zenon_H25 zenon_H124 zenon_H118 zenon_H110 zenon_H113 zenon_Hf1 zenon_Hef zenon_H130 zenon_H5f zenon_H2c zenon_H1f zenon_He8 zenon_Heb zenon_H14c zenon_H141 zenon_H7a zenon_H14b zenon_H93 zenon_H11f zenon_H83 zenon_H155 zenon_H156 zenon_H12f zenon_Hd1 zenon_H23 zenon_H13a zenon_H13d zenon_Hb8 zenon_H157 zenon_H30 zenon_Ha7 zenon_H2a. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H163). zenon_intro zenon_H97. zenon_intro zenon_H164. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H164). zenon_intro zenon_H9e. zenon_intro zenon_H165. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H165). zenon_intro zenon_H2e. zenon_intro zenon_H2e. % 9.94/10.19 apply (zenon_L101_); trivial. % 9.94/10.19 (* end of lemma zenon_L102_ *) % 9.94/10.19 assert (zenon_L103_ : ((op (e1) (e1)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H26 zenon_H65 zenon_H5f. % 9.94/10.19 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H60 | zenon_intro zenon_H61 ]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H5f. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H60. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H62. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H26. % 9.94/10.19 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H61. apply refl_equal. % 9.94/10.19 apply zenon_H66. apply sym_equal. exact zenon_H65. % 9.94/10.19 apply zenon_H61. apply refl_equal. % 9.94/10.19 apply zenon_H61. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L103_ *) % 9.94/10.19 assert (zenon_L104_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H96 zenon_Hd0 zenon_H166. % 9.94/10.19 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H96. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Hd0. % 9.94/10.19 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 9.94/10.19 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H9a. apply refl_equal. % 9.94/10.19 apply zenon_H167. apply sym_equal. exact zenon_H166. % 9.94/10.19 (* end of lemma zenon_L104_ *) % 9.94/10.19 assert (zenon_L105_ : ((op (e2) (e3)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H128 zenon_Hf4 zenon_H12a. % 9.94/10.19 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ]. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e0) (e3)) = (op (e2) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H12a. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H114. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e0) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H12b. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H128. % 9.94/10.19 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 9.94/10.19 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H115. apply refl_equal. % 9.94/10.19 apply zenon_H168. apply sym_equal. exact zenon_Hf4. % 9.94/10.19 apply zenon_H115. apply refl_equal. % 9.94/10.19 apply zenon_H115. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L105_ *) % 9.94/10.19 assert (zenon_L106_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H155 zenon_H1f zenon_H25 zenon_H5f zenon_H26 zenon_H166 zenon_H96 zenon_H128 zenon_H12a. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 9.94/10.19 apply (zenon_L30_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 9.94/10.19 apply (zenon_L103_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 9.94/10.19 apply (zenon_L104_); trivial. % 9.94/10.19 apply (zenon_L105_); trivial. % 9.94/10.19 (* end of lemma zenon_L106_ *) % 9.94/10.19 assert (zenon_L107_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H169 zenon_H155 zenon_H1f zenon_H25 zenon_H5f zenon_H26 zenon_H96 zenon_H12a. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H169). zenon_intro zenon_H97. zenon_intro zenon_H16a. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H16a). zenon_intro zenon_H9e. zenon_intro zenon_H16b. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 9.94/10.19 apply (zenon_L106_); trivial. % 9.94/10.19 (* end of lemma zenon_L107_ *) % 9.94/10.19 assert (zenon_L108_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_Ha7 zenon_H90 zenon_H16c. % 9.94/10.19 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 9.94/10.19 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H16c. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Haa. % 9.94/10.19 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 9.94/10.19 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H16d. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Ha7. % 9.94/10.19 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 9.94/10.19 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_Hab. apply refl_equal. % 9.94/10.19 apply zenon_H16e. apply sym_equal. exact zenon_H90. % 9.94/10.19 apply zenon_Hab. apply refl_equal. % 9.94/10.19 apply zenon_Hab. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L108_ *) % 9.94/10.19 assert (zenon_L109_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H16f zenon_Ha7 zenon_H16c. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hb7. zenon_intro zenon_H170. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_H90. zenon_intro zenon_H171. % 9.94/10.19 apply (zenon_L108_); trivial. % 9.94/10.19 (* end of lemma zenon_L109_ *) % 9.94/10.19 assert (zenon_L110_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H172 zenon_Ha7 zenon_H16c. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H172). zenon_intro zenon_Hb7. zenon_intro zenon_H173. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H173). zenon_intro zenon_H90. zenon_intro zenon_H174. % 9.94/10.19 apply (zenon_L108_); trivial. % 9.94/10.19 (* end of lemma zenon_L110_ *) % 9.94/10.19 assert (zenon_L111_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H175 zenon_Ha7 zenon_H16c. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H175). zenon_intro zenon_Hb7. zenon_intro zenon_H176. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H176). zenon_intro zenon_H90. zenon_intro zenon_H177. % 9.94/10.19 apply (zenon_L108_); trivial. % 9.94/10.19 (* end of lemma zenon_L111_ *) % 9.94/10.19 assert (zenon_L112_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H178 zenon_Ha7 zenon_H2a. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H178). zenon_intro zenon_Hb7. zenon_intro zenon_H179. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H179). zenon_intro zenon_H90. zenon_intro zenon_H17a. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 9.94/10.19 apply (zenon_L75_); trivial. % 9.94/10.19 (* end of lemma zenon_L112_ *) % 9.94/10.19 assert (zenon_L113_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e1)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H17b zenon_H1e zenon_H1f. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H68. zenon_intro zenon_H17c. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H17c). zenon_intro zenon_H5e. zenon_intro zenon_H6f. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H20. zenon_intro zenon_H20. % 9.94/10.19 apply (zenon_L2_); trivial. % 9.94/10.19 (* end of lemma zenon_L113_ *) % 9.94/10.19 assert (zenon_L114_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H17d zenon_Hae zenon_H9c zenon_Ha1 zenon_H2f zenon_H2a zenon_Ha7 zenon_Ha9. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H68. zenon_intro zenon_H17e. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H17e). zenon_intro zenon_H5e. zenon_intro zenon_Hb3. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 9.94/10.19 apply (zenon_L44_); trivial. % 9.94/10.19 (* end of lemma zenon_L114_ *) % 9.94/10.19 assert (zenon_L115_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e1)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H17f zenon_Hbe zenon_H1f. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H68. zenon_intro zenon_H180. % 9.94/10.19 apply (zenon_L49_); trivial. % 9.94/10.19 (* end of lemma zenon_L115_ *) % 9.94/10.19 assert (zenon_L116_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H181 zenon_Ha7 zenon_Hb8. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_H5e. zenon_intro zenon_Hbd. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 9.94/10.19 apply (zenon_L47_); trivial. % 9.94/10.19 (* end of lemma zenon_L116_ *) % 9.94/10.19 assert (zenon_L117_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H183 zenon_H5f. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H27. zenon_intro zenon_H184. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H184). zenon_intro zenon_H27. zenon_intro zenon_Hc2. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 9.94/10.19 apply (zenon_L18_); trivial. % 9.94/10.19 (* end of lemma zenon_L117_ *) % 9.94/10.19 assert (zenon_L118_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H185 zenon_H25 zenon_H26. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H185). zenon_intro zenon_H27. zenon_intro zenon_H186. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_H27. zenon_intro zenon_Hc5. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 9.94/10.19 apply (zenon_L5_); trivial. % 9.94/10.19 (* end of lemma zenon_L118_ *) % 9.94/10.19 assert (zenon_L119_ : (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H187 zenon_H27 zenon_H188. % 9.94/10.19 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e2)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H187. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H27. % 9.94/10.19 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H61. apply refl_equal. % 9.94/10.19 apply zenon_H189. apply sym_equal. exact zenon_H188. % 9.94/10.19 (* end of lemma zenon_L119_ *) % 9.94/10.19 assert (zenon_L120_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H18a zenon_H187. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H18a). zenon_intro zenon_H27. zenon_intro zenon_H18b. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H18b). zenon_intro zenon_H27. zenon_intro zenon_Hc8. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 9.94/10.19 apply (zenon_L119_); trivial. % 9.94/10.19 (* end of lemma zenon_L120_ *) % 9.94/10.19 assert (zenon_L121_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H18a zenon_H187. % 9.94/10.19 apply (zenon_L120_); trivial. % 9.94/10.19 (* end of lemma zenon_L121_ *) % 9.94/10.19 assert (zenon_L122_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H18d zenon_H25 zenon_H26. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H18d). zenon_intro zenon_H27. zenon_intro zenon_H18e. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H18e). zenon_intro zenon_H27. zenon_intro zenon_Hcb. % 9.94/10.19 apply (zenon_L5_); trivial. % 9.94/10.19 (* end of lemma zenon_L122_ *) % 9.94/10.19 assert (zenon_L123_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H11f zenon_H86 zenon_H91. % 9.94/10.19 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e3) (e0)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H11f. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H86. % 9.94/10.19 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 9.94/10.19 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H190. apply refl_equal. % 9.94/10.19 apply zenon_H18f. apply sym_equal. exact zenon_H91. % 9.94/10.19 (* end of lemma zenon_L123_ *) % 9.94/10.19 assert (zenon_L124_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H93 zenon_H26 zenon_H149. % 9.94/10.19 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H93. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H26. % 9.94/10.19 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 9.94/10.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H61. apply refl_equal. % 9.94/10.19 apply zenon_H14a. apply sym_equal. exact zenon_H149. % 9.94/10.19 (* end of lemma zenon_L124_ *) % 9.94/10.19 assert (zenon_L125_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 9.94/10.19 do 0 intro. intros zenon_Ha7 zenon_H82 zenon_H23. % 9.94/10.19 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H6a | zenon_intro zenon_H22 ]. % 9.94/10.19 cut (((e2) = (e2)) = ((e0) = (e2))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H23. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H6a. % 9.94/10.19 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.19 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e3) (e3)) = (e0)) = ((e2) = (e0))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H8a. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Ha7. % 9.94/10.19 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 9.94/10.19 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 9.94/10.19 congruence. % 9.94/10.19 exact (zenon_H191 zenon_H82). % 9.94/10.19 apply zenon_H34. apply refl_equal. % 9.94/10.19 apply zenon_H22. apply refl_equal. % 9.94/10.19 apply zenon_H22. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L125_ *) % 9.94/10.19 assert (zenon_L126_ : (((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) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H192 zenon_H86 zenon_H11f zenon_H26 zenon_H93 zenon_Hd0 zenon_H96 zenon_Ha7 zenon_H23. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 9.94/10.19 apply (zenon_L123_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 9.94/10.19 apply (zenon_L124_); trivial. % 9.94/10.19 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 9.94/10.19 apply (zenon_L104_); trivial. % 9.94/10.19 apply (zenon_L125_); trivial. % 9.94/10.19 (* end of lemma zenon_L126_ *) % 9.94/10.19 assert (zenon_L127_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H195 zenon_H192 zenon_H11f zenon_H26 zenon_H93 zenon_H96 zenon_Ha7 zenon_H23. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H188. zenon_intro zenon_H196. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H196). zenon_intro zenon_H18c. zenon_intro zenon_Hcf. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd0. zenon_intro zenon_H86. % 9.94/10.19 apply (zenon_L126_); trivial. % 9.94/10.19 (* end of lemma zenon_L127_ *) % 9.94/10.19 assert (zenon_L128_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H197 zenon_Hd1 zenon_H26. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H197). zenon_intro zenon_H188. zenon_intro zenon_H198. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H198). zenon_intro zenon_H18c. zenon_intro zenon_Hd6. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 9.94/10.19 apply (zenon_L56_); trivial. % 9.94/10.19 (* end of lemma zenon_L128_ *) % 9.94/10.19 assert (zenon_L129_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H199 zenon_H2f zenon_H30. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H199). zenon_intro zenon_H188. zenon_intro zenon_H19a. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H19a). zenon_intro zenon_H18c. zenon_intro zenon_H165. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H165). zenon_intro zenon_H2e. zenon_intro zenon_H2e. % 9.94/10.19 apply (zenon_L9_); trivial. % 9.94/10.19 (* end of lemma zenon_L129_ *) % 9.94/10.19 assert (zenon_L130_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H19b zenon_H155 zenon_H1f zenon_H25 zenon_H5f zenon_H26 zenon_H96 zenon_H12a. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H19b). zenon_intro zenon_H188. zenon_intro zenon_H19c. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H19c). zenon_intro zenon_H18c. zenon_intro zenon_H16b. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 9.94/10.19 apply (zenon_L106_); trivial. % 9.94/10.19 (* end of lemma zenon_L130_ *) % 9.94/10.19 assert (zenon_L131_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e0) (op (e0) (e3))) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H19d zenon_He1. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_Hf7. zenon_intro zenon_H19e. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H171. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 9.94/10.19 apply (zenon_L61_); trivial. % 9.94/10.19 (* end of lemma zenon_L131_ *) % 9.94/10.19 assert (zenon_L132_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hf7 zenon_H109 zenon_H2c. % 9.94/10.19 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 9.94/10.19 cut (((e3) = (e3)) = ((e1) = (e3))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H2c. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H31. % 9.94/10.19 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 9.94/10.19 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e1) (e3)) = (e1)) = ((e3) = (e1))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H19f. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Hf7. % 9.94/10.19 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 9.94/10.19 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 9.94/10.19 congruence. % 9.94/10.19 exact (zenon_H1a0 zenon_H109). % 9.94/10.19 apply zenon_H1d. apply refl_equal. % 9.94/10.19 apply zenon_H29. apply refl_equal. % 9.94/10.19 apply zenon_H29. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L132_ *) % 9.94/10.19 assert (zenon_L133_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1a1 zenon_H2c. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1a1). zenon_intro zenon_Hf7. zenon_intro zenon_H1a2. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H143. zenon_intro zenon_H174. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 9.94/10.19 apply (zenon_L132_); trivial. % 9.94/10.19 (* end of lemma zenon_L133_ *) % 9.94/10.19 assert (zenon_L134_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1a3 zenon_H7e zenon_H2f. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_Hf7. zenon_intro zenon_H1a4. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1a4). zenon_intro zenon_H143. zenon_intro zenon_H177. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 9.94/10.19 apply (zenon_L25_); trivial. % 9.94/10.19 (* end of lemma zenon_L134_ *) % 9.94/10.19 assert (zenon_L135_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1a5 zenon_Ha7 zenon_H2a. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_Hf7. zenon_intro zenon_H1a6. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1a6). zenon_intro zenon_H143. zenon_intro zenon_H17a. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 9.94/10.19 apply (zenon_L75_); trivial. % 9.94/10.19 (* end of lemma zenon_L135_ *) % 9.94/10.19 assert (zenon_L136_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1a7 zenon_H192 zenon_H11f zenon_H26 zenon_H93 zenon_H96 zenon_Ha7 zenon_H23. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H86. zenon_intro zenon_H1a8. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hd0. zenon_intro zenon_H6f. % 9.94/10.19 apply (zenon_L126_); trivial. % 9.94/10.19 (* end of lemma zenon_L136_ *) % 9.94/10.19 assert (zenon_L137_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1a9 zenon_H192 zenon_H11f zenon_H26 zenon_H93 zenon_H96 zenon_Ha7 zenon_H23. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1a9). zenon_intro zenon_H86. zenon_intro zenon_H1aa. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_Hd0. zenon_intro zenon_Hb3. % 9.94/10.19 apply (zenon_L126_); trivial. % 9.94/10.19 (* end of lemma zenon_L137_ *) % 9.94/10.19 assert (zenon_L138_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((e0) = (e2))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1ab zenon_H23. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1ab). zenon_intro zenon_H86. zenon_intro zenon_H1ac. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_Hd0. zenon_intro zenon_Hb6. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 9.94/10.19 apply (zenon_L54_); trivial. % 9.94/10.19 (* end of lemma zenon_L138_ *) % 9.94/10.19 assert (zenon_L139_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1ad zenon_Ha7 zenon_Hb8. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H86. zenon_intro zenon_H1ae. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_Hd0. zenon_intro zenon_Hbd. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 9.94/10.19 apply (zenon_L47_); trivial. % 9.94/10.19 (* end of lemma zenon_L139_ *) % 9.94/10.19 assert (zenon_L140_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1af zenon_Hd1 zenon_H26. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_Hd2. zenon_intro zenon_H1b0. % 9.94/10.19 apply (zenon_L56_); trivial. % 9.94/10.19 (* end of lemma zenon_L140_ *) % 9.94/10.19 assert (zenon_L141_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1b1 zenon_H25 zenon_H26. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_Hd2. zenon_intro zenon_H1b2. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_Hd7. zenon_intro zenon_Hc5. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 9.94/10.19 apply (zenon_L5_); trivial. % 9.94/10.19 (* end of lemma zenon_L141_ *) % 9.94/10.19 assert (zenon_L142_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1b3 zenon_Hd1 zenon_H26. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_Hd2. zenon_intro zenon_H1b4. % 9.94/10.19 apply (zenon_L56_); trivial. % 9.94/10.19 (* end of lemma zenon_L142_ *) % 9.94/10.19 assert (zenon_L143_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1b5 zenon_Hd1 zenon_H26. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_Hd2. zenon_intro zenon_H1b6. % 9.94/10.19 apply (zenon_L56_); trivial. % 9.94/10.19 (* end of lemma zenon_L143_ *) % 9.94/10.19 assert (zenon_L144_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1b7 zenon_H192 zenon_H11f zenon_H26 zenon_H93 zenon_H96 zenon_Ha7 zenon_H23. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_H2e. zenon_intro zenon_H1b8. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_H2e. zenon_intro zenon_Hcf. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd0. zenon_intro zenon_H86. % 9.94/10.19 apply (zenon_L126_); trivial. % 9.94/10.19 (* end of lemma zenon_L144_ *) % 9.94/10.19 assert (zenon_L145_ : ((op (e2) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H2e zenon_Hd7 zenon_H1b9. % 9.94/10.19 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hec | zenon_intro zenon_H81 ]. % 9.94/10.19 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H1b9. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_Hec. % 9.94/10.19 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 9.94/10.19 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H1ba. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H2e. % 9.94/10.19 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 9.94/10.19 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H81. apply refl_equal. % 9.94/10.19 apply zenon_H1bb. apply sym_equal. exact zenon_Hd7. % 9.94/10.19 apply zenon_H81. apply refl_equal. % 9.94/10.19 apply zenon_H81. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L145_ *) % 9.94/10.19 assert (zenon_L146_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1bc zenon_H1b9. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1bc). zenon_intro zenon_H2e. zenon_intro zenon_H1bd. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1bd). zenon_intro zenon_H2e. zenon_intro zenon_Hd6. % 9.94/10.19 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 9.94/10.19 apply (zenon_L145_); trivial. % 9.94/10.19 (* end of lemma zenon_L146_ *) % 9.94/10.19 assert (zenon_L147_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1be zenon_H2f zenon_H30. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_H2e. zenon_intro zenon_H1bf. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1bf). zenon_intro zenon_H2e. zenon_intro zenon_H165. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H165). zenon_intro zenon_H2e. zenon_intro zenon_H2e. % 9.94/10.19 apply (zenon_L9_); trivial. % 9.94/10.19 (* end of lemma zenon_L147_ *) % 9.94/10.19 assert (zenon_L148_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1c0 zenon_H127. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1c0). zenon_intro zenon_H2e. zenon_intro zenon_H1c1. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1c1). zenon_intro zenon_H2e. zenon_intro zenon_H16b. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 9.94/10.19 apply (zenon_L83_); trivial. % 9.94/10.19 (* end of lemma zenon_L148_ *) % 9.94/10.19 assert (zenon_L149_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1c0 zenon_H127. % 9.94/10.19 apply (zenon_L148_); trivial. % 9.94/10.19 (* end of lemma zenon_L149_ *) % 9.94/10.19 assert (zenon_L150_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e0) (op (e0) (e3))) = (e3))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H1c2 zenon_He1. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H128. zenon_intro zenon_H1c3. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H1c3). zenon_intro zenon_H166. zenon_intro zenon_H171. % 9.94/10.19 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 9.94/10.19 apply (zenon_L61_); trivial. % 9.94/10.19 (* end of lemma zenon_L150_ *) % 9.94/10.19 assert (zenon_L151_ : (~((op (e0) (op (e0) (e2))) = (e2))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> False). % 9.94/10.19 do 0 intro. intros zenon_H15c zenon_H24 zenon_H97. % 9.94/10.19 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (op (e0) (e2))) = (e2))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H15c. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H24. % 9.94/10.19 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.19 cut (((op (e0) (e0)) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1c4]. % 9.94/10.19 congruence. % 9.94/10.19 elim (classic ((op (e0) (op (e0) (e2))) = (op (e0) (op (e0) (e2))))); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H1c6 ]. % 9.94/10.19 cut (((op (e0) (op (e0) (e2))) = (op (e0) (op (e0) (e2)))) = ((op (e0) (e0)) = (op (e0) (op (e0) (e2))))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H1c4. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H1c5. % 9.94/10.19 cut (((op (e0) (op (e0) (e2))) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 9.94/10.19 cut (((op (e0) (op (e0) (e2))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1c7]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e0) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1c8]. % 9.94/10.19 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H34. apply refl_equal. % 9.94/10.19 exact (zenon_H1c8 zenon_H97). % 9.94/10.19 apply zenon_H1c6. apply refl_equal. % 9.94/10.19 apply zenon_H1c6. apply refl_equal. % 9.94/10.19 apply zenon_H22. apply refl_equal. % 9.94/10.19 (* end of lemma zenon_L151_ *) % 9.94/10.19 assert (zenon_L152_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> False). % 9.94/10.19 do 0 intro. intros zenon_Hef zenon_H24 zenon_Hd0. % 9.94/10.19 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e0) (e2)))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_Hef. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H24. % 9.94/10.19 cut (((e2) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hee]. % 9.94/10.19 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 9.94/10.19 congruence. % 9.94/10.19 apply zenon_H67. apply refl_equal. % 9.94/10.19 apply zenon_Hee. apply sym_equal. exact zenon_Hd0. % 9.94/10.19 (* end of lemma zenon_L152_ *) % 9.94/10.19 assert (zenon_L153_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 9.94/10.19 do 0 intro. intros zenon_H9d zenon_H69 zenon_H23. % 9.94/10.19 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H6a | zenon_intro zenon_H22 ]. % 9.94/10.19 cut (((e2) = (e2)) = ((e0) = (e2))). % 9.94/10.19 intro zenon_D_pnotp. % 9.94/10.19 apply zenon_H23. % 9.94/10.19 rewrite <- zenon_D_pnotp. % 9.94/10.19 exact zenon_H6a. % 9.94/10.19 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.94/10.19 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 9.94/10.19 congruence. % 9.94/10.19 cut (((op (e1) (e0)) = (e0)) = ((e2) = (e0))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H8a. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H9d. % 10.03/10.20 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.03/10.20 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 10.03/10.20 congruence. % 10.03/10.20 exact (zenon_H6c zenon_H69). % 10.03/10.20 apply zenon_H34. apply refl_equal. % 10.03/10.20 apply zenon_H22. apply refl_equal. % 10.03/10.20 apply zenon_H22. apply refl_equal. % 10.03/10.20 (* end of lemma zenon_L153_ *) % 10.03/10.20 assert (zenon_L154_ : (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1c9 zenon_H1f zenon_Hf3. % 10.03/10.20 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e0) (e3)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H1c9. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H1f. % 10.03/10.20 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 10.03/10.20 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H67. apply refl_equal. % 10.03/10.20 apply zenon_H1ca. apply sym_equal. exact zenon_Hf3. % 10.03/10.20 (* end of lemma zenon_L154_ *) % 10.03/10.20 assert (zenon_L155_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H12a zenon_Hf3 zenon_H102. % 10.03/10.20 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H12a. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_Hf3. % 10.03/10.20 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 10.03/10.20 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H108. apply refl_equal. % 10.03/10.20 apply zenon_H103. apply sym_equal. exact zenon_H102. % 10.03/10.20 (* end of lemma zenon_L155_ *) % 10.03/10.20 assert (zenon_L156_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1cb zenon_H91 zenon_H11f zenon_H26 zenon_Hd1 zenon_H30 zenon_H2f zenon_Hf4 zenon_H12a. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.03/10.20 apply (zenon_L123_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.03/10.20 apply (zenon_L56_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.03/10.20 apply (zenon_L9_); trivial. % 10.03/10.20 apply (zenon_L105_); trivial. % 10.03/10.20 (* end of lemma zenon_L156_ *) % 10.03/10.20 assert (zenon_L157_ : (((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) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1ce zenon_Hb8 zenon_Ha7 zenon_H102 zenon_H12a zenon_H2f zenon_H30 zenon_Hd1 zenon_H26 zenon_H11f zenon_H91 zenon_H1cb zenon_H109 zenon_H105. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H1cf ]. % 10.03/10.20 apply (zenon_L47_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1d0 ]. % 10.03/10.20 apply (zenon_L155_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hf4 | zenon_intro zenon_He2 ]. % 10.03/10.20 apply (zenon_L156_); trivial. % 10.03/10.20 apply (zenon_L71_); trivial. % 10.03/10.20 (* end of lemma zenon_L157_ *) % 10.03/10.20 assert (zenon_L158_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (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 (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H124 zenon_H1f zenon_H1c9 zenon_H2c zenon_H105 zenon_H109 zenon_H1cb zenon_H91 zenon_H11f zenon_H26 zenon_Hd1 zenon_H30 zenon_H2f zenon_H12a zenon_Hb8 zenon_H1ce zenon_Ha7 zenon_H1e. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.03/10.20 apply (zenon_L154_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.03/10.20 apply (zenon_L132_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.03/10.20 apply (zenon_L157_); trivial. % 10.03/10.20 apply (zenon_L77_); trivial. % 10.03/10.20 (* end of lemma zenon_L158_ *) % 10.03/10.20 assert (zenon_L159_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (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 (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1d1 zenon_Hef zenon_H9d zenon_H23 zenon_H96 zenon_Hd0 zenon_H93 zenon_H192 zenon_H124 zenon_H1f zenon_H1c9 zenon_H2c zenon_H105 zenon_H109 zenon_H1cb zenon_H11f zenon_H26 zenon_Hd1 zenon_H30 zenon_H2f zenon_H12a zenon_Hb8 zenon_H1ce zenon_Ha7 zenon_H1e. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.03/10.20 apply (zenon_L152_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.03/10.20 apply (zenon_L153_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.03/10.20 apply (zenon_L126_); trivial. % 10.03/10.20 apply (zenon_L158_); trivial. % 10.03/10.20 (* end of lemma zenon_L159_ *) % 10.03/10.20 assert (zenon_L160_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1d4 zenon_H1f zenon_H1d5. % 10.03/10.20 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H1d4. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H1f. % 10.03/10.20 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 10.03/10.20 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H67. apply refl_equal. % 10.03/10.20 apply zenon_H1d6. apply sym_equal. exact zenon_H1d5. % 10.03/10.20 (* end of lemma zenon_L160_ *) % 10.03/10.20 assert (zenon_L161_ : ((op (e2) (e2)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H2f zenon_H87 zenon_H1d7. % 10.03/10.20 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hec | zenon_intro zenon_H81 ]. % 10.03/10.20 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H1d7. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_Hec. % 10.03/10.20 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.20 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d8]. % 10.03/10.20 congruence. % 10.03/10.20 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e2) (e0)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H1d8. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H2f. % 10.03/10.20 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 10.03/10.20 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H81. apply refl_equal. % 10.03/10.20 apply zenon_H117. apply sym_equal. exact zenon_H87. % 10.03/10.20 apply zenon_H81. apply refl_equal. % 10.03/10.20 apply zenon_H81. apply refl_equal. % 10.03/10.20 (* end of lemma zenon_L161_ *) % 10.03/10.20 assert (zenon_L162_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1d9 zenon_H72 zenon_H79. % 10.03/10.20 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H1d9. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H72. % 10.03/10.20 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 10.03/10.20 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H76. apply refl_equal. % 10.03/10.20 apply zenon_H140. apply sym_equal. exact zenon_H79. % 10.03/10.20 (* end of lemma zenon_L162_ *) % 10.03/10.20 assert (zenon_L163_ : ((op (e1) (e1)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H26 zenon_H69 zenon_Hf1. % 10.03/10.20 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H60 | zenon_intro zenon_H61 ]. % 10.03/10.20 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (e0)) = (op (e1) (e1)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_Hf1. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H60. % 10.03/10.20 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 10.03/10.20 cut (((op (e1) (e1)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 10.03/10.20 congruence. % 10.03/10.20 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e1) (e0)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_Hf2. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H26. % 10.03/10.20 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 10.03/10.20 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H61. apply refl_equal. % 10.03/10.20 apply zenon_H1da. apply sym_equal. exact zenon_H69. % 10.03/10.20 apply zenon_H61. apply refl_equal. % 10.03/10.20 apply zenon_H61. apply refl_equal. % 10.03/10.20 (* end of lemma zenon_L163_ *) % 10.03/10.20 assert (zenon_L164_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (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 (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1d1 zenon_H25 zenon_Hf1 zenon_H9e zenon_H23 zenon_H124 zenon_H1f zenon_H1c9 zenon_H2c zenon_H105 zenon_H109 zenon_H1cb zenon_H11f zenon_H26 zenon_Hd1 zenon_H30 zenon_H2f zenon_H12a zenon_Hb8 zenon_H1ce zenon_Ha7 zenon_H1e. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.03/10.20 apply (zenon_L30_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.03/10.20 apply (zenon_L163_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.03/10.20 apply (zenon_L54_); trivial. % 10.03/10.20 apply (zenon_L158_); trivial. % 10.03/10.20 (* end of lemma zenon_L164_ *) % 10.03/10.20 assert (zenon_L165_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (op (e0) (e1))) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (op (e0) (e2))) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H156 zenon_Hd8 zenon_H16c zenon_H1d1 zenon_H25 zenon_Hf1 zenon_H23 zenon_H124 zenon_H1f zenon_H1c9 zenon_H2c zenon_H105 zenon_H109 zenon_H1cb zenon_H11f zenon_H26 zenon_Hd1 zenon_H30 zenon_H2f zenon_H12a zenon_H1ce zenon_H1e zenon_H155 zenon_H15c zenon_H5f zenon_H192 zenon_H93 zenon_H96 zenon_Hef zenon_He8 zenon_H79 zenon_H1d9 zenon_H1d7 zenon_H74 zenon_H1d4 zenon_H1db zenon_H64 zenon_H130 zenon_H2a zenon_H1dc zenon_Ha7 zenon_Hb8. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.03/10.20 apply (zenon_L2_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.03/10.20 apply (zenon_L58_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H20 | zenon_intro zenon_H1dd ]. % 10.03/10.20 apply (zenon_L2_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.03/10.20 apply (zenon_L151_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.03/10.20 apply (zenon_L103_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.03/10.20 apply (zenon_L159_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.03/10.20 apply (zenon_L32_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.03/10.20 apply (zenon_L22_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.03/10.20 apply (zenon_L66_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.03/10.20 apply (zenon_L132_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1db); [ zenon_intro zenon_H90 | zenon_intro zenon_H1df ]. % 10.03/10.20 apply (zenon_L108_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H1e0 ]. % 10.03/10.20 apply (zenon_L160_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H91 | zenon_intro zenon_H72 ]. % 10.03/10.20 apply (zenon_L157_); trivial. % 10.03/10.20 apply (zenon_L23_); trivial. % 10.03/10.20 apply (zenon_L77_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.03/10.20 apply (zenon_L161_); trivial. % 10.03/10.20 apply (zenon_L162_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.03/10.20 apply (zenon_L60_); trivial. % 10.03/10.20 apply (zenon_L71_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H9e | zenon_intro zenon_H90 ]. % 10.03/10.20 apply (zenon_L164_); trivial. % 10.03/10.20 apply (zenon_L108_); trivial. % 10.03/10.20 apply (zenon_L47_); trivial. % 10.03/10.20 (* end of lemma zenon_L165_ *) % 10.03/10.20 assert (zenon_L166_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H128 zenon_H112 zenon_H30. % 10.03/10.20 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 10.03/10.20 cut (((e3) = (e3)) = ((e2) = (e3))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H30. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H31. % 10.03/10.20 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.20 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 10.03/10.20 congruence. % 10.03/10.20 cut (((op (e2) (e3)) = (e2)) = ((e3) = (e2))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H32. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H128. % 10.03/10.20 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.20 cut (((op (e2) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 10.03/10.20 congruence. % 10.03/10.20 exact (zenon_H1e1 zenon_H112). % 10.03/10.20 apply zenon_H22. apply refl_equal. % 10.03/10.20 apply zenon_H29. apply refl_equal. % 10.03/10.20 apply zenon_H29. apply refl_equal. % 10.03/10.20 (* end of lemma zenon_L166_ *) % 10.03/10.20 assert (zenon_L167_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1e2 zenon_H30. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H128. zenon_intro zenon_H1e3. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1e3). zenon_intro zenon_H166. zenon_intro zenon_H177. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.03/10.20 apply (zenon_L166_); trivial. % 10.03/10.20 (* end of lemma zenon_L167_ *) % 10.03/10.20 assert (zenon_L168_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1e4 zenon_Ha7 zenon_H2a. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1e4). zenon_intro zenon_H128. zenon_intro zenon_H1e5. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1e5). zenon_intro zenon_H166. zenon_intro zenon_H17a. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 10.03/10.20 apply (zenon_L75_); trivial. % 10.03/10.20 (* end of lemma zenon_L168_ *) % 10.03/10.20 assert (zenon_L169_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e1)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1e6 zenon_H1e zenon_H1f. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H72. zenon_intro zenon_H1e7. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_He2. zenon_intro zenon_H6f. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H20. zenon_intro zenon_H20. % 10.03/10.20 apply (zenon_L2_); trivial. % 10.03/10.20 (* end of lemma zenon_L169_ *) % 10.03/10.20 assert (zenon_L170_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1e8 zenon_Hae zenon_H9c zenon_Ha1 zenon_H2f zenon_H2a zenon_Ha7 zenon_Ha9. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1e8). zenon_intro zenon_H72. zenon_intro zenon_H1e9. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1e9). zenon_intro zenon_He2. zenon_intro zenon_Hb3. % 10.03/10.20 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.03/10.20 apply (zenon_L44_); trivial. % 10.03/10.20 (* end of lemma zenon_L170_ *) % 10.03/10.20 assert (zenon_L171_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_Ha7 zenon_H98 zenon_H1ea. % 10.03/10.20 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.03/10.20 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H1ea. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_Haa. % 10.03/10.20 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.20 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1eb]. % 10.03/10.20 congruence. % 10.03/10.20 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H1eb. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_Ha7. % 10.03/10.20 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 10.03/10.20 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_Hab. apply refl_equal. % 10.03/10.20 apply zenon_H99. apply sym_equal. exact zenon_H98. % 10.03/10.20 apply zenon_Hab. apply refl_equal. % 10.03/10.20 apply zenon_Hab. apply refl_equal. % 10.03/10.20 (* end of lemma zenon_L171_ *) % 10.03/10.20 assert (zenon_L172_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1ec zenon_H188 zenon_H1ed. % 10.03/10.20 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H1ec. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H188. % 10.03/10.20 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 10.03/10.20 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H1ef. apply refl_equal. % 10.03/10.20 apply zenon_H1ee. apply sym_equal. exact zenon_H1ed. % 10.03/10.20 (* end of lemma zenon_L172_ *) % 10.03/10.20 assert (zenon_L173_ : (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H187 zenon_H26 zenon_Hd7. % 10.03/10.20 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e1) (e2)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H187. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H26. % 10.03/10.20 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 10.03/10.20 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H61. apply refl_equal. % 10.03/10.20 apply zenon_H1bb. apply sym_equal. exact zenon_Hd7. % 10.03/10.20 (* end of lemma zenon_L173_ *) % 10.03/10.20 assert (zenon_L174_ : ((op (e2) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H2f zenon_H1f0 zenon_H1b9. % 10.03/10.20 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hec | zenon_intro zenon_H81 ]. % 10.03/10.20 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H1b9. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_Hec. % 10.03/10.20 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.20 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 10.03/10.20 congruence. % 10.03/10.20 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H1ba. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H2f. % 10.03/10.20 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 10.03/10.20 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H81. apply refl_equal. % 10.03/10.20 apply zenon_H1f1. apply sym_equal. exact zenon_H1f0. % 10.03/10.20 apply zenon_H81. apply refl_equal. % 10.03/10.20 apply zenon_H81. apply refl_equal. % 10.03/10.20 (* end of lemma zenon_L174_ *) % 10.03/10.20 assert (zenon_L175_ : (((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 (e3) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1f2 zenon_H97 zenon_H13a zenon_H1ed zenon_H1ec zenon_H26 zenon_H187 zenon_H2f zenon_H1b9. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1f2); [ zenon_intro zenon_H13b | zenon_intro zenon_H1f3 ]. % 10.03/10.20 apply (zenon_L89_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1f3); [ zenon_intro zenon_H188 | zenon_intro zenon_H1f4 ]. % 10.03/10.20 apply (zenon_L172_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H1f0 ]. % 10.03/10.20 apply (zenon_L173_); trivial. % 10.03/10.20 apply (zenon_L174_); trivial. % 10.03/10.20 (* end of lemma zenon_L175_ *) % 10.03/10.20 assert (zenon_L176_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1f5 zenon_H72 zenon_H7f. % 10.03/10.20 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H1f5. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H72. % 10.03/10.20 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 10.03/10.20 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H76. apply refl_equal. % 10.03/10.20 apply zenon_H80. apply sym_equal. exact zenon_H7f. % 10.03/10.20 (* end of lemma zenon_L176_ *) % 10.03/10.20 assert (zenon_L177_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1d1 zenon_H1f zenon_H25 zenon_Hf1 zenon_H9e zenon_H23 zenon_H1cb zenon_H11f zenon_H26 zenon_Hd1 zenon_H30 zenon_H2f zenon_Hf4 zenon_H12a. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.03/10.20 apply (zenon_L30_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.03/10.20 apply (zenon_L163_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.03/10.20 apply (zenon_L54_); trivial. % 10.03/10.20 apply (zenon_L156_); trivial. % 10.03/10.20 (* end of lemma zenon_L177_ *) % 10.03/10.20 assert (zenon_L178_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (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 (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H155 zenon_H5f zenon_H72 zenon_H1f5 zenon_H96 zenon_H1f2 zenon_H97 zenon_H13a zenon_H1ec zenon_H187 zenon_H1b9 zenon_Ha7 zenon_H1ea zenon_H1f6 zenon_H1d1 zenon_H1f zenon_H25 zenon_Hf1 zenon_H9e zenon_H23 zenon_H1cb zenon_H11f zenon_H26 zenon_Hd1 zenon_H30 zenon_H2f zenon_H12a. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.03/10.20 apply (zenon_L30_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.03/10.20 apply (zenon_L103_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.03/10.20 apply (zenon_L171_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.03/10.20 apply (zenon_L175_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.03/10.20 apply (zenon_L104_); trivial. % 10.03/10.20 apply (zenon_L176_); trivial. % 10.03/10.20 apply (zenon_L177_); trivial. % 10.03/10.20 (* end of lemma zenon_L178_ *) % 10.03/10.20 assert (zenon_L179_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1f9 zenon_H155 zenon_H5f zenon_H1f5 zenon_H96 zenon_H1f2 zenon_H13a zenon_H1ec zenon_H187 zenon_H1b9 zenon_Ha7 zenon_H1ea zenon_H1f6 zenon_H1d1 zenon_H1f zenon_H25 zenon_Hf1 zenon_H23 zenon_H1cb zenon_H11f zenon_H26 zenon_Hd1 zenon_H30 zenon_H2f zenon_H12a. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1f9). zenon_intro zenon_H72. zenon_intro zenon_H1fa. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_He2. zenon_intro zenon_Hb6. % 10.03/10.20 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 10.03/10.20 apply (zenon_L178_); trivial. % 10.03/10.20 (* end of lemma zenon_L179_ *) % 10.03/10.20 assert (zenon_L180_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1fb zenon_Ha7 zenon_Hb8. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H72. zenon_intro zenon_H1fc. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_He2. zenon_intro zenon_Hbd. % 10.03/10.20 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.03/10.20 apply (zenon_L47_); trivial. % 10.03/10.20 (* end of lemma zenon_L180_ *) % 10.03/10.20 assert (zenon_L181_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e1)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1fd zenon_Hbe zenon_H1f. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H79. zenon_intro zenon_H1fe. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H109. zenon_intro zenon_Hc2. % 10.03/10.20 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.03/10.20 apply (zenon_L49_); trivial. % 10.03/10.20 (* end of lemma zenon_L181_ *) % 10.03/10.20 assert (zenon_L182_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e2)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1ff zenon_H25 zenon_H26. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1ff). zenon_intro zenon_H79. zenon_intro zenon_H200. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H200). zenon_intro zenon_H109. zenon_intro zenon_Hc5. % 10.03/10.20 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 10.03/10.20 apply (zenon_L5_); trivial. % 10.03/10.20 (* end of lemma zenon_L182_ *) % 10.03/10.20 assert (zenon_L183_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H201 zenon_H2c. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H201). zenon_intro zenon_H79. zenon_intro zenon_H202. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H202). zenon_intro zenon_H109. zenon_intro zenon_Hcb. % 10.03/10.20 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.20 apply (zenon_L132_); trivial. % 10.03/10.20 (* end of lemma zenon_L183_ *) % 10.03/10.20 assert (zenon_L184_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H203 zenon_H192 zenon_H11f zenon_H26 zenon_H93 zenon_H96 zenon_Ha7 zenon_H23. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H203). zenon_intro zenon_H7f. zenon_intro zenon_H204. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H204). zenon_intro zenon_H112. zenon_intro zenon_Hcf. % 10.03/10.20 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd0. zenon_intro zenon_H86. % 10.03/10.20 apply (zenon_L126_); trivial. % 10.03/10.20 (* end of lemma zenon_L184_ *) % 10.03/10.20 assert (zenon_L185_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H205 zenon_Hd1 zenon_H26. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H7f. zenon_intro zenon_H206. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H112. zenon_intro zenon_Hd6. % 10.03/10.20 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.03/10.20 apply (zenon_L56_); trivial. % 10.03/10.20 (* end of lemma zenon_L185_ *) % 10.03/10.20 assert (zenon_L186_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H207 zenon_H2f zenon_H30. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H7f. zenon_intro zenon_H208. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H208). zenon_intro zenon_H112. zenon_intro zenon_H165. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H165). zenon_intro zenon_H2e. zenon_intro zenon_H2e. % 10.03/10.20 apply (zenon_L9_); trivial. % 10.03/10.20 (* end of lemma zenon_L186_ *) % 10.03/10.20 assert (zenon_L187_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H209 zenon_H30. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H209). zenon_intro zenon_H7f. zenon_intro zenon_H20a. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H20a). zenon_intro zenon_H112. zenon_intro zenon_H16b. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.03/10.20 apply (zenon_L166_); trivial. % 10.03/10.20 (* end of lemma zenon_L187_ *) % 10.03/10.20 assert (zenon_L188_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H20b zenon_Ha7 zenon_H2a. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_H52. zenon_intro zenon_H20c. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H20c). zenon_intro zenon_H52. zenon_intro zenon_H171. % 10.03/10.20 apply (zenon_L75_); trivial. % 10.03/10.20 (* end of lemma zenon_L188_ *) % 10.03/10.20 assert (zenon_L189_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H20d zenon_Ha7 zenon_H2a. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H52. zenon_intro zenon_H20e. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H20e). zenon_intro zenon_H52. zenon_intro zenon_H174. % 10.03/10.20 apply (zenon_L75_); trivial. % 10.03/10.20 (* end of lemma zenon_L189_ *) % 10.03/10.20 assert (zenon_L190_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H20f zenon_Ha7 zenon_H2a. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H20f). zenon_intro zenon_H52. zenon_intro zenon_H210. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H210). zenon_intro zenon_H52. zenon_intro zenon_H177. % 10.03/10.20 apply (zenon_L75_); trivial. % 10.03/10.20 (* end of lemma zenon_L190_ *) % 10.03/10.20 assert (zenon_L191_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H211 zenon_Ha7 zenon_H2a. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H211). zenon_intro zenon_H52. zenon_intro zenon_H212. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H212). zenon_intro zenon_H52. zenon_intro zenon_H17a. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 10.03/10.20 apply (zenon_L75_); trivial. % 10.03/10.20 (* end of lemma zenon_L191_ *) % 10.03/10.20 assert (zenon_L192_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (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))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1dc zenon_H1e zenon_H43 zenon_H12a zenon_H2f zenon_H30 zenon_Hd1 zenon_H26 zenon_H11f zenon_H1cb zenon_H23 zenon_Hf1 zenon_H25 zenon_H1f zenon_H1d1 zenon_H1f6 zenon_H1ea zenon_H1b9 zenon_H187 zenon_H1ec zenon_H13a zenon_H97 zenon_H1f2 zenon_H96 zenon_H1f5 zenon_H72 zenon_H5f zenon_H155 zenon_Ha7 zenon_H16c. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H20 | zenon_intro zenon_H1dd ]. % 10.03/10.20 apply (zenon_L2_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 10.03/10.20 apply (zenon_L88_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H9e | zenon_intro zenon_H90 ]. % 10.03/10.20 apply (zenon_L178_); trivial. % 10.03/10.20 apply (zenon_L108_); trivial. % 10.03/10.20 (* end of lemma zenon_L192_ *) % 10.03/10.20 assert (zenon_L193_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1bc zenon_Hd1 zenon_H26. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1bc). zenon_intro zenon_H2e. zenon_intro zenon_H1bd. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1bd). zenon_intro zenon_H2e. zenon_intro zenon_Hd6. % 10.03/10.20 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.03/10.20 apply (zenon_L56_); trivial. % 10.03/10.20 (* end of lemma zenon_L193_ *) % 10.03/10.20 assert (zenon_L194_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1dc zenon_H43 zenon_H1e zenon_H1ce zenon_Hb8 zenon_H12a zenon_H2f zenon_H30 zenon_Hd1 zenon_H26 zenon_H11f zenon_H1cb zenon_H109 zenon_H105 zenon_H2c zenon_H1c9 zenon_H1f zenon_H124 zenon_H23 zenon_Hf1 zenon_H25 zenon_H1d1 zenon_Ha7 zenon_H16c. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H20 | zenon_intro zenon_H1dd ]. % 10.03/10.20 apply (zenon_L2_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 10.03/10.20 apply (zenon_L88_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H9e | zenon_intro zenon_H90 ]. % 10.03/10.20 apply (zenon_L164_); trivial. % 10.03/10.20 apply (zenon_L108_); trivial. % 10.03/10.20 (* end of lemma zenon_L194_ *) % 10.03/10.20 assert (zenon_L195_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1e8 zenon_H43. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1e8). zenon_intro zenon_H72. zenon_intro zenon_H1e9. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1e9). zenon_intro zenon_He2. zenon_intro zenon_Hb3. % 10.03/10.20 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.03/10.20 apply (zenon_L88_); trivial. % 10.03/10.20 (* end of lemma zenon_L195_ *) % 10.03/10.20 assert (zenon_L196_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H205 zenon_H7e zenon_H2f. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H7f. zenon_intro zenon_H206. % 10.03/10.20 apply (zenon_L25_); trivial. % 10.03/10.20 (* end of lemma zenon_L196_ *) % 10.03/10.20 assert (zenon_L197_ : (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e2) (e0)) = (e0)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H4d zenon_H9e. % 10.03/10.20 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (op (e2) (e0))) = (e0))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H4d. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H9e. % 10.03/10.20 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.03/10.20 cut (((op (e2) (e0)) = (op (e2) (op (e2) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H213]. % 10.03/10.20 congruence. % 10.03/10.20 elim (classic ((op (e2) (op (e2) (e0))) = (op (e2) (op (e2) (e0))))); [ zenon_intro zenon_H214 | zenon_intro zenon_H215 ]. % 10.03/10.20 cut (((op (e2) (op (e2) (e0))) = (op (e2) (op (e2) (e0)))) = ((op (e2) (e0)) = (op (e2) (op (e2) (e0))))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H213. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H214. % 10.03/10.20 cut (((op (e2) (op (e2) (e0))) = (op (e2) (op (e2) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 10.03/10.20 cut (((op (e2) (op (e2) (e0))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H216]. % 10.03/10.20 congruence. % 10.03/10.20 cut (((op (e2) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 10.03/10.20 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H22. apply refl_equal. % 10.03/10.20 exact (zenon_Hcc zenon_H9e). % 10.03/10.20 apply zenon_H215. apply refl_equal. % 10.03/10.20 apply zenon_H215. apply refl_equal. % 10.03/10.20 apply zenon_H34. apply refl_equal. % 10.03/10.20 (* end of lemma zenon_L197_ *) % 10.03/10.20 assert (zenon_L198_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H169 zenon_H4d. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H169). zenon_intro zenon_H97. zenon_intro zenon_H16a. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H16a). zenon_intro zenon_H9e. zenon_intro zenon_H16b. % 10.03/10.20 apply (zenon_L197_); trivial. % 10.03/10.20 (* end of lemma zenon_L198_ *) % 10.03/10.20 assert (zenon_L199_ : (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H50 zenon_H2f zenon_H128. % 10.03/10.20 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (op (e2) (e3))) = (e3))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H50. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H2f. % 10.03/10.20 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.20 cut (((op (e2) (e2)) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H217]. % 10.03/10.20 congruence. % 10.03/10.20 elim (classic ((op (e2) (op (e2) (e3))) = (op (e2) (op (e2) (e3))))); [ zenon_intro zenon_H218 | zenon_intro zenon_H219 ]. % 10.03/10.20 cut (((op (e2) (op (e2) (e3))) = (op (e2) (op (e2) (e3)))) = ((op (e2) (e2)) = (op (e2) (op (e2) (e3))))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H217. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H218. % 10.03/10.20 cut (((op (e2) (op (e2) (e3))) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 10.03/10.20 cut (((op (e2) (op (e2) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 10.03/10.20 congruence. % 10.03/10.20 cut (((op (e2) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 10.03/10.20 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H22. apply refl_equal. % 10.03/10.20 exact (zenon_H21b zenon_H128). % 10.03/10.20 apply zenon_H219. apply refl_equal. % 10.03/10.20 apply zenon_H219. apply refl_equal. % 10.03/10.20 apply zenon_H29. apply refl_equal. % 10.03/10.20 (* end of lemma zenon_L199_ *) % 10.03/10.20 assert (zenon_L200_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e2)) = (e3)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H19b zenon_H50 zenon_H2f. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H19b). zenon_intro zenon_H188. zenon_intro zenon_H19c. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H19c). zenon_intro zenon_H18c. zenon_intro zenon_H16b. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.03/10.20 apply (zenon_L199_); trivial. % 10.03/10.20 (* end of lemma zenon_L200_ *) % 10.03/10.20 assert (zenon_L201_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e2)) = (e3)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1c0 zenon_H50 zenon_H2f. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1c0). zenon_intro zenon_H2e. zenon_intro zenon_H1c1. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1c1). zenon_intro zenon_H2e. zenon_intro zenon_H16b. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.03/10.20 apply (zenon_L199_); trivial. % 10.03/10.20 (* end of lemma zenon_L201_ *) % 10.03/10.20 assert (zenon_L202_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e2)) = (e3)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1c2 zenon_H50 zenon_H2f. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H128. zenon_intro zenon_H1c3. % 10.03/10.20 apply (zenon_L199_); trivial. % 10.03/10.20 (* end of lemma zenon_L202_ *) % 10.03/10.20 assert (zenon_L203_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e2)) = (e3)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H21c zenon_H50 zenon_H2f. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H21c). zenon_intro zenon_H128. zenon_intro zenon_H21d. % 10.03/10.20 apply (zenon_L199_); trivial. % 10.03/10.20 (* end of lemma zenon_L203_ *) % 10.03/10.20 assert (zenon_L204_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1f9 zenon_H4d. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1f9). zenon_intro zenon_H72. zenon_intro zenon_H1fa. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_He2. zenon_intro zenon_Hb6. % 10.03/10.20 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 10.03/10.20 apply (zenon_L197_); trivial. % 10.03/10.20 (* end of lemma zenon_L204_ *) % 10.03/10.20 assert (zenon_L205_ : (~((op (e2) (op (e2) (e1))) = (e1))) -> ((op (e2) (e1)) = (e1)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H4f zenon_H18c. % 10.03/10.20 cut (((op (e2) (e1)) = (e1)) = ((op (e2) (op (e2) (e1))) = (e1))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H4f. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H18c. % 10.03/10.20 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.20 cut (((op (e2) (e1)) = (op (e2) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 10.03/10.20 congruence. % 10.03/10.20 elim (classic ((op (e2) (op (e2) (e1))) = (op (e2) (op (e2) (e1))))); [ zenon_intro zenon_H21f | zenon_intro zenon_H220 ]. % 10.03/10.20 cut (((op (e2) (op (e2) (e1))) = (op (e2) (op (e2) (e1)))) = ((op (e2) (e1)) = (op (e2) (op (e2) (e1))))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H21e. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H21f. % 10.03/10.20 cut (((op (e2) (op (e2) (e1))) = (op (e2) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H220]. % 10.03/10.20 cut (((op (e2) (op (e2) (e1))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 10.03/10.20 congruence. % 10.03/10.20 cut (((op (e2) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H222]. % 10.03/10.20 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H22. apply refl_equal. % 10.03/10.20 exact (zenon_H222 zenon_H18c). % 10.03/10.20 apply zenon_H220. apply refl_equal. % 10.03/10.20 apply zenon_H220. apply refl_equal. % 10.03/10.20 apply zenon_H1d. apply refl_equal. % 10.03/10.20 (* end of lemma zenon_L205_ *) % 10.03/10.20 assert (zenon_L206_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H223 zenon_H4f. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H79. zenon_intro zenon_H224. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H109. zenon_intro zenon_Hc8. % 10.03/10.20 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.03/10.20 apply (zenon_L205_); trivial. % 10.03/10.20 (* end of lemma zenon_L206_ *) % 10.03/10.20 assert (zenon_L207_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> False). % 10.03/10.20 do 0 intro. intros zenon_Hc9 zenon_H5c. % 10.03/10.20 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H89. zenon_intro zenon_Hca. % 10.03/10.20 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_H9d. zenon_intro zenon_Hcb. % 10.03/10.20 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.20 apply (zenon_L93_); trivial. % 10.03/10.20 (* end of lemma zenon_L207_ *) % 10.03/10.20 assert (zenon_L208_ : (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e3) (e2)) = (e2)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H5d zenon_H166. % 10.03/10.20 cut (((op (e3) (e2)) = (e2)) = ((op (e3) (op (e3) (e2))) = (e2))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H5d. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H166. % 10.03/10.20 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.20 cut (((op (e3) (e2)) = (op (e3) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H225]. % 10.03/10.20 congruence. % 10.03/10.20 elim (classic ((op (e3) (op (e3) (e2))) = (op (e3) (op (e3) (e2))))); [ zenon_intro zenon_H226 | zenon_intro zenon_H227 ]. % 10.03/10.20 cut (((op (e3) (op (e3) (e2))) = (op (e3) (op (e3) (e2)))) = ((op (e3) (e2)) = (op (e3) (op (e3) (e2))))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H225. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H226. % 10.03/10.20 cut (((op (e3) (op (e3) (e2))) = (op (e3) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H227]. % 10.03/10.20 cut (((op (e3) (op (e3) (e2))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H228]. % 10.03/10.20 congruence. % 10.03/10.20 cut (((op (e3) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H229]. % 10.03/10.20 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H29. apply refl_equal. % 10.03/10.20 exact (zenon_H229 zenon_H166). % 10.03/10.20 apply zenon_H227. apply refl_equal. % 10.03/10.20 apply zenon_H227. apply refl_equal. % 10.03/10.20 apply zenon_H22. apply refl_equal. % 10.03/10.20 (* end of lemma zenon_L208_ *) % 10.03/10.20 assert (zenon_L209_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H169 zenon_H5d. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H169). zenon_intro zenon_H97. zenon_intro zenon_H16a. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H16a). zenon_intro zenon_H9e. zenon_intro zenon_H16b. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.03/10.20 apply (zenon_L208_); trivial. % 10.03/10.20 (* end of lemma zenon_L209_ *) % 10.03/10.20 assert (zenon_L210_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e3) (e3)) = (e0)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H16f zenon_H5a zenon_Ha7. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hb7. zenon_intro zenon_H170. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_H90. zenon_intro zenon_H171. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.20 apply (zenon_L98_); trivial. % 10.03/10.20 (* end of lemma zenon_L210_ *) % 10.03/10.20 assert (zenon_L211_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H19b zenon_H5d. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H19b). zenon_intro zenon_H188. zenon_intro zenon_H19c. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H19c). zenon_intro zenon_H18c. zenon_intro zenon_H16b. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.03/10.20 apply (zenon_L208_); trivial. % 10.03/10.20 (* end of lemma zenon_L211_ *) % 10.03/10.20 assert (zenon_L212_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e3) (e3)) = (e0)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H19d zenon_H5a zenon_Ha7. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_Hf7. zenon_intro zenon_H19e. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H171. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.20 apply (zenon_L98_); trivial. % 10.03/10.20 (* end of lemma zenon_L212_ *) % 10.03/10.20 assert (zenon_L213_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1c0 zenon_H5d. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1c0). zenon_intro zenon_H2e. zenon_intro zenon_H1c1. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1c1). zenon_intro zenon_H2e. zenon_intro zenon_H16b. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.03/10.20 apply (zenon_L208_); trivial. % 10.03/10.20 (* end of lemma zenon_L213_ *) % 10.03/10.20 assert (zenon_L214_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e3) (e3)) = (e0)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1c2 zenon_H5a zenon_Ha7. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H128. zenon_intro zenon_H1c3. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1c3). zenon_intro zenon_H166. zenon_intro zenon_H171. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.20 apply (zenon_L98_); trivial. % 10.03/10.20 (* end of lemma zenon_L214_ *) % 10.03/10.20 assert (zenon_L215_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1f5 zenon_H1d5 zenon_H1ed. % 10.03/10.20 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H1f5. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H1d5. % 10.03/10.20 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 10.03/10.20 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H76. apply refl_equal. % 10.03/10.20 apply zenon_H1ee. apply sym_equal. exact zenon_H1ed. % 10.03/10.20 (* end of lemma zenon_L215_ *) % 10.03/10.20 assert (zenon_L216_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1f6 zenon_H1ea zenon_Ha7 zenon_H1d5 zenon_H1f5 zenon_H5d zenon_H14b zenon_H79. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.03/10.20 apply (zenon_L171_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.03/10.20 apply (zenon_L215_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.03/10.20 apply (zenon_L208_); trivial. % 10.03/10.20 apply (zenon_L95_); trivial. % 10.03/10.20 (* end of lemma zenon_L216_ *) % 10.03/10.20 assert (zenon_L217_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1d4 zenon_H24 zenon_H91. % 10.03/10.20 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H1d4. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_H24. % 10.03/10.20 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 10.03/10.20 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H67. apply refl_equal. % 10.03/10.20 apply zenon_H18f. apply sym_equal. exact zenon_H91. % 10.03/10.20 (* end of lemma zenon_L217_ *) % 10.03/10.20 assert (zenon_L218_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e3) (e3)) = (e0)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1db zenon_H16c zenon_H79 zenon_H14b zenon_H5d zenon_H1f5 zenon_H1ea zenon_H1f6 zenon_H24 zenon_H1d4 zenon_H5a zenon_Ha7. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1db); [ zenon_intro zenon_H90 | zenon_intro zenon_H1df ]. % 10.03/10.20 apply (zenon_L108_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H1e0 ]. % 10.03/10.20 apply (zenon_L216_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H91 | zenon_intro zenon_H72 ]. % 10.03/10.20 apply (zenon_L217_); trivial. % 10.03/10.20 apply (zenon_L98_); trivial. % 10.03/10.20 (* end of lemma zenon_L218_ *) % 10.03/10.20 assert (zenon_L219_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1ec zenon_Hd7 zenon_H166. % 10.03/10.20 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 10.03/10.20 intro zenon_D_pnotp. % 10.03/10.20 apply zenon_H1ec. % 10.03/10.20 rewrite <- zenon_D_pnotp. % 10.03/10.20 exact zenon_Hd7. % 10.03/10.20 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 10.03/10.20 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 10.03/10.20 congruence. % 10.03/10.20 apply zenon_H1ef. apply refl_equal. % 10.03/10.20 apply zenon_H167. apply sym_equal. exact zenon_H166. % 10.03/10.20 (* end of lemma zenon_L219_ *) % 10.03/10.20 assert (zenon_L220_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((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) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1dc zenon_H22a zenon_H96 zenon_H192 zenon_H1ec zenon_H2a zenon_H157 zenon_H13d zenon_H13a zenon_H12f zenon_H156 zenon_H155 zenon_H83 zenon_H93 zenon_H14b zenon_H7a zenon_H141 zenon_H14c zenon_Heb zenon_He8 zenon_H5f zenon_H130 zenon_Hef zenon_H113 zenon_H110 zenon_H118 zenon_H127 zenon_Ha9 zenon_H12c zenon_H101 zenon_Hfe zenon_H10d zenon_H154 zenon_H5d zenon_H1db zenon_H79 zenon_H1f5 zenon_H1ea zenon_H1f6 zenon_H1d4 zenon_H5a zenon_H1e zenon_H1ce zenon_Hb8 zenon_H12a zenon_H2f zenon_H30 zenon_Hd1 zenon_H26 zenon_H11f zenon_H1cb zenon_H109 zenon_H105 zenon_H2c zenon_H1c9 zenon_H1f zenon_H124 zenon_H23 zenon_Hf1 zenon_H25 zenon_H1d1 zenon_Ha7 zenon_H16c. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H20 | zenon_intro zenon_H1dd ]. % 10.03/10.20 apply (zenon_L2_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.03/10.20 apply (zenon_L30_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.03/10.20 apply (zenon_L103_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.03/10.20 apply (zenon_L159_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.03/10.20 apply (zenon_L218_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.03/10.20 apply (zenon_L163_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.03/10.20 apply (zenon_L126_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.03/10.20 apply (zenon_L66_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.03/10.20 apply (zenon_L132_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.03/10.20 apply (zenon_L157_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.03/10.20 apply (zenon_L124_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.03/10.20 apply (zenon_L219_); trivial. % 10.03/10.20 apply (zenon_L125_); trivial. % 10.03/10.20 apply (zenon_L77_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.03/10.20 apply (zenon_L101_); trivial. % 10.03/10.20 apply (zenon_L208_); trivial. % 10.03/10.20 apply (zenon_L156_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H9e | zenon_intro zenon_H90 ]. % 10.03/10.20 apply (zenon_L164_); trivial. % 10.03/10.20 apply (zenon_L108_); trivial. % 10.03/10.20 (* end of lemma zenon_L220_ *) % 10.03/10.20 assert (zenon_L221_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e3) (e3)) = (e0)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1e6 zenon_H5a zenon_Ha7. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H72. zenon_intro zenon_H1e7. % 10.03/10.20 apply (zenon_L98_); trivial. % 10.03/10.20 (* end of lemma zenon_L221_ *) % 10.03/10.20 assert (zenon_L222_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e3) (e3)) = (e0)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1e8 zenon_H5a zenon_Ha7. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1e8). zenon_intro zenon_H72. zenon_intro zenon_H1e9. % 10.03/10.20 apply (zenon_L98_); trivial. % 10.03/10.20 (* end of lemma zenon_L222_ *) % 10.03/10.20 assert (zenon_L223_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e3) (e3)) = (e0)) -> False). % 10.03/10.20 do 0 intro. intros zenon_H1f9 zenon_H5a zenon_Ha7. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1f9). zenon_intro zenon_H72. zenon_intro zenon_H1fa. % 10.03/10.20 apply (zenon_L98_); trivial. % 10.03/10.20 (* end of lemma zenon_L223_ *) % 10.03/10.20 assert (zenon_L224_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (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) (e1)) = (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 (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.03/10.20 do 0 intro. intros zenon_H22d zenon_H1d9 zenon_H1d7 zenon_H64 zenon_H1f2 zenon_H74 zenon_H22e zenon_H1b9 zenon_H22f zenon_Ha1 zenon_H9c zenon_Hae zenon_Hbe zenon_H187 zenon_H16c zenon_H1d1 zenon_H1c9 zenon_H1cb zenon_H1ce zenon_H1d4 zenon_H1f6 zenon_H1ea zenon_H1f5 zenon_H1db zenon_H1ec zenon_H22a zenon_H1dc zenon_H96 zenon_H192 zenon_H7e zenon_H2a zenon_H30 zenon_H157 zenon_Hb8 zenon_H13d zenon_H13a zenon_Hd1 zenon_H12f zenon_H156 zenon_H155 zenon_H83 zenon_H11f zenon_H93 zenon_H14b zenon_H7a zenon_H141 zenon_H14c zenon_Heb zenon_He8 zenon_H1f zenon_H2c zenon_H5f zenon_H130 zenon_Hef zenon_Hf1 zenon_H113 zenon_H110 zenon_H118 zenon_H124 zenon_H25 zenon_H12a zenon_H127 zenon_Ha9 zenon_H12c zenon_H105 zenon_H101 zenon_Hfe zenon_H10d zenon_H1e zenon_H154 zenon_Ha7 zenon_H23. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H24 | zenon_intro zenon_H230 ]. % 10.03/10.20 apply (zenon_L30_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H26 | zenon_intro zenon_H231 ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.03/10.20 apply (zenon_L32_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.03/10.20 apply (zenon_L38_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_Hd8. zenon_intro zenon_H15b. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_H15c. zenon_intro zenon_He1. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.20 apply (zenon_L39_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.20 apply (zenon_L45_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.20 apply (zenon_L46_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.20 apply (zenon_L48_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.20 apply (zenon_L50_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.20 apply (zenon_L51_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.20 apply (zenon_L52_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.20 apply (zenon_L53_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.20 apply (zenon_L55_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.20 apply (zenon_L57_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.20 apply (zenon_L102_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.20 apply (zenon_L107_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.20 apply (zenon_L109_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.20 apply (zenon_L110_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.20 apply (zenon_L111_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.20 apply (zenon_L112_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.20 apply (zenon_L113_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.20 apply (zenon_L114_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.20 apply (zenon_L115_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.20 apply (zenon_L116_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.20 apply (zenon_L117_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.20 apply (zenon_L118_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.20 apply (zenon_L121_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.20 apply (zenon_L122_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.20 apply (zenon_L127_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.20 apply (zenon_L128_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.20 apply (zenon_L129_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.20 apply (zenon_L130_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.20 apply (zenon_L131_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.20 apply (zenon_L133_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.20 apply (zenon_L134_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.20 apply (zenon_L135_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.20 apply (zenon_L136_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.20 apply (zenon_L137_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.20 apply (zenon_L138_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.20 apply (zenon_L139_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.20 apply (zenon_L140_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.20 apply (zenon_L141_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.20 apply (zenon_L142_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.20 apply (zenon_L143_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.20 apply (zenon_L144_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.20 apply (zenon_L146_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.20 apply (zenon_L147_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.20 apply (zenon_L149_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.20 apply (zenon_L150_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H21c). zenon_intro zenon_H128. zenon_intro zenon_H21d. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H166. zenon_intro zenon_H174. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.03/10.20 apply (zenon_L165_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.20 apply (zenon_L167_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.20 apply (zenon_L168_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.20 apply (zenon_L169_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.20 apply (zenon_L170_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.20 apply (zenon_L179_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.20 apply (zenon_L180_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.20 apply (zenon_L181_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.20 apply (zenon_L182_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H79. zenon_intro zenon_H224. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H109. zenon_intro zenon_Hc8. % 10.03/10.20 apply (zenon_L165_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.20 apply (zenon_L183_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.20 apply (zenon_L184_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.20 apply (zenon_L185_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.20 apply (zenon_L186_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.20 apply (zenon_L187_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.20 apply (zenon_L188_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.20 apply (zenon_L189_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.20 apply (zenon_L190_); trivial. % 10.03/10.20 apply (zenon_L191_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H3c. zenon_intro zenon_H44. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H160. zenon_intro zenon_Hf6. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.20 apply (zenon_L39_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.20 apply (zenon_L45_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.20 apply (zenon_L46_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.20 apply (zenon_L48_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.20 apply (zenon_L50_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.20 apply (zenon_L51_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.20 apply (zenon_L52_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.20 apply (zenon_L53_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.20 apply (zenon_L55_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.20 apply (zenon_L57_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.20 apply (zenon_L102_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.20 apply (zenon_L107_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.20 apply (zenon_L109_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.20 apply (zenon_L110_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.20 apply (zenon_L111_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.20 apply (zenon_L112_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.20 apply (zenon_L113_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.20 apply (zenon_L114_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.20 apply (zenon_L115_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.20 apply (zenon_L116_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.20 apply (zenon_L117_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.20 apply (zenon_L118_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.20 apply (zenon_L121_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.20 apply (zenon_L122_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.20 apply (zenon_L127_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.20 apply (zenon_L128_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.20 apply (zenon_L129_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.20 apply (zenon_L130_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_Hf7. zenon_intro zenon_H19e. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H171. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.03/10.20 apply (zenon_L2_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H20 | zenon_intro zenon_H1dd ]. % 10.03/10.20 apply (zenon_L2_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 10.03/10.20 apply (zenon_L88_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H9e | zenon_intro zenon_H90 ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.03/10.20 apply (zenon_L30_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.03/10.20 apply (zenon_L29_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.03/10.20 apply (zenon_L152_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.03/10.20 apply (zenon_L163_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.03/10.20 apply (zenon_L54_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.20 apply (zenon_L23_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.20 apply (zenon_L67_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.20 apply (zenon_L174_); trivial. % 10.03/10.20 apply (zenon_L158_); trivial. % 10.03/10.20 apply (zenon_L177_); trivial. % 10.03/10.20 apply (zenon_L108_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.03/10.20 apply (zenon_L192_); trivial. % 10.03/10.20 apply (zenon_L47_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.20 apply (zenon_L133_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.20 apply (zenon_L134_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.20 apply (zenon_L135_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.20 apply (zenon_L136_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.20 apply (zenon_L137_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.20 apply (zenon_L138_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.20 apply (zenon_L139_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.20 apply (zenon_L140_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.20 apply (zenon_L141_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.20 apply (zenon_L142_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.20 apply (zenon_L143_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.20 apply (zenon_L144_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.20 apply (zenon_L193_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.20 apply (zenon_L147_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.20 apply (zenon_L149_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H128. zenon_intro zenon_H1c3. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1c3). zenon_intro zenon_H166. zenon_intro zenon_H171. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.03/10.20 apply (zenon_L2_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.03/10.20 apply (zenon_L30_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.03/10.20 apply (zenon_L29_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.03/10.20 apply (zenon_L104_); trivial. % 10.03/10.20 apply (zenon_L105_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.03/10.20 apply (zenon_L192_); trivial. % 10.03/10.20 apply (zenon_L47_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H21c). zenon_intro zenon_H128. zenon_intro zenon_H21d. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H166. zenon_intro zenon_H174. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.03/10.20 apply (zenon_L194_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.20 apply (zenon_L167_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.20 apply (zenon_L168_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.20 apply (zenon_L169_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.20 apply (zenon_L195_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.20 apply (zenon_L179_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.20 apply (zenon_L180_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.20 apply (zenon_L181_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.20 apply (zenon_L182_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H79. zenon_intro zenon_H224. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H109. zenon_intro zenon_Hc8. % 10.03/10.20 apply (zenon_L194_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.20 apply (zenon_L183_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.20 apply (zenon_L184_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.20 apply (zenon_L196_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.20 apply (zenon_L186_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.20 apply (zenon_L187_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.20 apply (zenon_L188_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.20 apply (zenon_L189_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.20 apply (zenon_L190_); trivial. % 10.03/10.20 apply (zenon_L191_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.20 apply (zenon_L39_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.20 apply (zenon_L45_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.20 apply (zenon_L46_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.20 apply (zenon_L48_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.20 apply (zenon_L50_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.20 apply (zenon_L51_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.20 apply (zenon_L52_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.20 apply (zenon_L53_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.20 apply (zenon_L55_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.20 apply (zenon_L57_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.20 apply (zenon_L102_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.20 apply (zenon_L198_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.20 apply (zenon_L109_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.20 apply (zenon_L110_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.20 apply (zenon_L111_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.20 apply (zenon_L112_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.20 apply (zenon_L113_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.20 apply (zenon_L114_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.20 apply (zenon_L115_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.20 apply (zenon_L116_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.20 apply (zenon_L117_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.20 apply (zenon_L118_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.20 apply (zenon_L121_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.20 apply (zenon_L122_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.20 apply (zenon_L127_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.20 apply (zenon_L128_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.20 apply (zenon_L129_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.20 apply (zenon_L200_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_Hf7. zenon_intro zenon_H19e. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H171. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.03/10.20 apply (zenon_L30_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.03/10.20 apply (zenon_L103_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.03/10.20 apply (zenon_L126_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.03/10.20 apply (zenon_L56_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.03/10.20 apply (zenon_L85_); trivial. % 10.03/10.20 apply (zenon_L199_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.03/10.20 apply (zenon_L43_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.03/10.20 apply (zenon_L69_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.03/10.20 apply (zenon_L105_); trivial. % 10.03/10.20 apply (zenon_L84_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.20 apply (zenon_L133_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.20 apply (zenon_L134_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.20 apply (zenon_L135_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.20 apply (zenon_L136_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.20 apply (zenon_L137_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.20 apply (zenon_L138_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.20 apply (zenon_L139_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.20 apply (zenon_L140_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.20 apply (zenon_L141_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.20 apply (zenon_L142_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.20 apply (zenon_L143_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.20 apply (zenon_L144_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.20 apply (zenon_L146_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.20 apply (zenon_L147_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.20 apply (zenon_L201_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.20 apply (zenon_L202_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.20 apply (zenon_L203_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.20 apply (zenon_L167_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.20 apply (zenon_L168_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.20 apply (zenon_L169_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.20 apply (zenon_L170_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.20 apply (zenon_L204_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.20 apply (zenon_L180_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.20 apply (zenon_L181_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.20 apply (zenon_L182_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.20 apply (zenon_L206_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.20 apply (zenon_L183_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.20 apply (zenon_L184_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.20 apply (zenon_L185_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.20 apply (zenon_L186_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.20 apply (zenon_L187_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.20 apply (zenon_L188_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.20 apply (zenon_L189_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.20 apply (zenon_L190_); trivial. % 10.03/10.20 apply (zenon_L191_); trivial. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H51. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.20 apply (zenon_L39_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.20 apply (zenon_L45_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.20 apply (zenon_L46_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.20 apply (zenon_L48_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.20 apply (zenon_L50_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.20 apply (zenon_L51_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.20 apply (zenon_L52_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.20 apply (zenon_L207_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.20 apply (zenon_L55_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.20 apply (zenon_L57_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.20 apply (zenon_L102_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.20 apply (zenon_L209_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.20 apply (zenon_L210_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.20 apply (zenon_L110_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.20 apply (zenon_L111_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.20 apply (zenon_L112_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.20 apply (zenon_L113_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.20 apply (zenon_L114_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.20 apply (zenon_L115_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.20 apply (zenon_L116_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.20 apply (zenon_L117_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.20 apply (zenon_L118_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.20 apply (zenon_L121_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.20 apply (zenon_L122_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.20 apply (zenon_L127_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.20 apply (zenon_L128_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.20 apply (zenon_L129_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.20 apply (zenon_L211_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.20 apply (zenon_L212_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.20 apply (zenon_L133_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.20 apply (zenon_L134_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.20 apply (zenon_L135_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.20 apply (zenon_L136_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.20 apply (zenon_L137_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.20 apply (zenon_L138_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.20 apply (zenon_L139_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.20 apply (zenon_L140_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.20 apply (zenon_L141_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.20 apply (zenon_L142_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.20 apply (zenon_L143_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.20 apply (zenon_L144_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.20 apply (zenon_L193_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.20 apply (zenon_L147_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.20 apply (zenon_L213_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.20 apply (zenon_L214_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H21c). zenon_intro zenon_H128. zenon_intro zenon_H21d. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H166. zenon_intro zenon_H174. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.03/10.20 apply (zenon_L220_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.20 apply (zenon_L167_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.20 apply (zenon_L168_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.20 apply (zenon_L221_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.20 apply (zenon_L222_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.20 apply (zenon_L223_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.20 apply (zenon_L180_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H79. zenon_intro zenon_H1fe. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H109. zenon_intro zenon_Hc2. % 10.03/10.20 apply (zenon_L220_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.20 apply (zenon_L182_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H79. zenon_intro zenon_H224. % 10.03/10.20 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H109. zenon_intro zenon_Hc8. % 10.03/10.20 apply (zenon_L220_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.20 apply (zenon_L183_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.20 apply (zenon_L184_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.20 apply (zenon_L196_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.20 apply (zenon_L186_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.20 apply (zenon_L187_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.20 apply (zenon_L188_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.20 apply (zenon_L189_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.20 apply (zenon_L190_); trivial. % 10.03/10.20 apply (zenon_L191_); trivial. % 10.03/10.20 apply (zenon_L75_); trivial. % 10.03/10.20 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H2e | zenon_intro zenon_H82 ]. % 10.03/10.20 apply (zenon_L101_); trivial. % 10.03/10.20 apply (zenon_L125_); trivial. % 10.03/10.20 (* end of lemma zenon_L224_ *) % 10.03/10.20 assert (zenon_L225_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (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) (e1)) = (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 (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H272 zenon_H91 zenon_H8d zenon_H97 zenon_H22d zenon_H1d9 zenon_H1d7 zenon_H64 zenon_H1f2 zenon_H74 zenon_H22e zenon_H1b9 zenon_H22f zenon_Ha1 zenon_H9c zenon_Hae zenon_Hbe zenon_H187 zenon_H16c zenon_H1d1 zenon_H1c9 zenon_H1cb zenon_H1ce zenon_H1d4 zenon_H1f6 zenon_H1ea zenon_H1f5 zenon_H1db zenon_H1ec zenon_H22a zenon_H1dc zenon_H96 zenon_H192 zenon_H7e zenon_H2a zenon_H30 zenon_H157 zenon_Hb8 zenon_H13d zenon_H13a zenon_Hd1 zenon_H12f zenon_H156 zenon_H155 zenon_H83 zenon_H11f zenon_H93 zenon_H14b zenon_H7a zenon_H141 zenon_H14c zenon_Heb zenon_He8 zenon_H1f zenon_H2c zenon_H5f zenon_H130 zenon_Hef zenon_Hf1 zenon_H113 zenon_H110 zenon_H118 zenon_H124 zenon_H25 zenon_H12a zenon_H127 zenon_Ha9 zenon_H12c zenon_H105 zenon_H101 zenon_Hfe zenon_H10d zenon_H1e zenon_H154 zenon_H23. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.03/10.21 apply (zenon_L35_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.03/10.21 apply (zenon_L36_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.03/10.21 apply (zenon_L37_); trivial. % 10.03/10.21 apply (zenon_L224_); trivial. % 10.03/10.21 (* end of lemma zenon_L225_ *) % 10.03/10.21 assert (zenon_L226_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H7e zenon_H2e zenon_H166. % 10.03/10.21 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H7e. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H2e. % 10.03/10.21 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 10.03/10.21 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_H81. apply refl_equal. % 10.03/10.21 apply zenon_H167. apply sym_equal. exact zenon_H166. % 10.03/10.21 (* end of lemma zenon_L226_ *) % 10.03/10.21 assert (zenon_L227_ : (~((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))) -> ((op (e1) (e1)) = (e0)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H275 zenon_H8d. % 10.03/10.21 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.21 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 10.03/10.21 congruence. % 10.03/10.21 exact (zenon_H8e zenon_H8d). % 10.03/10.21 apply zenon_H1d. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L227_ *) % 10.03/10.21 assert (zenon_L228_ : ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((e3) = (op (op (e1) (e1)) (e1)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H70 zenon_H8d zenon_H276. % 10.03/10.21 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H277 | zenon_intro zenon_H278 ]. % 10.03/10.21 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e3) = (op (op (e1) (e1)) (e1)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H276. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H277. % 10.03/10.21 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 10.03/10.21 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e0) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H279. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H70. % 10.03/10.21 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.21 cut (((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 10.03/10.21 congruence. % 10.03/10.21 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H277 | zenon_intro zenon_H278 ]. % 10.03/10.21 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H27a. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H277. % 10.03/10.21 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 10.03/10.21 cut (((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H275]. % 10.03/10.21 congruence. % 10.03/10.21 apply (zenon_L227_); trivial. % 10.03/10.21 apply zenon_H278. apply refl_equal. % 10.03/10.21 apply zenon_H278. apply refl_equal. % 10.03/10.21 apply zenon_H29. apply refl_equal. % 10.03/10.21 apply zenon_H278. apply refl_equal. % 10.03/10.21 apply zenon_H278. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L228_ *) % 10.03/10.21 assert (zenon_L229_ : ((op (e3) (e3)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H52 zenon_He2 zenon_Hb8. % 10.03/10.21 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_Hb8. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Haa. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_Hb9. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H52. % 10.03/10.21 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 apply zenon_H10c. apply sym_equal. exact zenon_He2. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L229_ *) % 10.03/10.21 assert (zenon_L230_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_He8 zenon_H1f zenon_H2c zenon_H8d zenon_Hf4 zenon_H2a zenon_H97 zenon_H52 zenon_Hb8. % 10.03/10.21 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.03/10.21 apply (zenon_L32_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.03/10.21 apply (zenon_notand_s _ _ ax19); [ zenon_intro zenon_H27c | zenon_intro zenon_H27b ]. % 10.03/10.21 elim (classic ((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))); [ zenon_intro zenon_H27d | zenon_intro zenon_H27e ]. % 10.03/10.21 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1)))) = ((e2) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H27c. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H27d. % 10.03/10.21 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H27e]. % 10.03/10.21 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H27f]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e0) (e3)) = (e2)) = ((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (e2))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H27f. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Hf4. % 10.03/10.21 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.21 cut (((op (e0) (e3)) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H280]. % 10.03/10.21 congruence. % 10.03/10.21 elim (classic ((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))); [ zenon_intro zenon_H27d | zenon_intro zenon_H27e ]. % 10.03/10.21 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1)))) = ((op (e0) (e3)) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H280. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H27d. % 10.03/10.21 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H27e]. % 10.03/10.21 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H281]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 10.03/10.21 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 10.03/10.21 congruence. % 10.03/10.21 exact (zenon_H8e zenon_H8d). % 10.03/10.21 cut (((op (e0) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H279. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H70. % 10.03/10.21 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.21 cut (((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 10.03/10.21 congruence. % 10.03/10.21 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H277 | zenon_intro zenon_H278 ]. % 10.03/10.21 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H27a. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H277. % 10.03/10.21 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 10.03/10.21 cut (((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H275]. % 10.03/10.21 congruence. % 10.03/10.21 apply (zenon_L227_); trivial. % 10.03/10.21 apply zenon_H278. apply refl_equal. % 10.03/10.21 apply zenon_H278. apply refl_equal. % 10.03/10.21 apply zenon_H29. apply refl_equal. % 10.03/10.21 apply zenon_H27e. apply refl_equal. % 10.03/10.21 apply zenon_H27e. apply refl_equal. % 10.03/10.21 apply zenon_H22. apply refl_equal. % 10.03/10.21 apply zenon_H27e. apply refl_equal. % 10.03/10.21 apply zenon_H27e. apply refl_equal. % 10.03/10.21 apply (zenon_notand_s _ _ zenon_H27b); [ zenon_intro zenon_H282 | zenon_intro zenon_H276 ]. % 10.03/10.21 apply zenon_H282. apply sym_equal. exact zenon_H8d. % 10.03/10.21 apply (zenon_L228_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.03/10.21 apply (zenon_L60_); trivial. % 10.03/10.21 apply (zenon_L229_); trivial. % 10.03/10.21 (* end of lemma zenon_L230_ *) % 10.03/10.21 assert (zenon_L231_ : (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H1e zenon_H27 zenon_H8d. % 10.03/10.21 cut (((op (e1) (e1)) = (e1)) = ((e0) = (e1))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H1e. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H27. % 10.03/10.21 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.21 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 10.03/10.21 congruence. % 10.03/10.21 exact (zenon_H8e zenon_H8d). % 10.03/10.21 apply zenon_H1d. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L231_ *) % 10.03/10.21 assert (zenon_L232_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H12a zenon_Hb7 zenon_Ha8. % 10.03/10.21 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H12a. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Hb7. % 10.03/10.21 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 10.03/10.21 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_H108. apply refl_equal. % 10.03/10.21 apply zenon_Had. apply sym_equal. exact zenon_Ha8. % 10.03/10.21 (* end of lemma zenon_L232_ *) % 10.03/10.21 assert (zenon_L233_ : ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H52 zenon_H112 zenon_Ha9. % 10.03/10.21 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_Ha9. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Haa. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_Hac. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H52. % 10.03/10.21 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H283]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 apply zenon_H283. apply sym_equal. exact zenon_H112. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L233_ *) % 10.03/10.21 assert (zenon_L234_ : (((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 (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H12c zenon_Hb7 zenon_H12a zenon_Hf7 zenon_H101 zenon_H2e zenon_H127 zenon_H52 zenon_Ha9. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.03/10.21 apply (zenon_L232_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.03/10.21 apply (zenon_L69_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.03/10.21 apply (zenon_L83_); trivial. % 10.03/10.21 apply (zenon_L233_); trivial. % 10.03/10.21 (* end of lemma zenon_L234_ *) % 10.03/10.21 assert (zenon_L235_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H105 zenon_Hb7 zenon_Hfd. % 10.03/10.21 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H105. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Hb7. % 10.03/10.21 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 10.03/10.21 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_H108. apply refl_equal. % 10.03/10.21 apply zenon_H100. apply sym_equal. exact zenon_Hfd. % 10.03/10.21 (* end of lemma zenon_L235_ *) % 10.03/10.21 assert (zenon_L236_ : ((op (e3) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H52 zenon_H109 zenon_Hfe. % 10.03/10.21 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_Hfe. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Haa. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_Hff. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H52. % 10.03/10.21 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 apply zenon_H111. apply sym_equal. exact zenon_H109. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L236_ *) % 10.03/10.21 assert (zenon_L237_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H10d zenon_Hb7 zenon_H102 zenon_H101 zenon_Hf4 zenon_H105 zenon_H52 zenon_Hfe. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hfd | zenon_intro zenon_H10e ]. % 10.03/10.21 apply (zenon_L235_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H10f ]. % 10.03/10.21 apply (zenon_L69_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H106 | zenon_intro zenon_H109 ]. % 10.03/10.21 apply (zenon_L70_); trivial. % 10.03/10.21 apply (zenon_L236_); trivial. % 10.03/10.21 (* end of lemma zenon_L237_ *) % 10.03/10.21 assert (zenon_L238_ : (~((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e1)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H284 zenon_H1f. % 10.03/10.21 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.03/10.21 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 10.03/10.21 congruence. % 10.03/10.21 exact (zenon_H8c zenon_H1f). % 10.03/10.21 apply zenon_H34. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L238_ *) % 10.03/10.21 assert (zenon_L239_ : ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (~((e3) = (op (op (e0) (e0)) (e0)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H73 zenon_H1f zenon_H285. % 10.03/10.21 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H286 | zenon_intro zenon_H287 ]. % 10.03/10.21 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e3) = (op (op (e0) (e0)) (e0)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H285. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H286. % 10.03/10.21 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 10.03/10.21 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H288]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e1) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H288. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H73. % 10.03/10.21 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.21 cut (((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H289]. % 10.03/10.21 congruence. % 10.03/10.21 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H286 | zenon_intro zenon_H287 ]. % 10.03/10.21 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H289. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H286. % 10.03/10.21 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 10.03/10.21 cut (((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H284]. % 10.03/10.21 congruence. % 10.03/10.21 apply (zenon_L238_); trivial. % 10.03/10.21 apply zenon_H287. apply refl_equal. % 10.03/10.21 apply zenon_H287. apply refl_equal. % 10.03/10.21 apply zenon_H29. apply refl_equal. % 10.03/10.21 apply zenon_H287. apply refl_equal. % 10.03/10.21 apply zenon_H287. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L239_ *) % 10.03/10.21 assert (zenon_L240_ : ((op (e1) (e3)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H106 zenon_H73 zenon_H1f. % 10.03/10.21 apply (zenon_notand_s _ _ ax21); [ zenon_intro zenon_H28b | zenon_intro zenon_H28a ]. % 10.03/10.21 elim (classic ((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))); [ zenon_intro zenon_H28c | zenon_intro zenon_H28d ]. % 10.03/10.21 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0)))) = ((e2) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H28b. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H28c. % 10.03/10.21 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 10.03/10.21 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H28e]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e1) (e3)) = (e2)) = ((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (e2))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H28e. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H106. % 10.03/10.21 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.21 cut (((op (e1) (e3)) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H28f]. % 10.03/10.21 congruence. % 10.03/10.21 elim (classic ((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))); [ zenon_intro zenon_H28c | zenon_intro zenon_H28d ]. % 10.03/10.21 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0)))) = ((op (e1) (e3)) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H28f. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H28c. % 10.03/10.21 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 10.03/10.21 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H290]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H288]. % 10.03/10.21 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 10.03/10.21 congruence. % 10.03/10.21 exact (zenon_H8c zenon_H1f). % 10.03/10.21 cut (((op (e1) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H288. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H73. % 10.03/10.21 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.21 cut (((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H289]. % 10.03/10.21 congruence. % 10.03/10.21 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H286 | zenon_intro zenon_H287 ]. % 10.03/10.21 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H289. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H286. % 10.03/10.21 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 10.03/10.21 cut (((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H284]. % 10.03/10.21 congruence. % 10.03/10.21 apply (zenon_L238_); trivial. % 10.03/10.21 apply zenon_H287. apply refl_equal. % 10.03/10.21 apply zenon_H287. apply refl_equal. % 10.03/10.21 apply zenon_H29. apply refl_equal. % 10.03/10.21 apply zenon_H28d. apply refl_equal. % 10.03/10.21 apply zenon_H28d. apply refl_equal. % 10.03/10.21 apply zenon_H22. apply refl_equal. % 10.03/10.21 apply zenon_H28d. apply refl_equal. % 10.03/10.21 apply zenon_H28d. apply refl_equal. % 10.03/10.21 apply (zenon_notand_s _ _ zenon_H28a); [ zenon_intro zenon_H291 | zenon_intro zenon_H285 ]. % 10.03/10.21 apply zenon_H291. apply sym_equal. exact zenon_H1f. % 10.03/10.21 apply (zenon_L239_); trivial. % 10.03/10.21 (* end of lemma zenon_L240_ *) % 10.03/10.21 assert (zenon_L241_ : ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H128 zenon_H106 zenon_H101. % 10.03/10.21 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ]. % 10.03/10.21 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e1) (e3)) = (op (e2) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H101. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H114. % 10.03/10.21 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 10.03/10.21 cut (((op (e2) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e1) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H123. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H128. % 10.03/10.21 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 10.03/10.21 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_H115. apply refl_equal. % 10.03/10.21 apply zenon_H107. apply sym_equal. exact zenon_H106. % 10.03/10.21 apply zenon_H115. apply refl_equal. % 10.03/10.21 apply zenon_H115. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L241_ *) % 10.03/10.21 assert (zenon_L242_ : (((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) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H10d zenon_Hb7 zenon_H105 zenon_H102 zenon_H101 zenon_H128 zenon_H52 zenon_Hfe. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hfd | zenon_intro zenon_H10e ]. % 10.03/10.21 apply (zenon_L235_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H10f ]. % 10.03/10.21 apply (zenon_L69_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H106 | zenon_intro zenon_H109 ]. % 10.03/10.21 apply (zenon_L241_); trivial. % 10.03/10.21 apply (zenon_L236_); trivial. % 10.03/10.21 (* end of lemma zenon_L242_ *) % 10.03/10.21 assert (zenon_L243_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e1)) -> False). % 10.03/10.21 do 0 intro. intros zenon_Hb1 zenon_H1e zenon_H1f. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_H20. zenon_intro zenon_Hb2. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hb2). zenon_intro zenon_H20. zenon_intro zenon_Hb3. % 10.03/10.21 apply (zenon_L2_); trivial. % 10.03/10.21 (* end of lemma zenon_L243_ *) % 10.03/10.21 assert (zenon_L244_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e1)) -> False). % 10.03/10.21 do 0 intro. intros zenon_Hbb zenon_H1e zenon_H1f. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hbb). zenon_intro zenon_H20. zenon_intro zenon_Hbc. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_H20. zenon_intro zenon_Hbd. % 10.03/10.21 apply (zenon_L2_); trivial. % 10.03/10.21 (* end of lemma zenon_L244_ *) % 10.03/10.21 assert (zenon_L245_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H89 zenon_H5e zenon_H1e. % 10.03/10.21 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H11c | zenon_intro zenon_H1d ]. % 10.03/10.21 cut (((e1) = (e1)) = ((e0) = (e1))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H1e. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H11c. % 10.03/10.21 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.21 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e0) (e1)) = (e0)) = ((e1) = (e0))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H11d. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H89. % 10.03/10.21 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.03/10.21 cut (((op (e0) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H292]. % 10.03/10.21 congruence. % 10.03/10.21 exact (zenon_H292 zenon_H5e). % 10.03/10.21 apply zenon_H34. apply refl_equal. % 10.03/10.21 apply zenon_H1d. apply refl_equal. % 10.03/10.21 apply zenon_H1d. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L245_ *) % 10.03/10.21 assert (zenon_L246_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((e0) = (e1))) -> False). % 10.03/10.21 do 0 intro. intros zenon_Hc0 zenon_H1e. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_H89. zenon_intro zenon_Hc1. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H9d. zenon_intro zenon_Hc2. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.03/10.21 apply (zenon_L245_); trivial. % 10.03/10.21 (* end of lemma zenon_L246_ *) % 10.03/10.21 assert (zenon_L247_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> False). % 10.03/10.21 do 0 intro. intros zenon_Hc3 zenon_H1e zenon_H8d. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_H89. zenon_intro zenon_Hc4. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_H9d. zenon_intro zenon_Hc5. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 10.03/10.21 apply (zenon_L231_); trivial. % 10.03/10.21 (* end of lemma zenon_L247_ *) % 10.03/10.21 assert (zenon_L248_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e0) (op (e0) (e1))) = (e1))) -> ((op (e0) (e0)) = (e1)) -> False). % 10.03/10.21 do 0 intro. intros zenon_Hc6 zenon_Hd8 zenon_H1f. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_H89. zenon_intro zenon_Hc7. % 10.03/10.21 apply (zenon_L58_); trivial. % 10.03/10.21 (* end of lemma zenon_L248_ *) % 10.03/10.21 assert (zenon_L249_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e0) (op (e0) (e1))) = (e1))) -> ((op (e0) (e0)) = (e1)) -> False). % 10.03/10.21 do 0 intro. intros zenon_Hc9 zenon_Hd8 zenon_H1f. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H89. zenon_intro zenon_Hca. % 10.03/10.21 apply (zenon_L58_); trivial. % 10.03/10.21 (* end of lemma zenon_L249_ *) % 10.03/10.21 assert (zenon_L250_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H188 zenon_Hd7 zenon_H25. % 10.03/10.21 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H6a | zenon_intro zenon_H22 ]. % 10.03/10.21 cut (((e2) = (e2)) = ((e1) = (e2))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H25. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H6a. % 10.03/10.21 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.21 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e1) (e2)) = (e1)) = ((e2) = (e1))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H6b. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H188. % 10.03/10.21 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.21 cut (((op (e1) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H293]. % 10.03/10.21 congruence. % 10.03/10.21 exact (zenon_H293 zenon_Hd7). % 10.03/10.21 apply zenon_H1d. apply refl_equal. % 10.03/10.21 apply zenon_H22. apply refl_equal. % 10.03/10.21 apply zenon_H22. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L250_ *) % 10.03/10.21 assert (zenon_L251_ : ((op (e1) (e2)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.03/10.21 do 0 intro. intros zenon_Hd7 zenon_H1f0 zenon_H30. % 10.03/10.21 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 10.03/10.21 cut (((e3) = (e3)) = ((e2) = (e3))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H30. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H31. % 10.03/10.21 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.21 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e1) (e2)) = (e2)) = ((e3) = (e2))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H32. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Hd7. % 10.03/10.21 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.21 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H294]. % 10.03/10.21 congruence. % 10.03/10.21 exact (zenon_H294 zenon_H1f0). % 10.03/10.21 apply zenon_H22. apply refl_equal. % 10.03/10.21 apply zenon_H29. apply refl_equal. % 10.03/10.21 apply zenon_H29. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L251_ *) % 10.03/10.21 assert (zenon_L252_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H22e zenon_H82 zenon_H7e zenon_H2f zenon_H7a zenon_H74 zenon_H83 zenon_H5f zenon_H70 zenon_H30 zenon_Hd7 zenon_Hf7 zenon_H2c. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.21 apply (zenon_L27_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.21 apply (zenon_L59_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.21 apply (zenon_L251_); trivial. % 10.03/10.21 apply (zenon_L132_); trivial. % 10.03/10.21 (* end of lemma zenon_L252_ *) % 10.03/10.21 assert (zenon_L253_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (op (e0) (e3))) = (e3))) -> False). % 10.03/10.21 do 0 intro. intros zenon_He8 zenon_H1f zenon_H2c zenon_Hf7 zenon_Hd7 zenon_H30 zenon_H5f zenon_H83 zenon_H74 zenon_H7a zenon_H2f zenon_H7e zenon_H82 zenon_H22e zenon_H2a zenon_H97 zenon_He1. % 10.03/10.21 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.03/10.21 apply (zenon_L32_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.03/10.21 apply (zenon_L252_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.03/10.21 apply (zenon_L60_); trivial. % 10.03/10.21 apply (zenon_L61_); trivial. % 10.03/10.21 (* end of lemma zenon_L253_ *) % 10.03/10.21 assert (zenon_L254_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H163 zenon_H2f zenon_H30. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H163). zenon_intro zenon_H97. zenon_intro zenon_H164. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H164). zenon_intro zenon_H9e. zenon_intro zenon_H165. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H165). zenon_intro zenon_H2e. zenon_intro zenon_H2e. % 10.03/10.21 apply (zenon_L9_); trivial. % 10.03/10.21 (* end of lemma zenon_L254_ *) % 10.03/10.21 assert (zenon_L255_ : ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H82 zenon_H128 zenon_Ha9. % 10.03/10.21 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_Ha9. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Haa. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_Hac. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H82. % 10.03/10.21 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H129]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 apply zenon_H129. apply sym_equal. exact zenon_H128. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L255_ *) % 10.03/10.21 assert (zenon_L256_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H169 zenon_H82 zenon_Ha9. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H169). zenon_intro zenon_H97. zenon_intro zenon_H16a. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H16a). zenon_intro zenon_H9e. zenon_intro zenon_H16b. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.03/10.21 apply (zenon_L255_); trivial. % 10.03/10.21 (* end of lemma zenon_L256_ *) % 10.03/10.21 assert (zenon_L257_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H22e zenon_H74 zenon_H72 zenon_H8d zenon_H2a zenon_H1b9 zenon_H2f zenon_He2 zenon_H105. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.21 apply (zenon_L23_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.21 apply (zenon_L33_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.21 apply (zenon_L174_); trivial. % 10.03/10.21 apply (zenon_L71_); trivial. % 10.03/10.21 (* end of lemma zenon_L257_ *) % 10.03/10.21 assert (zenon_L258_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H16f zenon_H22e zenon_H74 zenon_H8d zenon_H2a zenon_H1b9 zenon_H2f zenon_H105. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hb7. zenon_intro zenon_H170. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_H90. zenon_intro zenon_H171. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.21 apply (zenon_L257_); trivial. % 10.03/10.21 (* end of lemma zenon_L258_ *) % 10.03/10.21 assert (zenon_L259_ : ((op (e2) (e2)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H2f zenon_Hde zenon_Heb. % 10.03/10.21 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hec | zenon_intro zenon_H81 ]. % 10.03/10.21 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_Heb. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Hec. % 10.03/10.21 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.21 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hed]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_Hed. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H2f. % 10.03/10.21 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 10.03/10.21 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_H81. apply refl_equal. % 10.03/10.21 apply zenon_Hf0. apply sym_equal. exact zenon_Hde. % 10.03/10.21 apply zenon_H81. apply refl_equal. % 10.03/10.21 apply zenon_H81. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L259_ *) % 10.03/10.21 assert (zenon_L260_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_He8 zenon_H1f zenon_H2c zenon_H7a zenon_H79 zenon_Heb zenon_H2f zenon_H109 zenon_H105. % 10.03/10.21 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.03/10.21 apply (zenon_L32_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.03/10.21 apply (zenon_L24_); trivial. % 10.03/10.21 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.03/10.21 apply (zenon_L259_); trivial. % 10.03/10.21 apply (zenon_L71_); trivial. % 10.03/10.21 (* end of lemma zenon_L260_ *) % 10.03/10.21 assert (zenon_L261_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H172 zenon_He8 zenon_H1f zenon_H2c zenon_H7a zenon_Heb zenon_H2f zenon_H105. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H172). zenon_intro zenon_Hb7. zenon_intro zenon_H173. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H173). zenon_intro zenon_H90. zenon_intro zenon_H174. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.03/10.21 apply (zenon_L260_); trivial. % 10.03/10.21 (* end of lemma zenon_L261_ *) % 10.03/10.21 assert (zenon_L262_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H175 zenon_H7e zenon_H2f. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H175). zenon_intro zenon_Hb7. zenon_intro zenon_H176. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H176). zenon_intro zenon_H90. zenon_intro zenon_H177. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.03/10.21 apply (zenon_L25_); trivial. % 10.03/10.21 (* end of lemma zenon_L262_ *) % 10.03/10.21 assert (zenon_L263_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H178 zenon_H82 zenon_H30. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H178). zenon_intro zenon_Hb7. zenon_intro zenon_H179. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H179). zenon_intro zenon_H90. zenon_intro zenon_H17a. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 10.03/10.21 apply (zenon_L26_); trivial. % 10.03/10.21 (* end of lemma zenon_L263_ *) % 10.03/10.21 assert (zenon_L264_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((e0) = (e1))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H17d zenon_H1e. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H68. zenon_intro zenon_H17e. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H17e). zenon_intro zenon_H5e. zenon_intro zenon_Hb3. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.03/10.21 apply (zenon_L245_); trivial. % 10.03/10.21 (* end of lemma zenon_L264_ *) % 10.03/10.21 assert (zenon_L265_ : (~((op (e0) (op (e0) (e1))) = (e1))) -> ((op (e0) (e1)) = (e1)) -> False). % 10.03/10.21 do 0 intro. intros zenon_Hd8 zenon_H5e. % 10.03/10.21 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (op (e0) (e1))) = (e1))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_Hd8. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H5e. % 10.03/10.21 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.21 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H295]. % 10.03/10.21 congruence. % 10.03/10.21 elim (classic ((op (e0) (op (e0) (e1))) = (op (e0) (op (e0) (e1))))); [ zenon_intro zenon_Hda | zenon_intro zenon_Hdb ]. % 10.03/10.21 cut (((op (e0) (op (e0) (e1))) = (op (e0) (op (e0) (e1)))) = ((op (e0) (e1)) = (op (e0) (op (e0) (e1))))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H295. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Hda. % 10.03/10.21 cut (((op (e0) (op (e0) (e1))) = (op (e0) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 10.03/10.21 cut (((op (e0) (op (e0) (e1))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H296]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e0) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H292]. % 10.03/10.21 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_H34. apply refl_equal. % 10.03/10.21 exact (zenon_H292 zenon_H5e). % 10.03/10.21 apply zenon_Hdb. apply refl_equal. % 10.03/10.21 apply zenon_Hdb. apply refl_equal. % 10.03/10.21 apply zenon_H1d. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L265_ *) % 10.03/10.21 assert (zenon_L266_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e0) (op (e0) (e1))) = (e1))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H17f zenon_Hd8. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H68. zenon_intro zenon_H180. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H5e. zenon_intro zenon_Hb6. % 10.03/10.21 apply (zenon_L265_); trivial. % 10.03/10.21 (* end of lemma zenon_L266_ *) % 10.03/10.21 assert (zenon_L267_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e0) (op (e0) (e1))) = (e1))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H181 zenon_Hd8. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_H5e. zenon_intro zenon_Hbd. % 10.03/10.21 apply (zenon_L265_); trivial. % 10.03/10.21 (* end of lemma zenon_L267_ *) % 10.03/10.21 assert (zenon_L268_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H185 zenon_H1e zenon_H8d. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H185). zenon_intro zenon_H27. zenon_intro zenon_H186. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_H27. zenon_intro zenon_Hc5. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 10.03/10.21 apply (zenon_L231_); trivial. % 10.03/10.21 (* end of lemma zenon_L268_ *) % 10.03/10.21 assert (zenon_L269_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H93 zenon_H27 zenon_H143. % 10.03/10.21 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H93. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H27. % 10.03/10.21 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H297]. % 10.03/10.21 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_H61. apply refl_equal. % 10.03/10.21 apply zenon_H297. apply sym_equal. exact zenon_H143. % 10.03/10.21 (* end of lemma zenon_L269_ *) % 10.03/10.21 assert (zenon_L270_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H18d zenon_H93. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H18d). zenon_intro zenon_H27. zenon_intro zenon_H18e. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H18e). zenon_intro zenon_H27. zenon_intro zenon_Hcb. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.21 apply (zenon_L269_); trivial. % 10.03/10.21 (* end of lemma zenon_L270_ *) % 10.03/10.21 assert (zenon_L271_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H18d zenon_H93. % 10.03/10.21 apply (zenon_L270_); trivial. % 10.03/10.21 (* end of lemma zenon_L271_ *) % 10.03/10.21 assert (zenon_L272_ : (~((op (e0) (op (e0) (e2))) = (e2))) -> ((op (e0) (e2)) = (e2)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H15c zenon_Hd0. % 10.03/10.21 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (op (e0) (e2))) = (e2))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H15c. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Hd0. % 10.03/10.21 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.21 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H298]. % 10.03/10.21 congruence. % 10.03/10.21 elim (classic ((op (e0) (op (e0) (e2))) = (op (e0) (op (e0) (e2))))); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H1c6 ]. % 10.03/10.21 cut (((op (e0) (op (e0) (e2))) = (op (e0) (op (e0) (e2)))) = ((op (e0) (e2)) = (op (e0) (op (e0) (e2))))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H298. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H1c5. % 10.03/10.21 cut (((op (e0) (op (e0) (e2))) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 10.03/10.21 cut (((op (e0) (op (e0) (e2))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H299]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H29a]. % 10.03/10.21 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_H34. apply refl_equal. % 10.03/10.21 exact (zenon_H29a zenon_Hd0). % 10.03/10.21 apply zenon_H1c6. apply refl_equal. % 10.03/10.21 apply zenon_H1c6. apply refl_equal. % 10.03/10.21 apply zenon_H22. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L272_ *) % 10.03/10.21 assert (zenon_L273_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e0) (op (e0) (e2))) = (e2))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H195 zenon_H15c. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H188. zenon_intro zenon_H196. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H196). zenon_intro zenon_H18c. zenon_intro zenon_Hcf. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd0. zenon_intro zenon_H86. % 10.03/10.21 apply (zenon_L272_); trivial. % 10.03/10.21 (* end of lemma zenon_L273_ *) % 10.03/10.21 assert (zenon_L274_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((e1) = (e2))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H197 zenon_H25. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H197). zenon_intro zenon_H188. zenon_intro zenon_H198. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H198). zenon_intro zenon_H18c. zenon_intro zenon_Hd6. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.03/10.21 apply (zenon_L250_); trivial. % 10.03/10.21 (* end of lemma zenon_L274_ *) % 10.03/10.21 assert (zenon_L275_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H19b zenon_H82 zenon_Ha9. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H19b). zenon_intro zenon_H188. zenon_intro zenon_H19c. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H19c). zenon_intro zenon_H18c. zenon_intro zenon_H16b. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.03/10.21 apply (zenon_L255_); trivial. % 10.03/10.21 (* end of lemma zenon_L275_ *) % 10.03/10.21 assert (zenon_L276_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H1a5 zenon_H82 zenon_H30. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_Hf7. zenon_intro zenon_H1a6. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1a6). zenon_intro zenon_H143. zenon_intro zenon_H17a. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 10.03/10.21 apply (zenon_L26_); trivial. % 10.03/10.21 (* end of lemma zenon_L276_ *) % 10.03/10.21 assert (zenon_L277_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e1)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H1a7 zenon_H1e zenon_H1f. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H86. zenon_intro zenon_H1a8. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hd0. zenon_intro zenon_H6f. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H20. zenon_intro zenon_H20. % 10.03/10.21 apply (zenon_L2_); trivial. % 10.03/10.21 (* end of lemma zenon_L277_ *) % 10.03/10.21 assert (zenon_L278_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((op (e0) (op (e0) (e1))) = (e1))) -> ((op (e0) (e0)) = (e1)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H1a9 zenon_Hd8 zenon_H1f. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1a9). zenon_intro zenon_H86. zenon_intro zenon_H1aa. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_Hd0. zenon_intro zenon_Hb3. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.03/10.21 apply (zenon_L58_); trivial. % 10.03/10.21 (* end of lemma zenon_L278_ *) % 10.03/10.21 assert (zenon_L279_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e0) (op (e0) (e2))) = (e2))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H1ad zenon_H15c. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H86. zenon_intro zenon_H1ae. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_Hd0. zenon_intro zenon_Hbd. % 10.03/10.21 apply (zenon_L272_); trivial. % 10.03/10.21 (* end of lemma zenon_L279_ *) % 10.03/10.21 assert (zenon_L280_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e0) (op (e0) (e1))) = (e1))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H1af zenon_Hd8. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_Hd2. zenon_intro zenon_H1b0. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hd7. zenon_intro zenon_Hc2. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.03/10.21 apply (zenon_L265_); trivial. % 10.03/10.21 (* end of lemma zenon_L280_ *) % 10.03/10.21 assert (zenon_L281_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H1b1 zenon_H1e zenon_H8d. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_Hd2. zenon_intro zenon_H1b2. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_Hd7. zenon_intro zenon_Hc5. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 10.03/10.21 apply (zenon_L231_); trivial. % 10.03/10.21 (* end of lemma zenon_L281_ *) % 10.03/10.21 assert (zenon_L282_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((e1) = (e2))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H1b3 zenon_H25. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_Hd2. zenon_intro zenon_H1b4. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1b4). zenon_intro zenon_Hd7. zenon_intro zenon_Hc8. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.03/10.21 apply (zenon_L250_); trivial. % 10.03/10.21 (* end of lemma zenon_L282_ *) % 10.03/10.21 assert (zenon_L283_ : (~((op (e0) (op (e0) (e3))) = (e3))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> False). % 10.03/10.21 do 0 intro. intros zenon_He1 zenon_H2b zenon_Hb7. % 10.03/10.21 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (op (e0) (e3))) = (e3))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_He1. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H2b. % 10.03/10.21 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.21 cut (((op (e0) (e0)) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H29b]. % 10.03/10.21 congruence. % 10.03/10.21 elim (classic ((op (e0) (op (e0) (e3))) = (op (e0) (op (e0) (e3))))); [ zenon_intro zenon_He4 | zenon_intro zenon_He5 ]. % 10.03/10.21 cut (((op (e0) (op (e0) (e3))) = (op (e0) (op (e0) (e3)))) = ((op (e0) (e0)) = (op (e0) (op (e0) (e3))))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H29b. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_He4. % 10.03/10.21 cut (((op (e0) (op (e0) (e3))) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 10.03/10.21 cut (((op (e0) (op (e0) (e3))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H29c]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e0) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H29d]. % 10.03/10.21 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_H34. apply refl_equal. % 10.03/10.21 exact (zenon_H29d zenon_Hb7). % 10.03/10.21 apply zenon_He5. apply refl_equal. % 10.03/10.21 apply zenon_He5. apply refl_equal. % 10.03/10.21 apply zenon_H29. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L283_ *) % 10.03/10.21 assert (zenon_L284_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H1b7 zenon_Heb. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_H2e. zenon_intro zenon_H1b8. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_H2e. zenon_intro zenon_Hcf. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd0. zenon_intro zenon_H86. % 10.03/10.21 apply (zenon_L63_); trivial. % 10.03/10.21 (* end of lemma zenon_L284_ *) % 10.03/10.21 assert (zenon_L285_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H21c zenon_He8 zenon_H1f zenon_H2c zenon_H7a zenon_Heb zenon_H2f zenon_H105. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H21c). zenon_intro zenon_H128. zenon_intro zenon_H21d. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H166. zenon_intro zenon_H174. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.03/10.21 apply (zenon_L260_); trivial. % 10.03/10.21 (* end of lemma zenon_L285_ *) % 10.03/10.21 assert (zenon_L286_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H1e4 zenon_H82 zenon_H30. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1e4). zenon_intro zenon_H128. zenon_intro zenon_H1e5. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1e5). zenon_intro zenon_H166. zenon_intro zenon_H17a. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 10.03/10.21 apply (zenon_L26_); trivial. % 10.03/10.21 (* end of lemma zenon_L286_ *) % 10.03/10.21 assert (zenon_L287_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H1e8 zenon_H8d zenon_H5f. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1e8). zenon_intro zenon_H72. zenon_intro zenon_H1e9. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1e9). zenon_intro zenon_He2. zenon_intro zenon_Hb3. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.03/10.21 apply (zenon_L34_); trivial. % 10.03/10.21 (* end of lemma zenon_L287_ *) % 10.03/10.21 assert (zenon_L288_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H1f9 zenon_H22e zenon_H74 zenon_H8d zenon_H2a zenon_H1b9 zenon_H2f zenon_H105. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1f9). zenon_intro zenon_H72. zenon_intro zenon_H1fa. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_He2. zenon_intro zenon_Hb6. % 10.03/10.21 apply (zenon_L257_); trivial. % 10.03/10.21 (* end of lemma zenon_L288_ *) % 10.03/10.21 assert (zenon_L289_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H1fb zenon_H22e zenon_H74 zenon_H8d zenon_H2a zenon_H1b9 zenon_H2f zenon_H105. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H72. zenon_intro zenon_H1fc. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_He2. zenon_intro zenon_Hbd. % 10.03/10.21 apply (zenon_L257_); trivial. % 10.03/10.21 (* end of lemma zenon_L289_ *) % 10.03/10.21 assert (zenon_L290_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e0) (op (e0) (e1))) = (e1))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H1fd zenon_Hd8. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H79. zenon_intro zenon_H1fe. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H109. zenon_intro zenon_Hc2. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.03/10.21 apply (zenon_L265_); trivial. % 10.03/10.21 (* end of lemma zenon_L290_ *) % 10.03/10.21 assert (zenon_L291_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H1ff zenon_H1e zenon_H8d. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H1ff). zenon_intro zenon_H79. zenon_intro zenon_H200. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H200). zenon_intro zenon_H109. zenon_intro zenon_Hc5. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 10.03/10.21 apply (zenon_L231_); trivial. % 10.03/10.21 (* end of lemma zenon_L291_ *) % 10.03/10.21 assert (zenon_L292_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H223 zenon_He8 zenon_H1f zenon_H2c zenon_H7a zenon_Heb zenon_H2f zenon_H105. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H79. zenon_intro zenon_H224. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H109. zenon_intro zenon_Hc8. % 10.03/10.21 apply (zenon_L260_); trivial. % 10.03/10.21 (* end of lemma zenon_L292_ *) % 10.03/10.21 assert (zenon_L293_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H127 zenon_H2f zenon_H112. % 10.03/10.21 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e2) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H127. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H2f. % 10.03/10.21 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H283]. % 10.03/10.21 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_H81. apply refl_equal. % 10.03/10.21 apply zenon_H283. apply sym_equal. exact zenon_H112. % 10.03/10.21 (* end of lemma zenon_L293_ *) % 10.03/10.21 assert (zenon_L294_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H203 zenon_H127 zenon_H2f. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H203). zenon_intro zenon_H7f. zenon_intro zenon_H204. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H204). zenon_intro zenon_H112. zenon_intro zenon_Hcf. % 10.03/10.21 apply (zenon_L293_); trivial. % 10.03/10.21 (* end of lemma zenon_L294_ *) % 10.03/10.21 assert (zenon_L295_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H52 zenon_H72 zenon_H16c. % 10.03/10.21 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H16c. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Haa. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H16d. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H52. % 10.03/10.21 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H29e]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 apply zenon_H29e. apply sym_equal. exact zenon_H72. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L295_ *) % 10.03/10.21 assert (zenon_L296_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H20b zenon_H16c. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_H52. zenon_intro zenon_H20c. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H20c). zenon_intro zenon_H52. zenon_intro zenon_H171. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.21 apply (zenon_L295_); trivial. % 10.03/10.21 (* end of lemma zenon_L296_ *) % 10.03/10.21 assert (zenon_L297_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H52 zenon_H79 zenon_H141. % 10.03/10.21 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H141. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Haa. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H142]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H142. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H52. % 10.03/10.21 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 apply zenon_H140. apply sym_equal. exact zenon_H79. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L297_ *) % 10.03/10.21 assert (zenon_L298_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H20d zenon_H141. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H52. zenon_intro zenon_H20e. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H20e). zenon_intro zenon_H52. zenon_intro zenon_H174. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.03/10.21 apply (zenon_L297_); trivial. % 10.03/10.21 (* end of lemma zenon_L298_ *) % 10.03/10.21 assert (zenon_L299_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H52 zenon_H7f zenon_H1ea. % 10.03/10.21 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H1ea. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Haa. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1eb]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H1eb. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H52. % 10.03/10.21 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 10.03/10.21 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 apply zenon_H80. apply sym_equal. exact zenon_H7f. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 apply zenon_Hab. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L299_ *) % 10.03/10.21 assert (zenon_L300_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H20f zenon_H1ea. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H20f). zenon_intro zenon_H52. zenon_intro zenon_H210. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H210). zenon_intro zenon_H52. zenon_intro zenon_H177. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.03/10.21 apply (zenon_L299_); trivial. % 10.03/10.21 (* end of lemma zenon_L300_ *) % 10.03/10.21 assert (zenon_L301_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H211 zenon_H82 zenon_H30. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H211). zenon_intro zenon_H52. zenon_intro zenon_H212. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H212). zenon_intro zenon_H52. zenon_intro zenon_H17a. % 10.03/10.21 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 10.03/10.21 apply (zenon_L26_); trivial. % 10.03/10.21 (* end of lemma zenon_L301_ *) % 10.03/10.21 assert (zenon_L302_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> False). % 10.03/10.21 do 0 intro. intros zenon_Hc0 zenon_H43. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_H89. zenon_intro zenon_Hc1. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H9d. zenon_intro zenon_Hc2. % 10.03/10.21 apply (zenon_L88_); trivial. % 10.03/10.21 (* end of lemma zenon_L302_ *) % 10.03/10.21 assert (zenon_L303_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> False). % 10.03/10.21 do 0 intro. intros zenon_Hc6 zenon_H43. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_H89. zenon_intro zenon_Hc7. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_H9d. zenon_intro zenon_Hc8. % 10.03/10.21 apply (zenon_L88_); trivial. % 10.03/10.21 (* end of lemma zenon_L303_ *) % 10.03/10.21 assert (zenon_L304_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> False). % 10.03/10.21 do 0 intro. intros zenon_Hc9 zenon_H43. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H89. zenon_intro zenon_Hca. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_H9d. zenon_intro zenon_Hcb. % 10.03/10.21 apply (zenon_L88_); trivial. % 10.03/10.21 (* end of lemma zenon_L304_ *) % 10.03/10.21 assert (zenon_L305_ : (~((op (e1) (op (e1) (e2))) = (e2))) -> ((op (e1) (e2)) = (e2)) -> False). % 10.03/10.21 do 0 intro. intros zenon_H160 zenon_Hd7. % 10.03/10.21 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (op (e1) (e2))) = (e2))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H160. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Hd7. % 10.03/10.21 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.21 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H29f]. % 10.03/10.21 congruence. % 10.03/10.21 elim (classic ((op (e1) (op (e1) (e2))) = (op (e1) (op (e1) (e2))))); [ zenon_intro zenon_H2a0 | zenon_intro zenon_H2a1 ]. % 10.03/10.21 cut (((op (e1) (op (e1) (e2))) = (op (e1) (op (e1) (e2)))) = ((op (e1) (e2)) = (op (e1) (op (e1) (e2))))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H29f. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H2a0. % 10.03/10.21 cut (((op (e1) (op (e1) (e2))) = (op (e1) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2a1]. % 10.03/10.21 cut (((op (e1) (op (e1) (e2))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a2]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e1) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H293]. % 10.03/10.21 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_H1d. apply refl_equal. % 10.03/10.21 exact (zenon_H293 zenon_Hd7). % 10.03/10.21 apply zenon_H2a1. apply refl_equal. % 10.03/10.21 apply zenon_H2a1. apply refl_equal. % 10.03/10.21 apply zenon_H22. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L305_ *) % 10.03/10.21 assert (zenon_L306_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> False). % 10.03/10.21 do 0 intro. intros zenon_Hd4 zenon_H160. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_H97. zenon_intro zenon_Hd5. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_H9e. zenon_intro zenon_Hd6. % 10.03/10.21 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.03/10.21 apply (zenon_L305_); trivial. % 10.03/10.21 (* end of lemma zenon_L306_ *) % 10.03/10.21 assert (zenon_L307_ : (~((op (e1) (op (e1) (e3))) = (e3))) -> ((op (e1) (e3)) = (e3)) -> False). % 10.03/10.21 do 0 intro. intros zenon_Hf6 zenon_H109. % 10.03/10.21 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (op (e1) (e3))) = (e3))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_Hf6. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_H109. % 10.03/10.21 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.21 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2a3]. % 10.03/10.21 congruence. % 10.03/10.21 elim (classic ((op (e1) (op (e1) (e3))) = (op (e1) (op (e1) (e3))))); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hfa ]. % 10.03/10.21 cut (((op (e1) (op (e1) (e3))) = (op (e1) (op (e1) (e3)))) = ((op (e1) (e3)) = (op (e1) (op (e1) (e3))))). % 10.03/10.21 intro zenon_D_pnotp. % 10.03/10.21 apply zenon_H2a3. % 10.03/10.21 rewrite <- zenon_D_pnotp. % 10.03/10.21 exact zenon_Hf9. % 10.03/10.21 cut (((op (e1) (op (e1) (e3))) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 10.03/10.21 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2a4]. % 10.03/10.21 congruence. % 10.03/10.21 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 10.03/10.21 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.21 congruence. % 10.03/10.21 apply zenon_H1d. apply refl_equal. % 10.03/10.21 exact (zenon_H1a0 zenon_H109). % 10.03/10.21 apply zenon_Hfa. apply refl_equal. % 10.03/10.21 apply zenon_Hfa. apply refl_equal. % 10.03/10.21 apply zenon_H29. apply refl_equal. % 10.03/10.21 (* end of lemma zenon_L307_ *) % 10.03/10.21 assert (zenon_L308_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> False). % 10.03/10.21 do 0 intro. intros zenon_H172 zenon_Hf6. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H172). zenon_intro zenon_Hb7. zenon_intro zenon_H173. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H173). zenon_intro zenon_H90. zenon_intro zenon_H174. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.03/10.22 apply (zenon_L307_); trivial. % 10.03/10.22 (* end of lemma zenon_L308_ *) % 10.03/10.22 assert (zenon_L309_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H17d zenon_H43. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H68. zenon_intro zenon_H17e. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H17e). zenon_intro zenon_H5e. zenon_intro zenon_Hb3. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.03/10.22 apply (zenon_L88_); trivial. % 10.03/10.22 (* end of lemma zenon_L309_ *) % 10.03/10.22 assert (zenon_L310_ : (~((op (e1) (op (e1) (e0))) = (e0))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H43 zenon_H8d zenon_H68. % 10.03/10.22 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (op (e1) (e0))) = (e0))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H43. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H8d. % 10.03/10.22 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.03/10.22 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2a5]. % 10.03/10.22 congruence. % 10.03/10.22 elim (classic ((op (e1) (op (e1) (e0))) = (op (e1) (op (e1) (e0))))); [ zenon_intro zenon_H136 | zenon_intro zenon_H137 ]. % 10.03/10.22 cut (((op (e1) (op (e1) (e0))) = (op (e1) (op (e1) (e0)))) = ((op (e1) (e1)) = (op (e1) (op (e1) (e0))))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2a5. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H136. % 10.03/10.22 cut (((op (e1) (op (e1) (e0))) = (op (e1) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 10.03/10.22 cut (((op (e1) (op (e1) (e0))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2a6]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e1) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2a7]. % 10.03/10.22 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H1d. apply refl_equal. % 10.03/10.22 exact (zenon_H2a7 zenon_H68). % 10.03/10.22 apply zenon_H137. apply refl_equal. % 10.03/10.22 apply zenon_H137. apply refl_equal. % 10.03/10.22 apply zenon_H34. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L310_ *) % 10.03/10.22 assert (zenon_L311_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> ((op (e1) (e1)) = (e0)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H17f zenon_H43 zenon_H8d. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H68. zenon_intro zenon_H180. % 10.03/10.22 apply (zenon_L310_); trivial. % 10.03/10.22 (* end of lemma zenon_L311_ *) % 10.03/10.22 assert (zenon_L312_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> ((op (e1) (e1)) = (e0)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H181 zenon_H43 zenon_H8d. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 10.03/10.22 apply (zenon_L310_); trivial. % 10.03/10.22 (* end of lemma zenon_L312_ *) % 10.03/10.22 assert (zenon_L313_ : ((op (e3) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H82 zenon_H106 zenon_Hfe. % 10.03/10.22 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_Hfe. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Haa. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_Hff. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H82. % 10.03/10.22 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_Hab. apply refl_equal. % 10.03/10.22 apply zenon_H107. apply sym_equal. exact zenon_H106. % 10.03/10.22 apply zenon_Hab. apply refl_equal. % 10.03/10.22 apply zenon_Hab. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L313_ *) % 10.03/10.22 assert (zenon_L314_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2a8 zenon_H9d zenon_H8d zenon_H23 zenon_H25 zenon_H188 zenon_H82 zenon_Hfe. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.03/10.22 apply (zenon_L153_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.03/10.22 apply (zenon_L31_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.03/10.22 apply (zenon_L250_); trivial. % 10.03/10.22 apply (zenon_L313_); trivial. % 10.03/10.22 (* end of lemma zenon_L314_ *) % 10.03/10.22 assert (zenon_L315_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H188 zenon_H1f0 zenon_H2c. % 10.03/10.22 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 10.03/10.22 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2c. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H31. % 10.03/10.22 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.22 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e1) (e2)) = (e1)) = ((e3) = (e1))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H19f. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H188. % 10.03/10.22 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.22 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H294]. % 10.03/10.22 congruence. % 10.03/10.22 exact (zenon_H294 zenon_H1f0). % 10.03/10.22 apply zenon_H1d. apply refl_equal. % 10.03/10.22 apply zenon_H29. apply refl_equal. % 10.03/10.22 apply zenon_H29. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L315_ *) % 10.03/10.22 assert (zenon_L316_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_Hbe zenon_H2b zenon_H73. % 10.03/10.22 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_Hbe. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2b. % 10.03/10.22 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 10.03/10.22 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H67. apply refl_equal. % 10.03/10.22 apply zenon_H78. apply sym_equal. exact zenon_H73. % 10.03/10.22 (* end of lemma zenon_L316_ *) % 10.03/10.22 assert (zenon_L317_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H22e zenon_H2b zenon_Hbe zenon_H8d zenon_H2a zenon_H2c zenon_H188 zenon_Hf6. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.22 apply (zenon_L316_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.22 apply (zenon_L33_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.22 apply (zenon_L315_); trivial. % 10.03/10.22 apply (zenon_L307_); trivial. % 10.03/10.22 (* end of lemma zenon_L317_ *) % 10.03/10.22 assert (zenon_L318_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1f5 zenon_H90 zenon_H98. % 10.03/10.22 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H1f5. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H90. % 10.03/10.22 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 10.03/10.22 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H76. apply refl_equal. % 10.03/10.22 apply zenon_H99. apply sym_equal. exact zenon_H98. % 10.03/10.22 (* end of lemma zenon_L318_ *) % 10.03/10.22 assert (zenon_L319_ : (((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)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1f6 zenon_H90 zenon_H1f5 zenon_H188 zenon_H1ec zenon_Hd0 zenon_H96 zenon_H14b zenon_H79. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.03/10.22 apply (zenon_L318_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.03/10.22 apply (zenon_L172_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.03/10.22 apply (zenon_L104_); trivial. % 10.03/10.22 apply (zenon_L95_); trivial. % 10.03/10.22 (* end of lemma zenon_L319_ *) % 10.03/10.22 assert (zenon_L320_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 10.03/10.22 do 0 intro. intros zenon_Hd1 zenon_H8d zenon_Ha2. % 10.03/10.22 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_Hd1. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H8d. % 10.03/10.22 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 10.03/10.22 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H61. apply refl_equal. % 10.03/10.22 apply zenon_Ha3. apply sym_equal. exact zenon_Ha2. % 10.03/10.22 (* end of lemma zenon_L320_ *) % 10.03/10.22 assert (zenon_L321_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_Hc3 zenon_H2c zenon_H2d. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_H89. zenon_intro zenon_Hc4. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_H9d. zenon_intro zenon_Hc5. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 10.03/10.22 apply (zenon_L8_); trivial. % 10.03/10.22 (* end of lemma zenon_L321_ *) % 10.03/10.22 assert (zenon_L322_ : ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_Ha5 zenon_H97 zenon_Heb. % 10.03/10.22 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hec | zenon_intro zenon_H81 ]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_Heb. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Hec. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hed]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_Hed. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Ha5. % 10.03/10.22 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2ab]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 apply zenon_H2ab. apply sym_equal. exact zenon_H97. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L322_ *) % 10.03/10.22 assert (zenon_L323_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_Hd4 zenon_Ha5 zenon_Heb. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_H97. zenon_intro zenon_Hd5. % 10.03/10.22 apply (zenon_L322_); trivial. % 10.03/10.22 (* end of lemma zenon_L323_ *) % 10.03/10.22 assert (zenon_L324_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.03/10.22 do 0 intro. intros zenon_Ha5 zenon_H2e zenon_H23. % 10.03/10.22 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H6a | zenon_intro zenon_H22 ]. % 10.03/10.22 cut (((e2) = (e2)) = ((e0) = (e2))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H23. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H6a. % 10.03/10.22 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.22 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e2) (e2)) = (e0)) = ((e2) = (e0))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H8a. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Ha5. % 10.03/10.22 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.03/10.22 cut (((op (e2) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 10.03/10.22 congruence. % 10.03/10.22 exact (zenon_H4a zenon_H2e). % 10.03/10.22 apply zenon_H34. apply refl_equal. % 10.03/10.22 apply zenon_H22. apply refl_equal. % 10.03/10.22 apply zenon_H22. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L324_ *) % 10.03/10.22 assert (zenon_L325_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H163 zenon_Ha5 zenon_H23. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H163). zenon_intro zenon_H97. zenon_intro zenon_H164. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H164). zenon_intro zenon_H9e. zenon_intro zenon_H165. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H165). zenon_intro zenon_H2e. zenon_intro zenon_H2e. % 10.03/10.22 apply (zenon_L324_); trivial. % 10.03/10.22 (* end of lemma zenon_L325_ *) % 10.03/10.22 assert (zenon_L326_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H12f zenon_H11f zenon_H72 zenon_H2d zenon_Hd1 zenon_Ha5 zenon_H2a zenon_He2 zenon_H12a. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.03/10.22 apply (zenon_L78_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.03/10.22 apply (zenon_L79_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.03/10.22 apply (zenon_L42_); trivial. % 10.03/10.22 apply (zenon_L84_); trivial. % 10.03/10.22 (* end of lemma zenon_L326_ *) % 10.03/10.22 assert (zenon_L327_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H16f zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_Ha5 zenon_H2a zenon_H12a. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hb7. zenon_intro zenon_H170. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_H90. zenon_intro zenon_H171. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.22 apply (zenon_L326_); trivial. % 10.03/10.22 (* end of lemma zenon_L327_ *) % 10.03/10.22 assert (zenon_L328_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H172 zenon_H93 zenon_H2d. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H172). zenon_intro zenon_Hb7. zenon_intro zenon_H173. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H173). zenon_intro zenon_H90. zenon_intro zenon_H174. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.03/10.22 apply (zenon_L91_); trivial. % 10.03/10.22 (* end of lemma zenon_L328_ *) % 10.03/10.22 assert (zenon_L329_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H130 zenon_Hde zenon_Hef zenon_Hf1 zenon_H2d zenon_H113 zenon_H112 zenon_H1f5 zenon_H7f. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.03/10.22 apply (zenon_L64_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.03/10.22 apply (zenon_L65_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.03/10.22 apply (zenon_L74_); trivial. % 10.03/10.22 apply (zenon_L176_); trivial. % 10.03/10.22 (* end of lemma zenon_L329_ *) % 10.03/10.22 assert (zenon_L330_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_He8 zenon_H1f zenon_H2c zenon_H5f zenon_H7f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H112 zenon_H12a. % 10.03/10.22 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.03/10.22 apply (zenon_L32_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.03/10.22 apply (zenon_L59_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.03/10.22 apply (zenon_L329_); trivial. % 10.03/10.22 apply (zenon_L84_); trivial. % 10.03/10.22 (* end of lemma zenon_L330_ *) % 10.03/10.22 assert (zenon_L331_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (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)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H175 zenon_He8 zenon_H1f zenon_H2c zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H175). zenon_intro zenon_Hb7. zenon_intro zenon_H176. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H176). zenon_intro zenon_H90. zenon_intro zenon_H177. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.03/10.22 apply (zenon_L330_); trivial. % 10.03/10.22 (* end of lemma zenon_L331_ *) % 10.03/10.22 assert (zenon_L332_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H17f zenon_Ha5 zenon_Heb. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H68. zenon_intro zenon_H180. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H5e. zenon_intro zenon_Hb6. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 10.03/10.22 apply (zenon_L322_); trivial. % 10.03/10.22 (* end of lemma zenon_L332_ *) % 10.03/10.22 assert (zenon_L333_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_Ha5 zenon_Ha2 zenon_H2ac. % 10.03/10.22 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hec | zenon_intro zenon_H81 ]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2ac. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Hec. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2ad]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e2) (e1)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2ad. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Ha5. % 10.03/10.22 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 apply zenon_Ha3. apply sym_equal. exact zenon_Ha2. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L333_ *) % 10.03/10.22 assert (zenon_L334_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1d9 zenon_H90 zenon_H94. % 10.03/10.22 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H1d9. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H90. % 10.03/10.22 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H95]. % 10.03/10.22 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H76. apply refl_equal. % 10.03/10.22 apply zenon_H95. apply sym_equal. exact zenon_H94. % 10.03/10.22 (* end of lemma zenon_L334_ *) % 10.03/10.22 assert (zenon_L335_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H181 zenon_H2ae zenon_H1e zenon_H2d zenon_H2a zenon_H2ac zenon_Ha5 zenon_H1d9. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_H5e. zenon_intro zenon_Hbd. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.03/10.22 apply (zenon_L245_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.03/10.22 apply (zenon_L33_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.03/10.22 apply (zenon_L333_); trivial. % 10.03/10.22 apply (zenon_L334_); trivial. % 10.03/10.22 (* end of lemma zenon_L335_ *) % 10.03/10.22 assert (zenon_L336_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H185 zenon_H2c zenon_H2d. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H185). zenon_intro zenon_H27. zenon_intro zenon_H186. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_H27. zenon_intro zenon_Hc5. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 10.03/10.22 apply (zenon_L8_); trivial. % 10.03/10.22 (* end of lemma zenon_L336_ *) % 10.03/10.22 assert (zenon_L337_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H199 zenon_Ha5 zenon_H23. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H199). zenon_intro zenon_H188. zenon_intro zenon_H19a. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H19a). zenon_intro zenon_H18c. zenon_intro zenon_H165. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H165). zenon_intro zenon_H2e. zenon_intro zenon_H2e. % 10.03/10.22 apply (zenon_L324_); trivial. % 10.03/10.22 (* end of lemma zenon_L337_ *) % 10.03/10.22 assert (zenon_L338_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (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)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1a3 zenon_He8 zenon_H1f zenon_H2c zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_Hf7. zenon_intro zenon_H1a4. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1a4). zenon_intro zenon_H143. zenon_intro zenon_H177. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.03/10.22 apply (zenon_L330_); trivial. % 10.03/10.22 (* end of lemma zenon_L338_ *) % 10.03/10.22 assert (zenon_L339_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e1)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1af zenon_Hbe zenon_H1f. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_Hd2. zenon_intro zenon_H1b0. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hd7. zenon_intro zenon_Hc2. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.03/10.22 apply (zenon_L49_); trivial. % 10.03/10.22 (* end of lemma zenon_L339_ *) % 10.03/10.22 assert (zenon_L340_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1b1 zenon_H2c zenon_H2d. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_Hd2. zenon_intro zenon_H1b2. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_Hd7. zenon_intro zenon_Hc5. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 10.03/10.22 apply (zenon_L8_); trivial. % 10.03/10.22 (* end of lemma zenon_L340_ *) % 10.03/10.22 assert (zenon_L341_ : ((op (e2) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_Ha5 zenon_H13b zenon_H1b9. % 10.03/10.22 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hec | zenon_intro zenon_H81 ]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H1b9. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Hec. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H1ba. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Ha5. % 10.03/10.22 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H13c]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 apply zenon_H13c. apply sym_equal. exact zenon_H13b. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L341_ *) % 10.03/10.22 assert (zenon_L342_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2b1 zenon_H86 zenon_Hd2. % 10.03/10.22 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2b1. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H86. % 10.03/10.22 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 10.03/10.22 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H190. apply refl_equal. % 10.03/10.22 apply zenon_Hd3. apply sym_equal. exact zenon_Hd2. % 10.03/10.22 (* end of lemma zenon_L342_ *) % 10.03/10.22 assert (zenon_L343_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H82 zenon_H91 zenon_H16c. % 10.03/10.22 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H16c. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Haa. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H16d. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H82. % 10.03/10.22 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_Hab. apply refl_equal. % 10.03/10.22 apply zenon_H18f. apply sym_equal. exact zenon_H91. % 10.03/10.22 apply zenon_Hab. apply refl_equal. % 10.03/10.22 apply zenon_Hab. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L343_ *) % 10.03/10.22 assert (zenon_L344_ : ((op (e3) (e3)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H82 zenon_Hf4 zenon_Hb8. % 10.03/10.22 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_Hb8. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Haa. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_Hb9. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H82. % 10.03/10.22 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_Hab. apply refl_equal. % 10.03/10.22 apply zenon_H168. apply sym_equal. exact zenon_Hf4. % 10.03/10.22 apply zenon_Hab. apply refl_equal. % 10.03/10.22 apply zenon_Hab. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L344_ *) % 10.03/10.22 assert (zenon_L345_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1be zenon_Ha5 zenon_H23. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_H2e. zenon_intro zenon_H1bf. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1bf). zenon_intro zenon_H2e. zenon_intro zenon_H165. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H165). zenon_intro zenon_H2e. zenon_intro zenon_H2e. % 10.03/10.22 apply (zenon_L324_); trivial. % 10.03/10.22 (* end of lemma zenon_L345_ *) % 10.03/10.22 assert (zenon_L346_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H21c zenon_H110 zenon_H2d. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H21c). zenon_intro zenon_H128. zenon_intro zenon_H21d. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H166. zenon_intro zenon_H174. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.03/10.22 apply (zenon_L73_); trivial. % 10.03/10.22 (* end of lemma zenon_L346_ *) % 10.03/10.22 assert (zenon_L347_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1e8 zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_Ha5 zenon_H2a zenon_H12a. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1e8). zenon_intro zenon_H72. zenon_intro zenon_H1e9. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1e9). zenon_intro zenon_He2. zenon_intro zenon_Hb3. % 10.03/10.22 apply (zenon_L326_); trivial. % 10.03/10.22 (* end of lemma zenon_L347_ *) % 10.03/10.22 assert (zenon_L348_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1f9 zenon_Ha5 zenon_Heb. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1f9). zenon_intro zenon_H72. zenon_intro zenon_H1fa. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_He2. zenon_intro zenon_Hb6. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 10.03/10.22 apply (zenon_L322_); trivial. % 10.03/10.22 (* end of lemma zenon_L348_ *) % 10.03/10.22 assert (zenon_L349_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1fb zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_Ha5 zenon_H2a zenon_H12a. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H72. zenon_intro zenon_H1fc. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_He2. zenon_intro zenon_Hbd. % 10.03/10.22 apply (zenon_L326_); trivial. % 10.03/10.22 (* end of lemma zenon_L349_ *) % 10.03/10.22 assert (zenon_L350_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1fd zenon_H110 zenon_H2d. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H79. zenon_intro zenon_H1fe. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H109. zenon_intro zenon_Hc2. % 10.03/10.22 apply (zenon_L73_); trivial. % 10.03/10.22 (* end of lemma zenon_L350_ *) % 10.03/10.22 assert (zenon_L351_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1ff zenon_H2c zenon_H2d. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1ff). zenon_intro zenon_H79. zenon_intro zenon_H200. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H200). zenon_intro zenon_H109. zenon_intro zenon_Hc5. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 10.03/10.22 apply (zenon_L8_); trivial. % 10.03/10.22 (* end of lemma zenon_L351_ *) % 10.03/10.22 assert (zenon_L352_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H223 zenon_H110 zenon_H2d. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H79. zenon_intro zenon_H224. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H109. zenon_intro zenon_Hc8. % 10.03/10.22 apply (zenon_L73_); trivial. % 10.03/10.22 (* end of lemma zenon_L352_ *) % 10.03/10.22 assert (zenon_L353_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H203 zenon_He8 zenon_H1f zenon_H2c zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H203). zenon_intro zenon_H7f. zenon_intro zenon_H204. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H204). zenon_intro zenon_H112. zenon_intro zenon_Hcf. % 10.03/10.22 apply (zenon_L330_); trivial. % 10.03/10.22 (* end of lemma zenon_L353_ *) % 10.03/10.22 assert (zenon_L354_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H205 zenon_He8 zenon_H1f zenon_H2c zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H7f. zenon_intro zenon_H206. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H112. zenon_intro zenon_Hd6. % 10.03/10.22 apply (zenon_L330_); trivial. % 10.03/10.22 (* end of lemma zenon_L354_ *) % 10.03/10.22 assert (zenon_L355_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H207 zenon_Ha5 zenon_H23. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H7f. zenon_intro zenon_H208. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H208). zenon_intro zenon_H112. zenon_intro zenon_H165. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H165). zenon_intro zenon_H2e. zenon_intro zenon_H2e. % 10.03/10.22 apply (zenon_L324_); trivial. % 10.03/10.22 (* end of lemma zenon_L355_ *) % 10.03/10.22 assert (zenon_L356_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H20b zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_Ha5 zenon_H2a zenon_H12a. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_H52. zenon_intro zenon_H20c. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H20c). zenon_intro zenon_H52. zenon_intro zenon_H171. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.22 apply (zenon_L326_); trivial. % 10.03/10.22 (* end of lemma zenon_L356_ *) % 10.03/10.22 assert (zenon_L357_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H20d zenon_H93 zenon_H2d. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H52. zenon_intro zenon_H20e. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H20e). zenon_intro zenon_H52. zenon_intro zenon_H174. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.03/10.22 apply (zenon_L91_); trivial. % 10.03/10.22 (* end of lemma zenon_L357_ *) % 10.03/10.22 assert (zenon_L358_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H82 zenon_H149 zenon_H141. % 10.03/10.22 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H141. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Haa. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H142]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H142. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H82. % 10.03/10.22 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 10.03/10.22 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_Hab. apply refl_equal. % 10.03/10.22 apply zenon_H14a. apply sym_equal. exact zenon_H149. % 10.03/10.22 apply zenon_Hab. apply refl_equal. % 10.03/10.22 apply zenon_Hab. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L358_ *) % 10.03/10.22 assert (zenon_L359_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H13d zenon_H43 zenon_H2d zenon_H2a zenon_H1b9 zenon_Ha5 zenon_H105 zenon_Hb7. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.03/10.22 apply (zenon_L88_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.03/10.22 apply (zenon_L33_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.03/10.22 apply (zenon_L341_); trivial. % 10.03/10.22 apply (zenon_L235_); trivial. % 10.03/10.22 (* end of lemma zenon_L359_ *) % 10.03/10.22 assert (zenon_L360_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H19d zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_Ha5 zenon_H2a zenon_H12a. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_Hf7. zenon_intro zenon_H19e. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H171. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.22 apply (zenon_L326_); trivial. % 10.03/10.22 (* end of lemma zenon_L360_ *) % 10.03/10.22 assert (zenon_L361_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1a9 zenon_H43. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1a9). zenon_intro zenon_H86. zenon_intro zenon_H1aa. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_Hd0. zenon_intro zenon_Hb3. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.03/10.22 apply (zenon_L88_); trivial. % 10.03/10.22 (* end of lemma zenon_L361_ *) % 10.03/10.22 assert (zenon_L362_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1c2 zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_Ha5 zenon_H2a zenon_H12a. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H128. zenon_intro zenon_H1c3. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1c3). zenon_intro zenon_H166. zenon_intro zenon_H171. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.22 apply (zenon_L326_); trivial. % 10.03/10.22 (* end of lemma zenon_L362_ *) % 10.03/10.22 assert (zenon_L363_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H207 zenon_He8 zenon_H1f zenon_H2c zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H7f. zenon_intro zenon_H208. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H208). zenon_intro zenon_H112. zenon_intro zenon_H165. % 10.03/10.22 apply (zenon_L330_); trivial. % 10.03/10.22 (* end of lemma zenon_L363_ *) % 10.03/10.22 assert (zenon_L364_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> False). % 10.03/10.22 do 0 intro. intros zenon_Hc6 zenon_H4f. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_H89. zenon_intro zenon_Hc7. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_H9d. zenon_intro zenon_Hc8. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.03/10.22 apply (zenon_L205_); trivial. % 10.03/10.22 (* end of lemma zenon_L364_ *) % 10.03/10.22 assert (zenon_L365_ : ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2b2 zenon_H87 zenon_H2c. % 10.03/10.22 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 10.03/10.22 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2c. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H31. % 10.03/10.22 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.22 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e2) (e0)) = (e1)) = ((e3) = (e1))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H19f. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2b2. % 10.03/10.22 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.22 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 10.03/10.22 congruence. % 10.03/10.22 exact (zenon_H88 zenon_H87). % 10.03/10.22 apply zenon_H1d. apply refl_equal. % 10.03/10.22 apply zenon_H29. apply refl_equal. % 10.03/10.22 apply zenon_H29. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L365_ *) % 10.03/10.22 assert (zenon_L366_ : (~((e0) = (e1))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1e zenon_H2b3 zenon_Ha5. % 10.03/10.22 cut (((op (e2) (e2)) = (e1)) = ((e0) = (e1))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H1e. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2b3. % 10.03/10.22 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.22 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 10.03/10.22 congruence. % 10.03/10.22 exact (zenon_Ha6 zenon_Ha5). % 10.03/10.22 apply zenon_H1d. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L366_ *) % 10.03/10.22 assert (zenon_L367_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2b4 zenon_H2c zenon_H87 zenon_H4f zenon_Ha5 zenon_H1e zenon_H101 zenon_Hf7. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b5 ]. % 10.03/10.22 apply (zenon_L365_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H18c | zenon_intro zenon_H2b6 ]. % 10.03/10.22 apply (zenon_L205_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H102 ]. % 10.03/10.22 apply (zenon_L366_); trivial. % 10.03/10.22 apply (zenon_L69_); trivial. % 10.03/10.22 (* end of lemma zenon_L367_ *) % 10.03/10.22 assert (zenon_L368_ : (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H50 zenon_H112. % 10.03/10.22 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (op (e2) (e3))) = (e3))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H50. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H112. % 10.03/10.22 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.22 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2b7]. % 10.03/10.22 congruence. % 10.03/10.22 elim (classic ((op (e2) (op (e2) (e3))) = (op (e2) (op (e2) (e3))))); [ zenon_intro zenon_H218 | zenon_intro zenon_H219 ]. % 10.03/10.22 cut (((op (e2) (op (e2) (e3))) = (op (e2) (op (e2) (e3)))) = ((op (e2) (e3)) = (op (e2) (op (e2) (e3))))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2b7. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H218. % 10.03/10.22 cut (((op (e2) (op (e2) (e3))) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 10.03/10.22 cut (((op (e2) (op (e2) (e3))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2b8]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e2) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 10.03/10.22 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H22. apply refl_equal. % 10.03/10.22 exact (zenon_H1e1 zenon_H112). % 10.03/10.22 apply zenon_H219. apply refl_equal. % 10.03/10.22 apply zenon_H219. apply refl_equal. % 10.03/10.22 apply zenon_H29. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L368_ *) % 10.03/10.22 assert (zenon_L369_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H12f zenon_H11f zenon_H72 zenon_H2d zenon_Hd1 zenon_Heb zenon_Hde zenon_H50. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.03/10.22 apply (zenon_L78_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.03/10.22 apply (zenon_L79_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.03/10.22 apply (zenon_L259_); trivial. % 10.03/10.22 apply (zenon_L368_); trivial. % 10.03/10.22 (* end of lemma zenon_L369_ *) % 10.03/10.22 assert (zenon_L370_ : (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1c9 zenon_H2b zenon_He2. % 10.03/10.22 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e0) (e3)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H1c9. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2b. % 10.03/10.22 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 10.03/10.22 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H67. apply refl_equal. % 10.03/10.22 apply zenon_H10c. apply sym_equal. exact zenon_He2. % 10.03/10.22 (* end of lemma zenon_L370_ *) % 10.03/10.22 assert (zenon_L371_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H9d zenon_H73 zenon_H2a. % 10.03/10.22 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 10.03/10.22 cut (((e3) = (e3)) = ((e0) = (e3))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2a. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H31. % 10.03/10.22 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.22 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e1) (e0)) = (e0)) = ((e3) = (e0))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_Hdf. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H9d. % 10.03/10.22 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.03/10.22 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2b9]. % 10.03/10.22 congruence. % 10.03/10.22 exact (zenon_H2b9 zenon_H73). % 10.03/10.22 apply zenon_H34. apply refl_equal. % 10.03/10.22 apply zenon_H29. apply refl_equal. % 10.03/10.22 apply zenon_H29. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L371_ *) % 10.03/10.22 assert (zenon_L372_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> False). % 10.03/10.22 do 0 intro. intros zenon_Hd4 zenon_H4d. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_H97. zenon_intro zenon_Hd5. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_H9e. zenon_intro zenon_Hd6. % 10.03/10.22 apply (zenon_L197_); trivial. % 10.03/10.22 (* end of lemma zenon_L372_ *) % 10.03/10.22 assert (zenon_L373_ : (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H4d zenon_Ha5 zenon_H86. % 10.03/10.22 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (op (e2) (e0))) = (e0))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H4d. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Ha5. % 10.03/10.22 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (op (e2) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2ba]. % 10.03/10.22 congruence. % 10.03/10.22 elim (classic ((op (e2) (op (e2) (e0))) = (op (e2) (op (e2) (e0))))); [ zenon_intro zenon_H214 | zenon_intro zenon_H215 ]. % 10.03/10.22 cut (((op (e2) (op (e2) (e0))) = (op (e2) (op (e2) (e0)))) = ((op (e2) (e2)) = (op (e2) (op (e2) (e0))))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2ba. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H214. % 10.03/10.22 cut (((op (e2) (op (e2) (e0))) = (op (e2) (op (e2) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 10.03/10.22 cut (((op (e2) (op (e2) (e0))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2bb]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e2) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2bc]. % 10.03/10.22 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H22. apply refl_equal. % 10.03/10.22 exact (zenon_H2bc zenon_H86). % 10.03/10.22 apply zenon_H215. apply refl_equal. % 10.03/10.22 apply zenon_H215. apply refl_equal. % 10.03/10.22 apply zenon_H34. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L373_ *) % 10.03/10.22 assert (zenon_L374_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H197 zenon_H4f. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H197). zenon_intro zenon_H188. zenon_intro zenon_H198. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H198). zenon_intro zenon_H18c. zenon_intro zenon_Hd6. % 10.03/10.22 apply (zenon_L205_); trivial. % 10.03/10.22 (* end of lemma zenon_L374_ *) % 10.03/10.22 assert (zenon_L375_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H19b zenon_H4f. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H19b). zenon_intro zenon_H188. zenon_intro zenon_H19c. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H19c). zenon_intro zenon_H18c. zenon_intro zenon_H16b. % 10.03/10.22 apply (zenon_L205_); trivial. % 10.03/10.22 (* end of lemma zenon_L375_ *) % 10.03/10.22 assert (zenon_L376_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e2) (e2)) = (e0)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1ad zenon_H4d zenon_Ha5. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H86. zenon_intro zenon_H1ae. % 10.03/10.22 apply (zenon_L373_); trivial. % 10.03/10.22 (* end of lemma zenon_L376_ *) % 10.03/10.22 assert (zenon_L377_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1b3 zenon_H4f. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_Hd2. zenon_intro zenon_H1b4. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H1b4). zenon_intro zenon_Hd7. zenon_intro zenon_Hc8. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.03/10.22 apply (zenon_L205_); trivial. % 10.03/10.22 (* end of lemma zenon_L377_ *) % 10.03/10.22 assert (zenon_L378_ : (~((op (e2) (op (e2) (e1))) = (e1))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H4f zenon_H2b3 zenon_Hd2. % 10.03/10.22 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (op (e2) (e1))) = (e1))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H4f. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2b3. % 10.03/10.22 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2bd]. % 10.03/10.22 congruence. % 10.03/10.22 elim (classic ((op (e2) (op (e2) (e1))) = (op (e2) (op (e2) (e1))))); [ zenon_intro zenon_H21f | zenon_intro zenon_H220 ]. % 10.03/10.22 cut (((op (e2) (op (e2) (e1))) = (op (e2) (op (e2) (e1)))) = ((op (e2) (e2)) = (op (e2) (op (e2) (e1))))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2bd. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H21f. % 10.03/10.22 cut (((op (e2) (op (e2) (e1))) = (op (e2) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H220]. % 10.03/10.22 cut (((op (e2) (op (e2) (e1))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2be]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e2) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2bf]. % 10.03/10.22 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H22. apply refl_equal. % 10.03/10.22 exact (zenon_H2bf zenon_Hd2). % 10.03/10.22 apply zenon_H220. apply refl_equal. % 10.03/10.22 apply zenon_H220. apply refl_equal. % 10.03/10.22 apply zenon_H1d. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L378_ *) % 10.03/10.22 assert (zenon_L379_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2b4 zenon_H2c zenon_H87 zenon_Hd2 zenon_H4f zenon_H101 zenon_Hf7. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b5 ]. % 10.03/10.22 apply (zenon_L365_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H18c | zenon_intro zenon_H2b6 ]. % 10.03/10.22 apply (zenon_L205_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H102 ]. % 10.03/10.22 apply (zenon_L378_); trivial. % 10.03/10.22 apply (zenon_L69_); trivial. % 10.03/10.22 (* end of lemma zenon_L379_ *) % 10.03/10.22 assert (zenon_L380_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H22e zenon_H74 zenon_H12a zenon_H2a zenon_Ha5 zenon_Hd1 zenon_H72 zenon_H11f zenon_H12f zenon_H30 zenon_Hd7 zenon_He2 zenon_H105. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.22 apply (zenon_L23_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.22 apply (zenon_L326_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.22 apply (zenon_L251_); trivial. % 10.03/10.22 apply (zenon_L71_); trivial. % 10.03/10.22 (* end of lemma zenon_L380_ *) % 10.03/10.22 assert (zenon_L381_ : (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e3) (e0)) = (e0)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H5a zenon_H90. % 10.03/10.22 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (op (e3) (e0))) = (e0))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H5a. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H90. % 10.03/10.22 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.03/10.22 cut (((op (e3) (e0)) = (op (e3) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2c0]. % 10.03/10.22 congruence. % 10.03/10.22 elim (classic ((op (e3) (op (e3) (e0))) = (op (e3) (op (e3) (e0))))); [ zenon_intro zenon_H150 | zenon_intro zenon_H151 ]. % 10.03/10.22 cut (((op (e3) (op (e3) (e0))) = (op (e3) (op (e3) (e0)))) = ((op (e3) (e0)) = (op (e3) (op (e3) (e0))))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2c0. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H150. % 10.03/10.22 cut (((op (e3) (op (e3) (e0))) = (op (e3) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 10.03/10.22 cut (((op (e3) (op (e3) (e0))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2c1]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e3) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H2c2]. % 10.03/10.22 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H29. apply refl_equal. % 10.03/10.22 exact (zenon_H2c2 zenon_H90). % 10.03/10.22 apply zenon_H151. apply refl_equal. % 10.03/10.22 apply zenon_H151. apply refl_equal. % 10.03/10.22 apply zenon_H34. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L381_ *) % 10.03/10.22 assert (zenon_L382_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H7a zenon_H89 zenon_H94. % 10.03/10.22 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H7a. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H89. % 10.03/10.22 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H95]. % 10.03/10.22 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_Ha4. apply refl_equal. % 10.03/10.22 apply zenon_H95. apply sym_equal. exact zenon_H94. % 10.03/10.22 (* end of lemma zenon_L382_ *) % 10.03/10.22 assert (zenon_L383_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H7e zenon_Ha5 zenon_H98. % 10.03/10.22 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H7e. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Ha5. % 10.03/10.22 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 apply zenon_H99. apply sym_equal. exact zenon_H98. % 10.03/10.22 (* end of lemma zenon_L383_ *) % 10.03/10.22 assert (zenon_L384_ : (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H30 zenon_H2b zenon_H24. % 10.03/10.22 cut (((op (e0) (e0)) = (e3)) = ((e2) = (e3))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H30. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2b. % 10.03/10.22 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.22 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2c3]. % 10.03/10.22 congruence. % 10.03/10.22 exact (zenon_H2c3 zenon_H24). % 10.03/10.22 apply zenon_H29. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L384_ *) % 10.03/10.22 assert (zenon_L385_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> False). % 10.03/10.22 do 0 intro. intros zenon_Hbe zenon_H24 zenon_H69. % 10.03/10.22 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_Hbe. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H24. % 10.03/10.22 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 10.03/10.22 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H67. apply refl_equal. % 10.03/10.22 apply zenon_H1da. apply sym_equal. exact zenon_H69. % 10.03/10.22 (* end of lemma zenon_L385_ *) % 10.03/10.22 assert (zenon_L386_ : (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2c4 zenon_Hd2 zenon_H149. % 10.03/10.22 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e3) (e1)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2c4. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Hd2. % 10.03/10.22 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 10.03/10.22 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2c5]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H2c5. apply refl_equal. % 10.03/10.22 apply zenon_H14a. apply sym_equal. exact zenon_H149. % 10.03/10.22 (* end of lemma zenon_L386_ *) % 10.03/10.22 assert (zenon_L387_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H192 zenon_H24 zenon_H1d4 zenon_Hd2 zenon_H2c4 zenon_Hd7 zenon_H1ec zenon_Ha7 zenon_H23. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.03/10.22 apply (zenon_L217_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.03/10.22 apply (zenon_L386_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.03/10.22 apply (zenon_L219_); trivial. % 10.03/10.22 apply (zenon_L125_); trivial. % 10.03/10.22 (* end of lemma zenon_L387_ *) % 10.03/10.22 assert (zenon_L388_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> False). % 10.03/10.22 do 0 intro. intros zenon_Hd1 zenon_H27 zenon_H18c. % 10.03/10.22 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_Hd1. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H27. % 10.03/10.22 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2c6]. % 10.03/10.22 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H61. apply refl_equal. % 10.03/10.22 apply zenon_H2c6. apply sym_equal. exact zenon_H18c. % 10.03/10.22 (* end of lemma zenon_L388_ *) % 10.03/10.22 assert (zenon_L389_ : ((op (e2) (e2)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2f zenon_H121 zenon_H2ac. % 10.03/10.22 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hec | zenon_intro zenon_H81 ]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2ac. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Hec. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2ad]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e2) (e1)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2ad. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2f. % 10.03/10.22 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 apply zenon_H122. apply sym_equal. exact zenon_H121. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L389_ *) % 10.03/10.22 assert (zenon_L390_ : (((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 (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2c7 zenon_H89 zenon_Ha1 zenon_H27 zenon_Hd1 zenon_H149 zenon_H2c4 zenon_H2f zenon_H2ac. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H2c8 ]. % 10.03/10.22 apply (zenon_L41_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2c8); [ zenon_intro zenon_H18c | zenon_intro zenon_H2c9 ]. % 10.03/10.22 apply (zenon_L388_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2c9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H121 ]. % 10.03/10.22 apply (zenon_L386_); trivial. % 10.03/10.22 apply (zenon_L389_); trivial. % 10.03/10.22 (* end of lemma zenon_L390_ *) % 10.03/10.22 assert (zenon_L391_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (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 (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2ca zenon_H64 zenon_H25 zenon_H23 zenon_Ha7 zenon_H1ec zenon_Hd7 zenon_H1d4 zenon_H24 zenon_H192 zenon_H2c7 zenon_H89 zenon_Ha1 zenon_H27 zenon_Hd1 zenon_H2c4 zenon_H2f zenon_H2ac. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.03/10.22 apply (zenon_L19_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.03/10.22 apply (zenon_L5_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.03/10.22 apply (zenon_L387_); trivial. % 10.03/10.22 apply (zenon_L390_); trivial. % 10.03/10.22 (* end of lemma zenon_L391_ *) % 10.03/10.22 assert (zenon_L392_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H12c zenon_Ha9 zenon_Ha7 zenon_Hf3 zenon_H12a zenon_H101 zenon_H106 zenon_H127 zenon_H2f. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.03/10.22 apply (zenon_L43_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.03/10.22 apply (zenon_L155_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.03/10.22 apply (zenon_L241_); trivial. % 10.03/10.22 apply (zenon_L293_); trivial. % 10.03/10.22 (* end of lemma zenon_L392_ *) % 10.03/10.22 assert (zenon_L393_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (op (e0) (e3))) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H118 zenon_He1 zenon_H2c zenon_Hf7 zenon_H2f zenon_H127 zenon_Ha7 zenon_H2a. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_He2 | zenon_intro zenon_H119 ]. % 10.03/10.22 apply (zenon_L61_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H109 | zenon_intro zenon_H11a ]. % 10.03/10.22 apply (zenon_L132_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H112 | zenon_intro zenon_H52 ]. % 10.03/10.22 apply (zenon_L293_); trivial. % 10.03/10.22 apply (zenon_L75_); trivial. % 10.03/10.22 (* end of lemma zenon_L393_ *) % 10.03/10.22 assert (zenon_L394_ : (~((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2cd zenon_Ha7. % 10.03/10.22 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.22 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H2ce]. % 10.03/10.22 congruence. % 10.03/10.22 exact (zenon_H2ce zenon_Ha7). % 10.03/10.22 apply zenon_H29. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L394_ *) % 10.03/10.22 assert (zenon_L395_ : ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> (~((e2) = (op (op (e3) (e3)) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_Hf4 zenon_Ha7 zenon_H2cf. % 10.03/10.22 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H2d0 | zenon_intro zenon_H2d1 ]. % 10.03/10.22 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e2) = (op (op (e3) (e3)) (e3)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2cf. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2d0. % 10.03/10.22 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d1]. % 10.03/10.22 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2d2]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e0) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2d2. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Hf4. % 10.03/10.22 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.22 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d3]. % 10.03/10.22 congruence. % 10.03/10.22 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H2d0 | zenon_intro zenon_H2d1 ]. % 10.03/10.22 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2d3. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2d0. % 10.03/10.22 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d1]. % 10.03/10.22 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2cd]. % 10.03/10.22 congruence. % 10.03/10.22 apply (zenon_L394_); trivial. % 10.03/10.22 apply zenon_H2d1. apply refl_equal. % 10.03/10.22 apply zenon_H2d1. apply refl_equal. % 10.03/10.22 apply zenon_H22. apply refl_equal. % 10.03/10.22 apply zenon_H2d1. apply refl_equal. % 10.03/10.22 apply zenon_H2d1. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L395_ *) % 10.03/10.22 assert (zenon_L396_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2d4 zenon_Hf4 zenon_Ha7. % 10.03/10.22 apply (zenon_notand_s _ _ ax12); [ zenon_intro zenon_H2d6 | zenon_intro zenon_H2d5 ]. % 10.03/10.22 elim (classic ((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))); [ zenon_intro zenon_H2d7 | zenon_intro zenon_H2d8 ]. % 10.03/10.22 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3)))) = ((e1) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2d6. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2d7. % 10.03/10.22 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2d8]. % 10.03/10.22 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2d9]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e0) (e2)) = (e1)) = ((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (e1))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2d9. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2d4. % 10.03/10.22 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.22 cut (((op (e0) (e2)) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2da]. % 10.03/10.22 congruence. % 10.03/10.22 elim (classic ((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))); [ zenon_intro zenon_H2d7 | zenon_intro zenon_H2d8 ]. % 10.03/10.22 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3)))) = ((op (e0) (e2)) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2da. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2d7. % 10.03/10.22 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2d8]. % 10.03/10.22 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2db]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2d2]. % 10.03/10.22 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H2ce]. % 10.03/10.22 congruence. % 10.03/10.22 exact (zenon_H2ce zenon_Ha7). % 10.03/10.22 cut (((op (e0) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2d2. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Hf4. % 10.03/10.22 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.22 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d3]. % 10.03/10.22 congruence. % 10.03/10.22 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H2d0 | zenon_intro zenon_H2d1 ]. % 10.03/10.22 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2d3. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2d0. % 10.03/10.22 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d1]. % 10.03/10.22 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2cd]. % 10.03/10.22 congruence. % 10.03/10.22 apply (zenon_L394_); trivial. % 10.03/10.22 apply zenon_H2d1. apply refl_equal. % 10.03/10.22 apply zenon_H2d1. apply refl_equal. % 10.03/10.22 apply zenon_H22. apply refl_equal. % 10.03/10.22 apply zenon_H2d8. apply refl_equal. % 10.03/10.22 apply zenon_H2d8. apply refl_equal. % 10.03/10.22 apply zenon_H1d. apply refl_equal. % 10.03/10.22 apply zenon_H2d8. apply refl_equal. % 10.03/10.22 apply zenon_H2d8. apply refl_equal. % 10.03/10.22 apply (zenon_notand_s _ _ zenon_H2d5); [ zenon_intro zenon_H2dc | zenon_intro zenon_H2cf ]. % 10.03/10.22 apply zenon_H2dc. apply sym_equal. exact zenon_Ha7. % 10.03/10.22 apply (zenon_L395_); trivial. % 10.03/10.22 (* end of lemma zenon_L396_ *) % 10.03/10.22 assert (zenon_L397_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1ce zenon_Hb8 zenon_H102 zenon_H12a zenon_Ha7 zenon_H2d4 zenon_H109 zenon_H105. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H1cf ]. % 10.03/10.22 apply (zenon_L47_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1d0 ]. % 10.03/10.22 apply (zenon_L155_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hf4 | zenon_intro zenon_He2 ]. % 10.03/10.22 apply (zenon_L396_); trivial. % 10.03/10.22 apply (zenon_L71_); trivial. % 10.03/10.22 (* end of lemma zenon_L397_ *) % 10.03/10.22 assert (zenon_L398_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2a8 zenon_Hbe zenon_H2ac zenon_H2c4 zenon_Hd1 zenon_H27 zenon_Ha1 zenon_H89 zenon_H2c7 zenon_H192 zenon_H24 zenon_H1d4 zenon_H1ec zenon_H23 zenon_H25 zenon_H64 zenon_H2ca zenon_H12c zenon_Ha9 zenon_Ha7 zenon_Hf3 zenon_H12a zenon_H101 zenon_H127 zenon_H2f. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.03/10.22 apply (zenon_L385_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.03/10.22 apply (zenon_L5_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.03/10.22 apply (zenon_L391_); trivial. % 10.03/10.22 apply (zenon_L392_); trivial. % 10.03/10.22 (* end of lemma zenon_L398_ *) % 10.03/10.22 assert (zenon_L399_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2dd zenon_H24 zenon_H86. % 10.03/10.22 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2dd. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H24. % 10.03/10.22 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2de]. % 10.03/10.22 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H67. apply refl_equal. % 10.03/10.22 apply zenon_H2de. apply sym_equal. exact zenon_H86. % 10.03/10.22 (* end of lemma zenon_L399_ *) % 10.03/10.22 assert (zenon_L400_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e2)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1cb zenon_H24 zenon_H2dd zenon_H149 zenon_H2c4 zenon_H1b9 zenon_Hd7 zenon_H50 zenon_H2f. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.03/10.22 apply (zenon_L399_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.03/10.22 apply (zenon_L386_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.03/10.22 apply (zenon_L145_); trivial. % 10.03/10.22 apply (zenon_L199_); trivial. % 10.03/10.22 (* end of lemma zenon_L400_ *) % 10.03/10.22 assert (zenon_L401_ : (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H187 zenon_H2d zenon_H1f0. % 10.03/10.22 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e1) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H187. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2d. % 10.03/10.22 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 10.03/10.22 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H61. apply refl_equal. % 10.03/10.22 apply zenon_H1f1. apply sym_equal. exact zenon_H1f0. % 10.03/10.22 (* end of lemma zenon_L401_ *) % 10.03/10.22 assert (zenon_L402_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1d4 zenon_H2b zenon_H72. % 10.03/10.22 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H1d4. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2b. % 10.03/10.22 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H29e]. % 10.03/10.22 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H67. apply refl_equal. % 10.03/10.22 apply zenon_H29e. apply sym_equal. exact zenon_H72. % 10.03/10.22 (* end of lemma zenon_L402_ *) % 10.03/10.22 assert (zenon_L403_ : ((op (e3) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H79 zenon_H121 zenon_H2c4. % 10.03/10.22 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H7b | zenon_intro zenon_H7c ]. % 10.03/10.22 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e2) (e1)) = (op (e3) (e1)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2c4. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H7b. % 10.03/10.22 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 10.03/10.22 cut (((op (e3) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2df]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e2) (e1)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2df. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H79. % 10.03/10.22 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 10.03/10.22 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H7c. apply refl_equal. % 10.03/10.22 apply zenon_H122. apply sym_equal. exact zenon_H121. % 10.03/10.22 apply zenon_H7c. apply refl_equal. % 10.03/10.22 apply zenon_H7c. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L403_ *) % 10.03/10.22 assert (zenon_L404_ : ((op (e3) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H7f zenon_H1f0 zenon_H1ec. % 10.03/10.22 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H2e0 | zenon_intro zenon_H2e1 ]. % 10.03/10.22 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e1) (e2)) = (op (e3) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H1ec. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2e0. % 10.03/10.22 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2e1]. % 10.03/10.22 cut (((op (e3) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2e2]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e1) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2e2. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H7f. % 10.03/10.22 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 10.03/10.22 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2e1]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H2e1. apply refl_equal. % 10.03/10.22 apply zenon_H1f1. apply sym_equal. exact zenon_H1f0. % 10.03/10.22 apply zenon_H2e1. apply refl_equal. % 10.03/10.22 apply zenon_H2e1. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L404_ *) % 10.03/10.22 assert (zenon_L405_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H83 zenon_H2b zenon_H1d4 zenon_H2c4 zenon_H121 zenon_H1ec zenon_H1f0 zenon_Ha7 zenon_H2a. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.03/10.22 apply (zenon_L402_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.03/10.22 apply (zenon_L403_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.03/10.22 apply (zenon_L404_); trivial. % 10.03/10.22 apply (zenon_L75_); trivial. % 10.03/10.22 (* end of lemma zenon_L405_ *) % 10.03/10.22 assert (zenon_L406_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2dd zenon_H2b zenon_H87. % 10.03/10.22 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2dd. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2b. % 10.03/10.22 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 10.03/10.22 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H67. apply refl_equal. % 10.03/10.22 apply zenon_H117. apply sym_equal. exact zenon_H87. % 10.03/10.22 (* end of lemma zenon_L406_ *) % 10.03/10.22 assert (zenon_L407_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H22e zenon_H2b zenon_Hbe zenon_H27 zenon_H2c zenon_H1ec zenon_H7f zenon_H112 zenon_H101. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.22 apply (zenon_L316_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.22 apply (zenon_L8_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.22 apply (zenon_L404_); trivial. % 10.03/10.22 apply (zenon_L80_); trivial. % 10.03/10.22 (* end of lemma zenon_L407_ *) % 10.03/10.22 assert (zenon_L408_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (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 (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1f6 zenon_H1ea zenon_Ha7 zenon_H1d5 zenon_H1f5 zenon_H2e zenon_H7e zenon_H22e zenon_H2b zenon_Hbe zenon_H27 zenon_H2c zenon_H1ec zenon_H112 zenon_H101. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.03/10.22 apply (zenon_L171_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.03/10.22 apply (zenon_L215_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.03/10.22 apply (zenon_L226_); trivial. % 10.03/10.22 apply (zenon_L407_); trivial. % 10.03/10.22 (* end of lemma zenon_L408_ *) % 10.03/10.22 assert (zenon_L409_ : (~((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2e3 zenon_H2b. % 10.03/10.22 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.03/10.22 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2e4]. % 10.03/10.22 congruence. % 10.03/10.22 exact (zenon_H2e4 zenon_H2b). % 10.03/10.22 apply zenon_H34. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L409_ *) % 10.03/10.22 assert (zenon_L410_ : ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (op (op (e0) (e0)) (e0)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H91 zenon_H2b zenon_H2e5. % 10.03/10.22 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H286 | zenon_intro zenon_H287 ]. % 10.03/10.22 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e2) = (op (op (e0) (e0)) (e0)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2e5. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H286. % 10.03/10.22 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 10.03/10.22 cut (((op (op (e0) (e0)) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2e6]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e3) (e0)) = (e2)) = ((op (op (e0) (e0)) (e0)) = (e2))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2e6. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H91. % 10.03/10.22 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.22 cut (((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2e7]. % 10.03/10.22 congruence. % 10.03/10.22 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H286 | zenon_intro zenon_H287 ]. % 10.03/10.22 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2e7. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H286. % 10.03/10.22 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 10.03/10.22 cut (((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2e3]. % 10.03/10.22 congruence. % 10.03/10.22 apply (zenon_L409_); trivial. % 10.03/10.22 apply zenon_H287. apply refl_equal. % 10.03/10.22 apply zenon_H287. apply refl_equal. % 10.03/10.22 apply zenon_H22. apply refl_equal. % 10.03/10.22 apply zenon_H287. apply refl_equal. % 10.03/10.22 apply zenon_H287. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L410_ *) % 10.03/10.22 assert (zenon_L411_ : ((op (e3) (e2)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1ed zenon_H91 zenon_H2b. % 10.03/10.22 apply (zenon_notand_s _ _ ax17); [ zenon_intro zenon_H2e9 | zenon_intro zenon_H2e8 ]. % 10.03/10.22 elim (classic ((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))); [ zenon_intro zenon_H28c | zenon_intro zenon_H28d ]. % 10.03/10.22 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0)))) = ((e1) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2e9. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H28c. % 10.03/10.22 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 10.03/10.22 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2ea]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e3) (e2)) = (e1)) = ((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (e1))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2ea. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H1ed. % 10.03/10.22 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.22 cut (((op (e3) (e2)) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2eb]. % 10.03/10.22 congruence. % 10.03/10.22 elim (classic ((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))); [ zenon_intro zenon_H28c | zenon_intro zenon_H28d ]. % 10.03/10.22 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0)))) = ((op (e3) (e2)) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2eb. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H28c. % 10.03/10.22 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 10.03/10.22 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2ec]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (op (e0) (e0)) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2e6]. % 10.03/10.22 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2e4]. % 10.03/10.22 congruence. % 10.03/10.22 exact (zenon_H2e4 zenon_H2b). % 10.03/10.22 cut (((op (e3) (e0)) = (e2)) = ((op (op (e0) (e0)) (e0)) = (e2))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2e6. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H91. % 10.03/10.22 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.22 cut (((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2e7]. % 10.03/10.22 congruence. % 10.03/10.22 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H286 | zenon_intro zenon_H287 ]. % 10.03/10.22 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2e7. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H286. % 10.03/10.22 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 10.03/10.22 cut (((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2e3]. % 10.03/10.22 congruence. % 10.03/10.22 apply (zenon_L409_); trivial. % 10.03/10.22 apply zenon_H287. apply refl_equal. % 10.03/10.22 apply zenon_H287. apply refl_equal. % 10.03/10.22 apply zenon_H22. apply refl_equal. % 10.03/10.22 apply zenon_H28d. apply refl_equal. % 10.03/10.22 apply zenon_H28d. apply refl_equal. % 10.03/10.22 apply zenon_H1d. apply refl_equal. % 10.03/10.22 apply zenon_H28d. apply refl_equal. % 10.03/10.22 apply zenon_H28d. apply refl_equal. % 10.03/10.22 apply (zenon_notand_s _ _ zenon_H2e8); [ zenon_intro zenon_H2ed | zenon_intro zenon_H2e5 ]. % 10.03/10.22 apply zenon_H2ed. apply sym_equal. exact zenon_H2b. % 10.03/10.22 apply (zenon_L410_); trivial. % 10.03/10.22 (* end of lemma zenon_L411_ *) % 10.03/10.22 assert (zenon_L412_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (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 (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1f6 zenon_H1ea zenon_Ha7 zenon_H91 zenon_H2e zenon_H7e zenon_H22e zenon_H2b zenon_Hbe zenon_H27 zenon_H2c zenon_H1ec zenon_H112 zenon_H101. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.03/10.22 apply (zenon_L171_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.03/10.22 apply (zenon_L411_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.03/10.22 apply (zenon_L226_); trivial. % 10.03/10.22 apply (zenon_L407_); trivial. % 10.03/10.22 (* end of lemma zenon_L412_ *) % 10.03/10.22 assert (zenon_L413_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H12f zenon_H2dd zenon_H2c4 zenon_H79 zenon_H30 zenon_H1db zenon_H16c zenon_H1f5 zenon_H101 zenon_H1ec zenon_H2c zenon_H27 zenon_Hbe zenon_H22e zenon_H7e zenon_H2e zenon_Ha7 zenon_H1ea zenon_H1f6 zenon_H1d4 zenon_H2b. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.03/10.22 apply (zenon_L406_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.03/10.22 apply (zenon_L403_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.03/10.22 apply (zenon_L9_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1db); [ zenon_intro zenon_H90 | zenon_intro zenon_H1df ]. % 10.03/10.22 apply (zenon_L108_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H1e0 ]. % 10.03/10.22 apply (zenon_L408_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H91 | zenon_intro zenon_H72 ]. % 10.03/10.22 apply (zenon_L412_); trivial. % 10.03/10.22 apply (zenon_L402_); trivial. % 10.03/10.22 (* end of lemma zenon_L413_ *) % 10.03/10.22 assert (zenon_L414_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2ee zenon_H64 zenon_H187 zenon_H2a zenon_H1f0 zenon_H83 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H30 zenon_H1db zenon_H16c zenon_H1f5 zenon_H101 zenon_H1ec zenon_H2c zenon_H27 zenon_Hbe zenon_H22e zenon_H7e zenon_H2e zenon_Ha7 zenon_H1ea zenon_H1f6 zenon_H1d4 zenon_H2b. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.03/10.22 apply (zenon_L22_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.03/10.22 apply (zenon_L401_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.03/10.22 apply (zenon_L405_); trivial. % 10.03/10.22 apply (zenon_L413_); trivial. % 10.03/10.22 (* end of lemma zenon_L414_ *) % 10.03/10.22 assert (zenon_L415_ : (((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) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1f2 zenon_H97 zenon_H13a zenon_H27 zenon_H187 zenon_H1b9 zenon_H2e zenon_H7f zenon_H1ec. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1f2); [ zenon_intro zenon_H13b | zenon_intro zenon_H1f3 ]. % 10.03/10.22 apply (zenon_L89_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1f3); [ zenon_intro zenon_H188 | zenon_intro zenon_H1f4 ]. % 10.03/10.22 apply (zenon_L119_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H1f0 ]. % 10.03/10.22 apply (zenon_L145_); trivial. % 10.03/10.22 apply (zenon_L404_); trivial. % 10.03/10.22 (* end of lemma zenon_L415_ *) % 10.03/10.22 assert (zenon_L416_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H12c zenon_Ha9 zenon_Ha7 zenon_Hf3 zenon_H12a zenon_H106 zenon_H22e zenon_H2b zenon_Hbe zenon_H27 zenon_H2c zenon_H1ec zenon_H7f zenon_H101. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.03/10.22 apply (zenon_L43_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.03/10.22 apply (zenon_L155_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.03/10.22 apply (zenon_L241_); trivial. % 10.03/10.22 apply (zenon_L407_); trivial. % 10.03/10.22 (* end of lemma zenon_L416_ *) % 10.03/10.22 assert (zenon_L417_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((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)) = (e1)) -> (~((op (e2) (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)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2f1 zenon_H25 zenon_H101 zenon_H7f zenon_H1ec zenon_H2c zenon_H27 zenon_Hbe zenon_H2b zenon_H22e zenon_H12a zenon_Hf3 zenon_Ha9 zenon_H12c zenon_H2e zenon_H127 zenon_Ha7 zenon_H23. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2f1); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H2f2 ]. % 10.03/10.22 apply (zenon_L66_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2f2); [ zenon_intro zenon_H106 | zenon_intro zenon_H2f3 ]. % 10.03/10.22 apply (zenon_L416_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H128 | zenon_intro zenon_H82 ]. % 10.03/10.22 apply (zenon_L83_); trivial. % 10.03/10.22 apply (zenon_L125_); trivial. % 10.03/10.22 (* end of lemma zenon_L417_ *) % 10.03/10.22 assert (zenon_L418_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (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))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1ce zenon_Hb8 zenon_H23 zenon_H127 zenon_H2e zenon_H12c zenon_Ha9 zenon_H12a zenon_H22e zenon_Hbe zenon_H27 zenon_H2c zenon_H1ec zenon_H7f zenon_H101 zenon_H25 zenon_H2f1 zenon_Ha7 zenon_H2d4 zenon_H1c9 zenon_H2b. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H1cf ]. % 10.03/10.22 apply (zenon_L47_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1d0 ]. % 10.03/10.22 apply (zenon_L417_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hf4 | zenon_intro zenon_He2 ]. % 10.03/10.22 apply (zenon_L396_); trivial. % 10.03/10.22 apply (zenon_L370_); trivial. % 10.03/10.22 (* end of lemma zenon_L418_ *) % 10.03/10.22 assert (zenon_L419_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2f4 zenon_H1b9 zenon_H187 zenon_H13a zenon_H1f2 zenon_H1c9 zenon_Ha7 zenon_H2f1 zenon_H25 zenon_H101 zenon_H7f zenon_H1ec zenon_H2c zenon_H27 zenon_Hbe zenon_H22e zenon_H12a zenon_Ha9 zenon_H12c zenon_H127 zenon_H23 zenon_Hb8 zenon_H1ce zenon_Heb zenon_H2e zenon_Hef zenon_H2b. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2f4); [ zenon_intro zenon_H97 | zenon_intro zenon_H2f5 ]. % 10.03/10.22 apply (zenon_L415_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H2d4 | zenon_intro zenon_H2f6 ]. % 10.03/10.22 apply (zenon_L418_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hde ]. % 10.03/10.22 apply (zenon_L63_); trivial. % 10.03/10.22 apply (zenon_L64_); trivial. % 10.03/10.22 (* end of lemma zenon_L419_ *) % 10.03/10.22 assert (zenon_L420_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (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) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H154 zenon_H1d4 zenon_H1f6 zenon_H1ea zenon_H7e zenon_H22e zenon_Hbe zenon_H1ec zenon_H101 zenon_H1f5 zenon_H16c zenon_H1db zenon_H2c4 zenon_H2dd zenon_H12f zenon_H2f7 zenon_H83 zenon_H2f4 zenon_H1b9 zenon_H187 zenon_H13a zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H25 zenon_H12a zenon_Ha9 zenon_H12c zenon_H127 zenon_H23 zenon_Hb8 zenon_H1ce zenon_Heb zenon_Hef zenon_H110 zenon_H64 zenon_H2ee zenon_H27 zenon_H2c zenon_H30 zenon_H2e zenon_Ha7 zenon_H2a. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.22 apply (zenon_L316_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.22 apply (zenon_L8_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.22 apply (zenon_L414_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.03/10.22 apply (zenon_L22_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.03/10.22 apply (zenon_L73_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.03/10.22 apply (zenon_L64_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.03/10.22 apply (zenon_L405_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.03/10.22 apply (zenon_L9_); trivial. % 10.03/10.22 apply (zenon_L419_); trivial. % 10.03/10.22 apply (zenon_L413_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.03/10.22 apply (zenon_L8_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.03/10.22 apply (zenon_L9_); trivial. % 10.03/10.22 apply (zenon_L75_); trivial. % 10.03/10.22 (* end of lemma zenon_L420_ *) % 10.03/10.22 assert (zenon_L421_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1cb zenon_H24 zenon_H149 zenon_H2a zenon_Ha7 zenon_H30 zenon_H2c zenon_H27 zenon_H2ee zenon_H64 zenon_H110 zenon_Hef zenon_Heb zenon_H1ce zenon_Hb8 zenon_H23 zenon_H127 zenon_H12c zenon_Ha9 zenon_H12a zenon_H25 zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H13a zenon_H187 zenon_H1b9 zenon_H2f4 zenon_H83 zenon_H2f7 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1db zenon_H16c zenon_H1f5 zenon_H1ec zenon_Hbe zenon_H22e zenon_H7e zenon_H1ea zenon_H1f6 zenon_H1d4 zenon_H154 zenon_H106 zenon_H101. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.03/10.22 apply (zenon_L399_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.03/10.22 apply (zenon_L386_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.03/10.22 apply (zenon_L420_); trivial. % 10.03/10.22 apply (zenon_L241_); trivial. % 10.03/10.22 (* end of lemma zenon_L421_ *) % 10.03/10.22 assert (zenon_L422_ : (((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) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H1f2 zenon_H97 zenon_H13a zenon_H27 zenon_H187 zenon_H166 zenon_H1ec zenon_H2f zenon_H1b9. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1f2); [ zenon_intro zenon_H13b | zenon_intro zenon_H1f3 ]. % 10.03/10.22 apply (zenon_L89_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1f3); [ zenon_intro zenon_H188 | zenon_intro zenon_H1f4 ]. % 10.03/10.22 apply (zenon_L119_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H1f0 ]. % 10.03/10.22 apply (zenon_L219_); trivial. % 10.03/10.22 apply (zenon_L174_); trivial. % 10.03/10.22 (* end of lemma zenon_L422_ *) % 10.03/10.22 assert (zenon_L423_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (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) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (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) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((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))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H192 zenon_H101 zenon_H106 zenon_H154 zenon_H1d4 zenon_H1f6 zenon_H1ea zenon_H7e zenon_H22e zenon_Hbe zenon_H1f5 zenon_H16c zenon_H1db zenon_H2c4 zenon_H2dd zenon_H12f zenon_H2f7 zenon_H83 zenon_H2f4 zenon_H1c9 zenon_H2f1 zenon_H25 zenon_H12a zenon_Ha9 zenon_H12c zenon_H127 zenon_Hb8 zenon_H1ce zenon_Heb zenon_Hef zenon_H110 zenon_H64 zenon_H2ee zenon_H2c zenon_H30 zenon_H2a zenon_H24 zenon_H1cb zenon_H1b9 zenon_H2f zenon_H1ec zenon_H187 zenon_H27 zenon_H13a zenon_H97 zenon_H1f2 zenon_Ha7 zenon_H23. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.03/10.22 apply (zenon_L217_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.03/10.22 apply (zenon_L421_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.03/10.22 apply (zenon_L422_); trivial. % 10.03/10.22 apply (zenon_L125_); trivial. % 10.03/10.22 (* end of lemma zenon_L423_ *) % 10.03/10.22 assert (zenon_L424_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H6d zenon_H23 zenon_H24. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H20. zenon_intro zenon_H6e. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H20. zenon_intro zenon_H6f. % 10.03/10.22 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H20. zenon_intro zenon_H20. % 10.03/10.22 apply (zenon_L4_); trivial. % 10.03/10.22 (* end of lemma zenon_L424_ *) % 10.03/10.22 assert (zenon_L425_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.22 do 0 intro. intros zenon_Hb1 zenon_H23 zenon_H24. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_H20. zenon_intro zenon_Hb2. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hb2). zenon_intro zenon_H20. zenon_intro zenon_Hb3. % 10.03/10.22 apply (zenon_L4_); trivial. % 10.03/10.22 (* end of lemma zenon_L425_ *) % 10.03/10.22 assert (zenon_L426_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.22 do 0 intro. intros zenon_Hb4 zenon_H23 zenon_H24. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hb4). zenon_intro zenon_H20. zenon_intro zenon_Hb5. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hb5). zenon_intro zenon_H20. zenon_intro zenon_Hb6. % 10.03/10.22 apply (zenon_L4_); trivial. % 10.03/10.22 (* end of lemma zenon_L426_ *) % 10.03/10.22 assert (zenon_L427_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H74 zenon_H68 zenon_H1d5. % 10.03/10.22 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e3) (e0)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H74. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H68. % 10.03/10.22 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 10.03/10.22 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_Ha0. apply refl_equal. % 10.03/10.22 apply zenon_H1d6. apply sym_equal. exact zenon_H1d5. % 10.03/10.22 (* end of lemma zenon_L427_ *) % 10.03/10.22 assert (zenon_L428_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H7a zenon_H5e zenon_H143. % 10.03/10.22 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H7a. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H5e. % 10.03/10.22 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H297]. % 10.03/10.22 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_Ha4. apply refl_equal. % 10.03/10.22 apply zenon_H297. apply sym_equal. exact zenon_H143. % 10.03/10.22 (* end of lemma zenon_L428_ *) % 10.03/10.22 assert (zenon_L429_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 10.03/10.22 do 0 intro. intros zenon_H7e zenon_H2b3 zenon_H1ed. % 10.03/10.22 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H7e. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2b3. % 10.03/10.22 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 apply zenon_H1ee. apply sym_equal. exact zenon_H1ed. % 10.03/10.22 (* end of lemma zenon_L429_ *) % 10.03/10.22 assert (zenon_L430_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2fa zenon_H68 zenon_H74 zenon_H5e zenon_H7a zenon_H2b3 zenon_H7e zenon_Ha7 zenon_H1e. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.03/10.22 apply (zenon_L427_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.03/10.22 apply (zenon_L428_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.03/10.22 apply (zenon_L429_); trivial. % 10.03/10.22 apply (zenon_L77_); trivial. % 10.03/10.22 (* end of lemma zenon_L430_ *) % 10.03/10.22 assert (zenon_L431_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.03/10.22 do 0 intro. intros zenon_Hc0 zenon_H2fa zenon_H74 zenon_H7a zenon_H2b3 zenon_H7e zenon_Ha7 zenon_H1e. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_H89. zenon_intro zenon_Hc1. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H9d. zenon_intro zenon_Hc2. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.03/10.22 apply (zenon_L430_); trivial. % 10.03/10.22 (* end of lemma zenon_L431_ *) % 10.03/10.22 assert (zenon_L432_ : ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2b3 zenon_H188 zenon_H1b9. % 10.03/10.22 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hec | zenon_intro zenon_H81 ]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H1b9. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Hec. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H1ba. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2b3. % 10.03/10.22 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 apply zenon_H189. apply sym_equal. exact zenon_H188. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L432_ *) % 10.03/10.22 assert (zenon_L433_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_Hc6 zenon_H2b3 zenon_H1b9. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_H89. zenon_intro zenon_Hc7. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_H9d. zenon_intro zenon_Hc8. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.03/10.22 apply (zenon_L432_); trivial. % 10.03/10.22 (* end of lemma zenon_L433_ *) % 10.03/10.22 assert (zenon_L434_ : ((op (e2) (e2)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2b3 zenon_H2d4 zenon_Heb. % 10.03/10.22 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hec | zenon_intro zenon_H81 ]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_Heb. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Hec. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hed]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_Hed. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H2b3. % 10.03/10.22 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2fd]. % 10.03/10.22 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 apply zenon_H2fd. apply sym_equal. exact zenon_H2d4. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 apply zenon_H81. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L434_ *) % 10.03/10.22 assert (zenon_L435_ : ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_Hf7 zenon_Hf3 zenon_H105. % 10.03/10.22 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H10a | zenon_intro zenon_H104 ]. % 10.03/10.22 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e0) (e3)) = (op (e1) (e3)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H105. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H10a. % 10.03/10.22 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 10.03/10.22 cut (((op (e1) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10b]. % 10.03/10.22 congruence. % 10.03/10.22 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e0) (e3)))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H10b. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_Hf7. % 10.03/10.22 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 10.03/10.22 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 10.03/10.22 congruence. % 10.03/10.22 apply zenon_H104. apply refl_equal. % 10.03/10.22 apply zenon_H1ca. apply sym_equal. exact zenon_Hf3. % 10.03/10.22 apply zenon_H104. apply refl_equal. % 10.03/10.22 apply zenon_H104. apply refl_equal. % 10.03/10.22 (* end of lemma zenon_L435_ *) % 10.03/10.22 assert (zenon_L436_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2fe zenon_H24 zenon_H25 zenon_H143 zenon_H7a zenon_Heb zenon_H2b3 zenon_Hf7 zenon_H105. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.03/10.22 apply (zenon_L30_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.03/10.22 apply (zenon_L428_); trivial. % 10.03/10.22 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.03/10.22 apply (zenon_L434_); trivial. % 10.03/10.22 apply (zenon_L435_); trivial. % 10.03/10.22 (* end of lemma zenon_L436_ *) % 10.03/10.22 assert (zenon_L437_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.22 do 0 intro. intros zenon_Hc9 zenon_H2fe zenon_H24 zenon_H25 zenon_H7a zenon_Heb zenon_H2b3 zenon_H105. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H89. zenon_intro zenon_Hca. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_H9d. zenon_intro zenon_Hcb. % 10.03/10.22 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.22 apply (zenon_L436_); trivial. % 10.03/10.22 (* end of lemma zenon_L437_ *) % 10.03/10.22 assert (zenon_L438_ : ((op (e2) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.03/10.22 do 0 intro. intros zenon_H2b3 zenon_H2f zenon_H2c. % 10.03/10.22 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 10.03/10.22 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.03/10.22 intro zenon_D_pnotp. % 10.03/10.22 apply zenon_H2c. % 10.03/10.22 rewrite <- zenon_D_pnotp. % 10.03/10.22 exact zenon_H31. % 10.03/10.22 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.22 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 10.03/10.23 congruence. % 10.03/10.23 cut (((op (e2) (e2)) = (e1)) = ((e3) = (e1))). % 10.03/10.23 intro zenon_D_pnotp. % 10.03/10.23 apply zenon_H19f. % 10.03/10.23 rewrite <- zenon_D_pnotp. % 10.03/10.23 exact zenon_H2b3. % 10.03/10.23 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.23 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 10.03/10.23 congruence. % 10.03/10.23 exact (zenon_H33 zenon_H2f). % 10.03/10.23 apply zenon_H1d. apply refl_equal. % 10.03/10.23 apply zenon_H29. apply refl_equal. % 10.03/10.23 apply zenon_H29. apply refl_equal. % 10.03/10.23 (* end of lemma zenon_L438_ *) % 10.03/10.23 assert (zenon_L439_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.03/10.23 do 0 intro. intros zenon_H14c zenon_H141 zenon_Ha7 zenon_H5e zenon_H7a zenon_Hd2 zenon_H2c4 zenon_H14b zenon_H7f. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H94 | zenon_intro zenon_H14d ]. % 10.03/10.23 apply (zenon_L92_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 10.03/10.23 apply (zenon_L428_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H149 | zenon_intro zenon_H79 ]. % 10.03/10.23 apply (zenon_L386_); trivial. % 10.03/10.23 apply (zenon_L95_); trivial. % 10.03/10.23 (* end of lemma zenon_L439_ *) % 10.03/10.23 assert (zenon_L440_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H301 zenon_H1d5 zenon_H74 zenon_H2d zenon_H2c zenon_H1b9 zenon_H2b3 zenon_Hf3 zenon_H105. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.03/10.23 apply (zenon_L427_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.03/10.23 apply (zenon_L8_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.03/10.23 apply (zenon_L432_); trivial. % 10.03/10.23 apply (zenon_L435_); trivial. % 10.03/10.23 (* end of lemma zenon_L440_ *) % 10.03/10.23 assert (zenon_L441_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1db zenon_H16c zenon_Ha7 zenon_H105 zenon_Hf3 zenon_H2b3 zenon_H1b9 zenon_H2c zenon_H2d zenon_H74 zenon_H301 zenon_H24 zenon_H1d4 zenon_H1f5 zenon_H7f. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H1db); [ zenon_intro zenon_H90 | zenon_intro zenon_H1df ]. % 10.03/10.23 apply (zenon_L108_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H1e0 ]. % 10.03/10.23 apply (zenon_L440_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H91 | zenon_intro zenon_H72 ]. % 10.03/10.23 apply (zenon_L217_); trivial. % 10.03/10.23 apply (zenon_L176_); trivial. % 10.03/10.23 (* end of lemma zenon_L441_ *) % 10.03/10.23 assert (zenon_L442_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.03/10.23 do 0 intro. intros zenon_H2fe zenon_H25 zenon_H14b zenon_H2c4 zenon_Hd2 zenon_H7a zenon_H141 zenon_H14c zenon_Heb zenon_H1db zenon_H16c zenon_Ha7 zenon_H105 zenon_H2b3 zenon_H1b9 zenon_H2c zenon_H2d zenon_H74 zenon_H301 zenon_H24 zenon_H1d4 zenon_H1f5 zenon_H7f. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.03/10.23 apply (zenon_L30_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.03/10.23 apply (zenon_L439_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.03/10.23 apply (zenon_L434_); trivial. % 10.03/10.23 apply (zenon_L441_); trivial. % 10.03/10.23 (* end of lemma zenon_L442_ *) % 10.03/10.23 assert (zenon_L443_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H2f7 zenon_H2a zenon_H97 zenon_H187 zenon_H2fe zenon_H25 zenon_H14b zenon_H2c4 zenon_Hd2 zenon_H7a zenon_H141 zenon_H14c zenon_Heb zenon_H1db zenon_H16c zenon_Ha7 zenon_H105 zenon_H2b3 zenon_H1b9 zenon_H2c zenon_H2d zenon_H74 zenon_H301 zenon_H24 zenon_H1d4 zenon_H1f5. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.03/10.23 apply (zenon_L60_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.03/10.23 apply (zenon_L401_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.03/10.23 apply (zenon_L438_); trivial. % 10.03/10.23 apply (zenon_L442_); trivial. % 10.03/10.23 (* end of lemma zenon_L443_ *) % 10.03/10.23 assert (zenon_L444_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_Hd4 zenon_H2f7 zenon_H2a zenon_H187 zenon_H2fe zenon_H25 zenon_H14b zenon_H2c4 zenon_H7a zenon_H141 zenon_H14c zenon_Heb zenon_H1db zenon_H16c zenon_Ha7 zenon_H105 zenon_H2b3 zenon_H1b9 zenon_H2c zenon_H2d zenon_H74 zenon_H301 zenon_H24 zenon_H1d4 zenon_H1f5. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_H97. zenon_intro zenon_Hd5. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_H9e. zenon_intro zenon_Hd6. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.03/10.23 apply (zenon_L443_); trivial. % 10.03/10.23 (* end of lemma zenon_L444_ *) % 10.03/10.23 assert (zenon_L445_ : ((op (e2) (e2)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H2b3 zenon_H2e zenon_H25. % 10.03/10.23 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H6a | zenon_intro zenon_H22 ]. % 10.03/10.23 cut (((e2) = (e2)) = ((e1) = (e2))). % 10.03/10.23 intro zenon_D_pnotp. % 10.03/10.23 apply zenon_H25. % 10.03/10.23 rewrite <- zenon_D_pnotp. % 10.03/10.23 exact zenon_H6a. % 10.03/10.23 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.23 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 10.03/10.23 congruence. % 10.03/10.23 cut (((op (e2) (e2)) = (e1)) = ((e2) = (e1))). % 10.03/10.23 intro zenon_D_pnotp. % 10.03/10.23 apply zenon_H6b. % 10.03/10.23 rewrite <- zenon_D_pnotp. % 10.03/10.23 exact zenon_H2b3. % 10.03/10.23 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.23 cut (((op (e2) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 10.03/10.23 congruence. % 10.03/10.23 exact (zenon_H4a zenon_H2e). % 10.03/10.23 apply zenon_H1d. apply refl_equal. % 10.03/10.23 apply zenon_H22. apply refl_equal. % 10.03/10.23 apply zenon_H22. apply refl_equal. % 10.03/10.23 (* end of lemma zenon_L445_ *) % 10.03/10.23 assert (zenon_L446_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H163 zenon_H2b3 zenon_H25. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H163). zenon_intro zenon_H97. zenon_intro zenon_H164. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H164). zenon_intro zenon_H9e. zenon_intro zenon_H165. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H165). zenon_intro zenon_H2e. zenon_intro zenon_H2e. % 10.03/10.23 apply (zenon_L445_); trivial. % 10.03/10.23 (* end of lemma zenon_L446_ *) % 10.03/10.23 assert (zenon_L447_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H13d zenon_H9e zenon_H9c zenon_H2d zenon_H2a zenon_H97 zenon_H13a zenon_Ha7 zenon_Hfe. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.03/10.23 apply (zenon_L40_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.03/10.23 apply (zenon_L33_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.03/10.23 apply (zenon_L89_); trivial. % 10.03/10.23 apply (zenon_L68_); trivial. % 10.03/10.23 (* end of lemma zenon_L447_ *) % 10.03/10.23 assert (zenon_L448_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H17b zenon_H2fa zenon_H74 zenon_H7a zenon_H2b3 zenon_H7e zenon_Ha7 zenon_H1e. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H68. zenon_intro zenon_H17c. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H17c). zenon_intro zenon_H5e. zenon_intro zenon_H6f. % 10.03/10.23 apply (zenon_L430_); trivial. % 10.03/10.23 (* end of lemma zenon_L448_ *) % 10.03/10.23 assert (zenon_L449_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H17d zenon_H2fa zenon_H74 zenon_H7a zenon_H2b3 zenon_H7e zenon_Ha7 zenon_H1e. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H68. zenon_intro zenon_H17e. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H17e). zenon_intro zenon_H5e. zenon_intro zenon_Hb3. % 10.03/10.23 apply (zenon_L430_); trivial. % 10.03/10.23 (* end of lemma zenon_L449_ *) % 10.03/10.23 assert (zenon_L450_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H17f zenon_H2fa zenon_H74 zenon_H7a zenon_H2b3 zenon_H7e zenon_Ha7 zenon_H1e. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H68. zenon_intro zenon_H180. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H5e. zenon_intro zenon_Hb6. % 10.03/10.23 apply (zenon_L430_); trivial. % 10.03/10.23 (* end of lemma zenon_L450_ *) % 10.03/10.23 assert (zenon_L451_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H183 zenon_H2fa zenon_H74 zenon_H7a zenon_H2b3 zenon_H7e zenon_Ha7 zenon_H1e. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H27. zenon_intro zenon_H184. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H184). zenon_intro zenon_H27. zenon_intro zenon_Hc2. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.03/10.23 apply (zenon_L430_); trivial. % 10.03/10.23 (* end of lemma zenon_L451_ *) % 10.03/10.23 assert (zenon_L452_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H18a zenon_H2b3 zenon_H1b9. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H18a). zenon_intro zenon_H27. zenon_intro zenon_H18b. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H18b). zenon_intro zenon_H27. zenon_intro zenon_Hc8. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.03/10.23 apply (zenon_L432_); trivial. % 10.03/10.23 (* end of lemma zenon_L452_ *) % 10.03/10.23 assert (zenon_L453_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H18d zenon_H2fe zenon_H24 zenon_H25 zenon_H7a zenon_Heb zenon_H2b3 zenon_H105. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H18d). zenon_intro zenon_H27. zenon_intro zenon_H18e. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H18e). zenon_intro zenon_H27. zenon_intro zenon_Hcb. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.23 apply (zenon_L436_); trivial. % 10.03/10.23 (* end of lemma zenon_L453_ *) % 10.03/10.23 assert (zenon_L454_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.23 do 0 intro. intros zenon_H195 zenon_H2dd zenon_H24. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H188. zenon_intro zenon_H196. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H196). zenon_intro zenon_H18c. zenon_intro zenon_Hcf. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd0. zenon_intro zenon_H86. % 10.03/10.23 apply (zenon_L399_); trivial. % 10.03/10.23 (* end of lemma zenon_L454_ *) % 10.03/10.23 assert (zenon_L455_ : ((op (e2) (e2)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H2b3 zenon_H18c zenon_H2ac. % 10.03/10.23 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hec | zenon_intro zenon_H81 ]. % 10.03/10.23 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))). % 10.03/10.23 intro zenon_D_pnotp. % 10.03/10.23 apply zenon_H2ac. % 10.03/10.23 rewrite <- zenon_D_pnotp. % 10.03/10.23 exact zenon_Hec. % 10.03/10.23 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.23 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2ad]. % 10.03/10.23 congruence. % 10.03/10.23 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e2) (e1)))). % 10.03/10.23 intro zenon_D_pnotp. % 10.03/10.23 apply zenon_H2ad. % 10.03/10.23 rewrite <- zenon_D_pnotp. % 10.03/10.23 exact zenon_H2b3. % 10.03/10.23 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2c6]. % 10.03/10.23 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.23 congruence. % 10.03/10.23 apply zenon_H81. apply refl_equal. % 10.03/10.23 apply zenon_H2c6. apply sym_equal. exact zenon_H18c. % 10.03/10.23 apply zenon_H81. apply refl_equal. % 10.03/10.23 apply zenon_H81. apply refl_equal. % 10.03/10.23 (* end of lemma zenon_L455_ *) % 10.03/10.23 assert (zenon_L456_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H197 zenon_H2b3 zenon_H2ac. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H197). zenon_intro zenon_H188. zenon_intro zenon_H198. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H198). zenon_intro zenon_H18c. zenon_intro zenon_Hd6. % 10.03/10.23 apply (zenon_L455_); trivial. % 10.03/10.23 (* end of lemma zenon_L456_ *) % 10.03/10.23 assert (zenon_L457_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H199 zenon_H2b3 zenon_H25. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H199). zenon_intro zenon_H188. zenon_intro zenon_H19a. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H19a). zenon_intro zenon_H18c. zenon_intro zenon_H165. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H165). zenon_intro zenon_H2e. zenon_intro zenon_H2e. % 10.03/10.23 apply (zenon_L445_); trivial. % 10.03/10.23 (* end of lemma zenon_L457_ *) % 10.03/10.23 assert (zenon_L458_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H19b zenon_H2b3 zenon_H1b9. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H19b). zenon_intro zenon_H188. zenon_intro zenon_H19c. % 10.03/10.23 apply (zenon_L432_); trivial. % 10.03/10.23 (* end of lemma zenon_L458_ *) % 10.03/10.23 assert (zenon_L459_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H19d zenon_H2fe zenon_H24 zenon_H25 zenon_H7a zenon_Heb zenon_H2b3 zenon_H105. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_Hf7. zenon_intro zenon_H19e. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H171. % 10.03/10.23 apply (zenon_L436_); trivial. % 10.03/10.23 (* end of lemma zenon_L459_ *) % 10.03/10.23 assert (zenon_L460_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1a3 zenon_H2fe zenon_H24 zenon_H25 zenon_H7a zenon_Heb zenon_H2b3 zenon_H105. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_Hf7. zenon_intro zenon_H1a4. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1a4). zenon_intro zenon_H143. zenon_intro zenon_H177. % 10.03/10.23 apply (zenon_L436_); trivial. % 10.03/10.23 (* end of lemma zenon_L460_ *) % 10.03/10.23 assert (zenon_L461_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1a7 zenon_H2dd zenon_H24. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H86. zenon_intro zenon_H1a8. % 10.03/10.23 apply (zenon_L399_); trivial. % 10.03/10.23 (* end of lemma zenon_L461_ *) % 10.03/10.23 assert (zenon_L462_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1a9 zenon_H2dd zenon_H24. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1a9). zenon_intro zenon_H86. zenon_intro zenon_H1aa. % 10.03/10.23 apply (zenon_L399_); trivial. % 10.03/10.23 (* end of lemma zenon_L462_ *) % 10.03/10.23 assert (zenon_L463_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1af zenon_H2fa zenon_H74 zenon_H7a zenon_H2b3 zenon_H7e zenon_Ha7 zenon_H1e. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_Hd2. zenon_intro zenon_H1b0. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hd7. zenon_intro zenon_Hc2. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.03/10.23 apply (zenon_L430_); trivial. % 10.03/10.23 (* end of lemma zenon_L463_ *) % 10.03/10.23 assert (zenon_L464_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1b3 zenon_H2b3 zenon_H1b9. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_Hd2. zenon_intro zenon_H1b4. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1b4). zenon_intro zenon_Hd7. zenon_intro zenon_Hc8. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.03/10.23 apply (zenon_L432_); trivial. % 10.03/10.23 (* end of lemma zenon_L464_ *) % 10.03/10.23 assert (zenon_L465_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1b5 zenon_H2fe zenon_H24 zenon_H25 zenon_H7a zenon_Heb zenon_H2b3 zenon_H105. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_Hd2. zenon_intro zenon_H1b6. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_Hd7. zenon_intro zenon_Hcb. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.23 apply (zenon_L436_); trivial. % 10.03/10.23 (* end of lemma zenon_L465_ *) % 10.03/10.23 assert (zenon_L466_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1b7 zenon_H2dd zenon_H24. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_H2e. zenon_intro zenon_H1b8. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_H2e. zenon_intro zenon_Hcf. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd0. zenon_intro zenon_H86. % 10.03/10.23 apply (zenon_L399_); trivial. % 10.03/10.23 (* end of lemma zenon_L466_ *) % 10.03/10.23 assert (zenon_L467_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1bc zenon_H2b3 zenon_H25. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1bc). zenon_intro zenon_H2e. zenon_intro zenon_H1bd. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1bd). zenon_intro zenon_H2e. zenon_intro zenon_Hd6. % 10.03/10.23 apply (zenon_L445_); trivial. % 10.03/10.23 (* end of lemma zenon_L467_ *) % 10.03/10.23 assert (zenon_L468_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1be zenon_H2b3 zenon_H25. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_H2e. zenon_intro zenon_H1bf. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1bf). zenon_intro zenon_H2e. zenon_intro zenon_H165. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H165). zenon_intro zenon_H2e. zenon_intro zenon_H2e. % 10.03/10.23 apply (zenon_L445_); trivial. % 10.03/10.23 (* end of lemma zenon_L468_ *) % 10.03/10.23 assert (zenon_L469_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1c0 zenon_H2b3 zenon_H25. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1c0). zenon_intro zenon_H2e. zenon_intro zenon_H1c1. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1c1). zenon_intro zenon_H2e. zenon_intro zenon_H16b. % 10.03/10.23 apply (zenon_L445_); trivial. % 10.03/10.23 (* end of lemma zenon_L469_ *) % 10.03/10.23 assert (zenon_L470_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H12f zenon_H11f zenon_H72 zenon_H2d zenon_Hd1 zenon_H2c zenon_H2b3 zenon_H128 zenon_H30. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.03/10.23 apply (zenon_L78_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.03/10.23 apply (zenon_L79_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.03/10.23 apply (zenon_L438_); trivial. % 10.03/10.23 apply (zenon_L166_); trivial. % 10.03/10.23 (* end of lemma zenon_L470_ *) % 10.03/10.23 assert (zenon_L471_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1c2 zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_H2c zenon_H2b3 zenon_H30. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H128. zenon_intro zenon_H1c3. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1c3). zenon_intro zenon_H166. zenon_intro zenon_H171. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.23 apply (zenon_L470_); trivial. % 10.03/10.23 (* end of lemma zenon_L471_ *) % 10.03/10.23 assert (zenon_L472_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1e6 zenon_H23 zenon_H24. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H72. zenon_intro zenon_H1e7. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_He2. zenon_intro zenon_H6f. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H20. zenon_intro zenon_H20. % 10.03/10.23 apply (zenon_L4_); trivial. % 10.03/10.23 (* end of lemma zenon_L472_ *) % 10.03/10.23 assert (zenon_L473_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.23 do 0 intro. intros zenon_Hb1 zenon_H2a zenon_H2b. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_H20. zenon_intro zenon_Hb2. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hb2). zenon_intro zenon_H20. zenon_intro zenon_Hb3. % 10.03/10.23 apply (zenon_L7_); trivial. % 10.03/10.23 (* end of lemma zenon_L473_ *) % 10.03/10.23 assert (zenon_L474_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.23 do 0 intro. intros zenon_Hb4 zenon_H2a zenon_H2b. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hb4). zenon_intro zenon_H20. zenon_intro zenon_Hb5. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hb5). zenon_intro zenon_H20. zenon_intro zenon_Hb6. % 10.03/10.23 apply (zenon_L7_); trivial. % 10.03/10.23 (* end of lemma zenon_L474_ *) % 10.03/10.23 assert (zenon_L475_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H2fe zenon_H2b zenon_H2c zenon_H143 zenon_H7a zenon_Heb zenon_H2b3 zenon_Hf7 zenon_H105. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.03/10.23 apply (zenon_L32_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.03/10.23 apply (zenon_L428_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.03/10.23 apply (zenon_L434_); trivial. % 10.03/10.23 apply (zenon_L435_); trivial. % 10.03/10.23 (* end of lemma zenon_L475_ *) % 10.03/10.23 assert (zenon_L476_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_Hc9 zenon_H2fe zenon_H2b zenon_H2c zenon_H7a zenon_Heb zenon_H2b3 zenon_H105. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H89. zenon_intro zenon_Hca. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_H9d. zenon_intro zenon_Hcb. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.23 apply (zenon_L475_); trivial. % 10.03/10.23 (* end of lemma zenon_L476_ *) % 10.03/10.23 assert (zenon_L477_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H155 zenon_H2b zenon_H30 zenon_H5f zenon_H26 zenon_H166 zenon_H96 zenon_H128 zenon_H12a. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.03/10.23 apply (zenon_L384_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.03/10.23 apply (zenon_L103_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.03/10.23 apply (zenon_L104_); trivial. % 10.03/10.23 apply (zenon_L105_); trivial. % 10.03/10.23 (* end of lemma zenon_L477_ *) % 10.03/10.23 assert (zenon_L478_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H169 zenon_H155 zenon_H2b zenon_H30 zenon_H5f zenon_H26 zenon_H96 zenon_H12a. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H169). zenon_intro zenon_H97. zenon_intro zenon_H16a. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H16a). zenon_intro zenon_H9e. zenon_intro zenon_H16b. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.03/10.23 apply (zenon_L477_); trivial. % 10.03/10.23 (* end of lemma zenon_L478_ *) % 10.03/10.23 assert (zenon_L479_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.23 do 0 intro. intros zenon_H16f zenon_H1d4 zenon_H2b. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hb7. zenon_intro zenon_H170. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_H90. zenon_intro zenon_H171. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.23 apply (zenon_L402_); trivial. % 10.03/10.23 (* end of lemma zenon_L479_ *) % 10.03/10.23 assert (zenon_L480_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.23 do 0 intro. intros zenon_H19d zenon_H1d4 zenon_H2b. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_Hf7. zenon_intro zenon_H19e. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H171. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.23 apply (zenon_L402_); trivial. % 10.03/10.23 (* end of lemma zenon_L480_ *) % 10.03/10.23 assert (zenon_L481_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H22e zenon_H2b zenon_Hbe zenon_H30 zenon_H26 zenon_H1ec zenon_H7f zenon_Hf7 zenon_H2c. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.23 apply (zenon_L316_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.23 apply (zenon_L38_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.23 apply (zenon_L404_); trivial. % 10.03/10.23 apply (zenon_L132_); trivial. % 10.03/10.23 (* end of lemma zenon_L481_ *) % 10.03/10.23 assert (zenon_L482_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1a3 zenon_H22e zenon_H2b zenon_Hbe zenon_H30 zenon_H26 zenon_H1ec zenon_H2c. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_Hf7. zenon_intro zenon_H1a4. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1a4). zenon_intro zenon_H143. zenon_intro zenon_H177. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.03/10.23 apply (zenon_L481_); trivial. % 10.03/10.23 (* end of lemma zenon_L482_ *) % 10.03/10.23 assert (zenon_L483_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1c2 zenon_H1d4 zenon_H2b. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H128. zenon_intro zenon_H1c3. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1c3). zenon_intro zenon_H166. zenon_intro zenon_H171. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.23 apply (zenon_L402_); trivial. % 10.03/10.23 (* end of lemma zenon_L483_ *) % 10.03/10.23 assert (zenon_L484_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_H79 zenon_H2c zenon_H2b3 zenon_H128 zenon_H30. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.03/10.23 apply (zenon_L406_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.03/10.23 apply (zenon_L403_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.03/10.23 apply (zenon_L438_); trivial. % 10.03/10.23 apply (zenon_L166_); trivial. % 10.03/10.23 (* end of lemma zenon_L484_ *) % 10.03/10.23 assert (zenon_L485_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H21c zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_H2c zenon_H2b3 zenon_H30. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H21c). zenon_intro zenon_H128. zenon_intro zenon_H21d. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H166. zenon_intro zenon_H174. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.03/10.23 apply (zenon_L484_); trivial. % 10.03/10.23 (* end of lemma zenon_L485_ *) % 10.03/10.23 assert (zenon_L486_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1e6 zenon_H1d4 zenon_H2b. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H72. zenon_intro zenon_H1e7. % 10.03/10.23 apply (zenon_L402_); trivial. % 10.03/10.23 (* end of lemma zenon_L486_ *) % 10.03/10.23 assert (zenon_L487_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1e8 zenon_H1d4 zenon_H2b. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1e8). zenon_intro zenon_H72. zenon_intro zenon_H1e9. % 10.03/10.23 apply (zenon_L402_); trivial. % 10.03/10.23 (* end of lemma zenon_L487_ *) % 10.03/10.23 assert (zenon_L488_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1f9 zenon_H1d4 zenon_H2b. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1f9). zenon_intro zenon_H72. zenon_intro zenon_H1fa. % 10.03/10.23 apply (zenon_L402_); trivial. % 10.03/10.23 (* end of lemma zenon_L488_ *) % 10.03/10.23 assert (zenon_L489_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H1fd zenon_H2fa zenon_H74 zenon_H7a zenon_H2b3 zenon_H7e zenon_Ha7 zenon_H1e. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H79. zenon_intro zenon_H1fe. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H109. zenon_intro zenon_Hc2. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.03/10.23 apply (zenon_L430_); trivial. % 10.03/10.23 (* end of lemma zenon_L489_ *) % 10.03/10.23 assert (zenon_L490_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H223 zenon_H2b3 zenon_H1b9. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H79. zenon_intro zenon_H224. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H109. zenon_intro zenon_Hc8. % 10.03/10.23 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.03/10.23 apply (zenon_L432_); trivial. % 10.03/10.23 (* end of lemma zenon_L490_ *) % 10.03/10.23 assert (zenon_L491_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H207 zenon_H2b3 zenon_H25. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H7f. zenon_intro zenon_H208. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H208). zenon_intro zenon_H112. zenon_intro zenon_H165. % 10.03/10.23 apply (zenon_and_s _ _ zenon_H165). zenon_intro zenon_H2e. zenon_intro zenon_H2e. % 10.03/10.23 apply (zenon_L445_); trivial. % 10.03/10.23 (* end of lemma zenon_L491_ *) % 10.03/10.23 assert (zenon_L492_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.03/10.23 do 0 intro. intros zenon_H154 zenon_H25 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H23 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_H1e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H26 zenon_H2c zenon_H2b3 zenon_Ha7 zenon_H2a. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.23 apply (zenon_L21_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.23 apply (zenon_L473_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.23 apply (zenon_L474_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.23 apply (zenon_L48_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.23 apply (zenon_L431_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.23 apply (zenon_L51_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.23 apply (zenon_L433_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.23 apply (zenon_L476_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.23 apply (zenon_L55_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.23 apply (zenon_L57_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.23 apply (zenon_L446_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.23 apply (zenon_L478_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.23 apply (zenon_L479_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.23 apply (zenon_L110_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.23 apply (zenon_L111_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.23 apply (zenon_L112_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.23 apply (zenon_L448_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.23 apply (zenon_L449_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.23 apply (zenon_L450_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.23 apply (zenon_L116_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.23 apply (zenon_L451_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.23 apply (zenon_L118_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.23 apply (zenon_L452_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.23 apply (zenon_L122_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.23 apply (zenon_L127_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.23 apply (zenon_L128_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.23 apply (zenon_L457_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.23 apply (zenon_L458_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.23 apply (zenon_L480_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.23 apply (zenon_L133_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.23 apply (zenon_L482_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.23 apply (zenon_L135_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.23 apply (zenon_L136_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.23 apply (zenon_L137_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.23 apply (zenon_L138_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.23 apply (zenon_L139_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.23 apply (zenon_L463_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.23 apply (zenon_L141_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.23 apply (zenon_L464_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.23 apply (zenon_L143_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.23 apply (zenon_L144_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.23 apply (zenon_L193_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.23 apply (zenon_L468_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.23 apply (zenon_L469_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.23 apply (zenon_L483_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.23 apply (zenon_L485_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.23 apply (zenon_L167_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.23 apply (zenon_L168_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.23 apply (zenon_L486_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.23 apply (zenon_L487_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.23 apply (zenon_L488_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.23 apply (zenon_L180_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.23 apply (zenon_L489_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.23 apply (zenon_L182_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.23 apply (zenon_L490_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.23 apply (zenon_L183_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.23 apply (zenon_L184_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.23 apply (zenon_L185_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.23 apply (zenon_L491_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.23 apply (zenon_L187_); trivial. % 10.03/10.23 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.24 apply (zenon_L188_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.24 apply (zenon_L189_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.24 apply (zenon_L190_); trivial. % 10.03/10.24 apply (zenon_L191_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.03/10.24 apply (zenon_L38_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.03/10.24 apply (zenon_L438_); trivial. % 10.03/10.24 apply (zenon_L75_); trivial. % 10.03/10.24 (* end of lemma zenon_L492_ *) % 10.03/10.24 assert (zenon_L493_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H1cb zenon_H9e zenon_H23 zenon_H149 zenon_H2c4 zenon_H25 zenon_H12f zenon_H11f zenon_H72 zenon_H2d zenon_Hd1 zenon_H2c zenon_H2b3 zenon_H30. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.03/10.24 apply (zenon_L54_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.03/10.24 apply (zenon_L386_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.03/10.24 apply (zenon_L445_); trivial. % 10.03/10.24 apply (zenon_L470_); trivial. % 10.03/10.24 (* end of lemma zenon_L493_ *) % 10.03/10.24 assert (zenon_L494_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((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) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (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)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H2ca zenon_H64 zenon_H22f zenon_H12a zenon_H5f zenon_H155 zenon_H1ec zenon_Hbe zenon_H22e zenon_H2dd zenon_Hb8 zenon_H1e zenon_H7e zenon_H2fa zenon_H96 zenon_H93 zenon_H192 zenon_H154 zenon_H1f5 zenon_H1d4 zenon_H24 zenon_H301 zenon_H74 zenon_H1b9 zenon_H105 zenon_Ha7 zenon_H16c zenon_H1db zenon_Heb zenon_H14c zenon_H141 zenon_H7a zenon_H14b zenon_H2fe zenon_H187 zenon_H97 zenon_H2a zenon_H2f7 zenon_H1cb zenon_H9e zenon_H23 zenon_H2c4 zenon_H25 zenon_H12f zenon_H11f zenon_H72 zenon_H2d zenon_Hd1 zenon_H2c zenon_H2b3 zenon_H30. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.03/10.24 apply (zenon_L19_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.03/10.24 apply (zenon_L492_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.03/10.24 apply (zenon_L443_); trivial. % 10.03/10.24 apply (zenon_L493_); trivial. % 10.03/10.24 (* end of lemma zenon_L494_ *) % 10.03/10.24 assert (zenon_L495_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((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) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (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)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H1f9 zenon_H2ca zenon_H64 zenon_H22f zenon_H12a zenon_H5f zenon_H155 zenon_H1ec zenon_Hbe zenon_H22e zenon_H2dd zenon_Hb8 zenon_H1e zenon_H7e zenon_H2fa zenon_H96 zenon_H93 zenon_H192 zenon_H154 zenon_H1f5 zenon_H1d4 zenon_H24 zenon_H301 zenon_H74 zenon_H1b9 zenon_H105 zenon_Ha7 zenon_H16c zenon_H1db zenon_Heb zenon_H14c zenon_H141 zenon_H7a zenon_H14b zenon_H2fe zenon_H187 zenon_H2a zenon_H2f7 zenon_H1cb zenon_H23 zenon_H2c4 zenon_H25 zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_H2c zenon_H2b3 zenon_H30. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1f9). zenon_intro zenon_H72. zenon_intro zenon_H1fa. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_He2. zenon_intro zenon_Hb6. % 10.03/10.24 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 10.03/10.24 apply (zenon_L494_); trivial. % 10.03/10.24 (* end of lemma zenon_L495_ *) % 10.03/10.24 assert (zenon_L496_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.24 do 0 intro. intros zenon_H203 zenon_H2dd zenon_H24. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H203). zenon_intro zenon_H7f. zenon_intro zenon_H204. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H204). zenon_intro zenon_H112. zenon_intro zenon_Hcf. % 10.03/10.24 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd0. zenon_intro zenon_H86. % 10.03/10.24 apply (zenon_L399_); trivial. % 10.03/10.24 (* end of lemma zenon_L496_ *) % 10.03/10.24 assert (zenon_L497_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H205 zenon_H2fe zenon_H25 zenon_H14b zenon_H2c4 zenon_H7a zenon_H141 zenon_H14c zenon_Heb zenon_H1db zenon_H16c zenon_Ha7 zenon_H105 zenon_H2b3 zenon_H1b9 zenon_H2c zenon_H2d zenon_H74 zenon_H301 zenon_H24 zenon_H1d4 zenon_H1f5. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H7f. zenon_intro zenon_H206. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H112. zenon_intro zenon_Hd6. % 10.03/10.24 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.03/10.24 apply (zenon_L442_); trivial. % 10.03/10.24 (* end of lemma zenon_L497_ *) % 10.03/10.24 assert (zenon_L498_ : (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((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) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (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) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H30 zenon_H25 zenon_H2fe zenon_H14b zenon_H2c4 zenon_H7a zenon_H141 zenon_H14c zenon_Heb zenon_H1db zenon_H16c zenon_H105 zenon_H1b9 zenon_H74 zenon_H301 zenon_H24 zenon_H1d4 zenon_H1f5 zenon_H2dd zenon_H2fa zenon_H7e zenon_H1e zenon_Hb8 zenon_H2ca zenon_H64 zenon_H22f zenon_H12a zenon_H5f zenon_H155 zenon_H1ec zenon_Hbe zenon_H22e zenon_H96 zenon_H93 zenon_H192 zenon_H154 zenon_H187 zenon_H2f7 zenon_H1cb zenon_H23 zenon_H12f zenon_H11f zenon_Hd1 zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H2c zenon_H2b3 zenon_Ha7 zenon_H2a. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.03/10.24 apply (zenon_L384_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.24 apply (zenon_L424_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.24 apply (zenon_L425_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.24 apply (zenon_L426_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.24 apply (zenon_L48_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.24 apply (zenon_L431_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.24 apply (zenon_L321_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.24 apply (zenon_L433_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.24 apply (zenon_L437_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.24 apply (zenon_L55_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.24 apply (zenon_L444_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.24 apply (zenon_L446_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H169). zenon_intro zenon_H97. zenon_intro zenon_H16a. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H16a). zenon_intro zenon_H9e. zenon_intro zenon_H16b. % 10.03/10.24 apply (zenon_L447_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.24 apply (zenon_L109_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.24 apply (zenon_L110_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.24 apply (zenon_L111_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.24 apply (zenon_L112_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.24 apply (zenon_L448_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.24 apply (zenon_L449_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.24 apply (zenon_L450_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.24 apply (zenon_L116_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.24 apply (zenon_L451_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.24 apply (zenon_L336_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.24 apply (zenon_L452_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.24 apply (zenon_L453_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.24 apply (zenon_L454_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.24 apply (zenon_L456_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.24 apply (zenon_L457_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.24 apply (zenon_L458_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.24 apply (zenon_L459_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.24 apply (zenon_L133_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.24 apply (zenon_L460_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.24 apply (zenon_L135_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.24 apply (zenon_L461_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.24 apply (zenon_L462_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.24 apply (zenon_L138_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.24 apply (zenon_L139_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.24 apply (zenon_L463_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.24 apply (zenon_L340_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.24 apply (zenon_L464_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.24 apply (zenon_L465_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.24 apply (zenon_L466_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.24 apply (zenon_L467_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.24 apply (zenon_L468_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.24 apply (zenon_L469_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.24 apply (zenon_L471_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.24 apply (zenon_L346_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.24 apply (zenon_L167_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.24 apply (zenon_L168_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.24 apply (zenon_L472_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1e8). zenon_intro zenon_H72. zenon_intro zenon_H1e9. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1e9). zenon_intro zenon_He2. zenon_intro zenon_Hb3. % 10.03/10.24 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.03/10.24 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.03/10.24 apply (zenon_L40_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.03/10.24 apply (zenon_L41_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.03/10.24 apply (zenon_L366_); trivial. % 10.03/10.24 apply (zenon_L43_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.24 apply (zenon_L495_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.24 apply (zenon_L180_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.24 apply (zenon_L489_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.24 apply (zenon_L351_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.24 apply (zenon_L490_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.24 apply (zenon_L183_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.24 apply (zenon_L496_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.24 apply (zenon_L497_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.24 apply (zenon_L491_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.24 apply (zenon_L187_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.24 apply (zenon_L188_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.24 apply (zenon_L189_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.24 apply (zenon_L190_); trivial. % 10.03/10.24 apply (zenon_L191_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.03/10.24 apply (zenon_L438_); trivial. % 10.03/10.24 apply (zenon_L75_); trivial. % 10.03/10.24 (* end of lemma zenon_L498_ *) % 10.03/10.24 assert (zenon_L499_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H2c zenon_H30 zenon_H22f zenon_H105 zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H16c zenon_H1ec zenon_Hbe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H1e zenon_H7e zenon_H7a zenon_H74 zenon_H2fa zenon_H1b9 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H25 zenon_H2b3 zenon_Ha7 zenon_H23. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H24 | zenon_intro zenon_H230 ]. % 10.03/10.24 apply (zenon_L498_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H26 | zenon_intro zenon_H231 ]. % 10.03/10.24 apply (zenon_L492_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H2e | zenon_intro zenon_H82 ]. % 10.03/10.24 apply (zenon_L445_); trivial. % 10.03/10.24 apply (zenon_L125_); trivial. % 10.03/10.24 (* end of lemma zenon_L499_ *) % 10.03/10.24 assert (zenon_L500_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2c zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_Ha7 zenon_H1e. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H1f | zenon_intro zenon_H305 ]. % 10.03/10.24 apply (zenon_L224_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H27 | zenon_intro zenon_H306 ]. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H24 | zenon_intro zenon_H230 ]. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.03/10.24 apply (zenon_L384_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.03/10.24 apply (zenon_L8_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_Hd8. zenon_intro zenon_H15b. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_H15c. zenon_intro zenon_He1. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.03/10.24 apply (zenon_L4_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.03/10.24 apply (zenon_L30_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.03/10.24 apply (zenon_L18_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.03/10.24 apply (zenon_L385_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.03/10.24 apply (zenon_L5_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.03/10.24 apply (zenon_L391_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.03/10.24 apply (zenon_L392_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.03/10.24 apply (zenon_L393_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_He2 | zenon_intro zenon_H119 ]. % 10.03/10.24 apply (zenon_L61_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H109 | zenon_intro zenon_H11a ]. % 10.03/10.24 apply (zenon_L397_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H112 | zenon_intro zenon_H52 ]. % 10.03/10.24 apply (zenon_L293_); trivial. % 10.03/10.24 apply (zenon_L75_); trivial. % 10.03/10.24 apply (zenon_L77_); trivial. % 10.03/10.24 apply (zenon_L398_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.03/10.24 apply (zenon_L151_); trivial. % 10.03/10.24 apply (zenon_L47_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.03/10.24 apply (zenon_L13_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.03/10.24 apply (zenon_L4_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H20 | zenon_intro zenon_H1dd ]. % 10.03/10.24 apply (zenon_L4_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 10.03/10.24 apply (zenon_L44_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H9e | zenon_intro zenon_H90 ]. % 10.03/10.24 apply (zenon_L197_); trivial. % 10.03/10.24 apply (zenon_L108_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.03/10.24 apply (zenon_L385_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.03/10.24 apply (zenon_L5_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.03/10.24 apply (zenon_L19_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.03/10.24 apply (zenon_L5_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.03/10.24 apply (zenon_L387_); trivial. % 10.03/10.24 apply (zenon_L400_); trivial. % 10.03/10.24 apply (zenon_L423_); trivial. % 10.03/10.24 apply (zenon_L47_); trivial. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H51. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.03/10.24 apply (zenon_L98_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.03/10.24 apply (zenon_L218_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.03/10.24 apply (zenon_L25_); trivial. % 10.03/10.24 apply (zenon_L75_); trivial. % 10.03/10.24 apply (zenon_L75_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H26 | zenon_intro zenon_H231 ]. % 10.03/10.24 apply (zenon_L5_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H2e | zenon_intro zenon_H82 ]. % 10.03/10.24 apply (zenon_L420_); trivial. % 10.03/10.24 apply (zenon_L125_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H306); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H11b ]. % 10.03/10.24 apply (zenon_L499_); trivial. % 10.03/10.24 apply (zenon_L77_); trivial. % 10.03/10.24 (* end of lemma zenon_L500_ *) % 10.03/10.24 assert (zenon_L501_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H272 zenon_H5a zenon_H89 zenon_Ha5 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2c zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.03/10.24 apply (zenon_L381_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.03/10.24 apply (zenon_L382_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.03/10.24 apply (zenon_L383_); trivial. % 10.03/10.24 apply (zenon_L500_); trivial. % 10.03/10.24 (* end of lemma zenon_L501_ *) % 10.03/10.24 assert (zenon_L502_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> False). % 10.03/10.24 do 0 intro. intros zenon_Hbb zenon_H5a. % 10.03/10.24 apply (zenon_and_s _ _ zenon_Hbb). zenon_intro zenon_H20. zenon_intro zenon_Hbc. % 10.03/10.24 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_H20. zenon_intro zenon_Hbd. % 10.03/10.24 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.03/10.24 apply (zenon_L381_); trivial. % 10.03/10.24 (* end of lemma zenon_L502_ *) % 10.03/10.24 assert (zenon_L503_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.24 do 0 intro. intros zenon_Hbb zenon_H23 zenon_H24. % 10.03/10.24 apply (zenon_and_s _ _ zenon_Hbb). zenon_intro zenon_H20. zenon_intro zenon_Hbc. % 10.03/10.24 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_H20. zenon_intro zenon_Hbd. % 10.03/10.24 apply (zenon_L4_); trivial. % 10.03/10.24 (* end of lemma zenon_L503_ *) % 10.03/10.24 assert (zenon_L504_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.24 do 0 intro. intros zenon_Hbb zenon_H2a zenon_H2b. % 10.03/10.24 apply (zenon_and_s _ _ zenon_Hbb). zenon_intro zenon_H20. zenon_intro zenon_Hbc. % 10.03/10.24 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_H20. zenon_intro zenon_Hbd. % 10.03/10.24 apply (zenon_L7_); trivial. % 10.03/10.24 (* end of lemma zenon_L504_ *) % 10.03/10.24 assert (zenon_L505_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H11b zenon_H52 zenon_H2c. % 10.03/10.24 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 10.03/10.24 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.03/10.24 intro zenon_D_pnotp. % 10.03/10.24 apply zenon_H2c. % 10.03/10.24 rewrite <- zenon_D_pnotp. % 10.03/10.24 exact zenon_H31. % 10.03/10.24 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.24 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 10.03/10.24 congruence. % 10.03/10.24 cut (((op (e3) (e3)) = (e1)) = ((e3) = (e1))). % 10.03/10.24 intro zenon_D_pnotp. % 10.03/10.24 apply zenon_H19f. % 10.03/10.24 rewrite <- zenon_D_pnotp. % 10.03/10.24 exact zenon_H11b. % 10.03/10.24 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.24 cut (((op (e3) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 10.03/10.24 congruence. % 10.03/10.24 exact (zenon_H57 zenon_H52). % 10.03/10.24 apply zenon_H1d. apply refl_equal. % 10.03/10.24 apply zenon_H29. apply refl_equal. % 10.03/10.24 apply zenon_H29. apply refl_equal. % 10.03/10.24 (* end of lemma zenon_L505_ *) % 10.03/10.24 assert (zenon_L506_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H83 zenon_H2b zenon_H1d4 zenon_H2c4 zenon_H121 zenon_H1ec zenon_H1f0 zenon_H11b zenon_H2c. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.03/10.24 apply (zenon_L402_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.03/10.24 apply (zenon_L403_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.03/10.24 apply (zenon_L404_); trivial. % 10.03/10.24 apply (zenon_L505_); trivial. % 10.03/10.24 (* end of lemma zenon_L506_ *) % 10.03/10.24 assert (zenon_L507_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H11b zenon_H143 zenon_H141. % 10.03/10.24 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.03/10.24 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 10.03/10.24 intro zenon_D_pnotp. % 10.03/10.24 apply zenon_H141. % 10.03/10.24 rewrite <- zenon_D_pnotp. % 10.03/10.24 exact zenon_Haa. % 10.03/10.24 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.24 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H142]. % 10.03/10.24 congruence. % 10.03/10.24 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 10.03/10.24 intro zenon_D_pnotp. % 10.03/10.24 apply zenon_H142. % 10.03/10.24 rewrite <- zenon_D_pnotp. % 10.03/10.24 exact zenon_H11b. % 10.03/10.24 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H297]. % 10.03/10.24 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.24 congruence. % 10.03/10.24 apply zenon_Hab. apply refl_equal. % 10.03/10.24 apply zenon_H297. apply sym_equal. exact zenon_H143. % 10.03/10.24 apply zenon_Hab. apply refl_equal. % 10.03/10.24 apply zenon_Hab. apply refl_equal. % 10.03/10.24 (* end of lemma zenon_L507_ *) % 10.03/10.24 assert (zenon_L508_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.03/10.24 do 0 intro. intros zenon_H14c zenon_H90 zenon_H1d9 zenon_H141 zenon_H11b zenon_H26 zenon_H93 zenon_H14b zenon_H7f. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H94 | zenon_intro zenon_H14d ]. % 10.03/10.24 apply (zenon_L334_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 10.03/10.24 apply (zenon_L507_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H149 | zenon_intro zenon_H79 ]. % 10.03/10.24 apply (zenon_L124_); trivial. % 10.03/10.24 apply (zenon_L95_); trivial. % 10.03/10.24 (* end of lemma zenon_L508_ *) % 10.03/10.24 assert (zenon_L509_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_H79 zenon_Ha5 zenon_H2a zenon_H109 zenon_H101. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.03/10.24 apply (zenon_L406_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.03/10.24 apply (zenon_L403_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.03/10.24 apply (zenon_L42_); trivial. % 10.03/10.24 apply (zenon_L80_); trivial. % 10.03/10.24 (* end of lemma zenon_L509_ *) % 10.03/10.24 assert (zenon_L510_ : ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H11b zenon_Hf7 zenon_Hfe. % 10.03/10.24 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.03/10.24 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 10.03/10.24 intro zenon_D_pnotp. % 10.03/10.24 apply zenon_Hfe. % 10.03/10.24 rewrite <- zenon_D_pnotp. % 10.03/10.24 exact zenon_Haa. % 10.03/10.24 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.24 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 10.03/10.24 congruence. % 10.03/10.24 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 10.03/10.24 intro zenon_D_pnotp. % 10.03/10.24 apply zenon_Hff. % 10.03/10.24 rewrite <- zenon_D_pnotp. % 10.03/10.24 exact zenon_H11b. % 10.03/10.24 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H307]. % 10.03/10.24 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.24 congruence. % 10.03/10.24 apply zenon_Hab. apply refl_equal. % 10.03/10.24 apply zenon_H307. apply sym_equal. exact zenon_Hf7. % 10.03/10.24 apply zenon_Hab. apply refl_equal. % 10.03/10.24 apply zenon_Hab. apply refl_equal. % 10.03/10.24 (* end of lemma zenon_L510_ *) % 10.03/10.24 assert (zenon_L511_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_Hc9 zenon_H11b zenon_Hfe. % 10.03/10.24 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H89. zenon_intro zenon_Hca. % 10.03/10.24 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_H9d. zenon_intro zenon_Hcb. % 10.03/10.24 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.24 apply (zenon_L510_); trivial. % 10.03/10.24 (* end of lemma zenon_L511_ *) % 10.03/10.24 assert (zenon_L512_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H172 zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_Ha5 zenon_H2a zenon_H101. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H172). zenon_intro zenon_Hb7. zenon_intro zenon_H173. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H173). zenon_intro zenon_H90. zenon_intro zenon_H174. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.03/10.24 apply (zenon_L509_); trivial. % 10.03/10.24 (* end of lemma zenon_L512_ *) % 10.03/10.24 assert (zenon_L513_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H22e zenon_H2b zenon_Hbe zenon_H30 zenon_H26 zenon_H1ec zenon_H7f zenon_H112 zenon_H101. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.24 apply (zenon_L316_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.24 apply (zenon_L38_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.24 apply (zenon_L404_); trivial. % 10.03/10.24 apply (zenon_L80_); trivial. % 10.03/10.24 (* end of lemma zenon_L513_ *) % 10.03/10.24 assert (zenon_L514_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H175 zenon_H22e zenon_H2b zenon_Hbe zenon_H30 zenon_H26 zenon_H1ec zenon_H101. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H175). zenon_intro zenon_Hb7. zenon_intro zenon_H176. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H176). zenon_intro zenon_H90. zenon_intro zenon_H177. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.03/10.24 apply (zenon_L513_); trivial. % 10.03/10.24 (* end of lemma zenon_L514_ *) % 10.03/10.24 assert (zenon_L515_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H178 zenon_H11b zenon_H2c. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H178). zenon_intro zenon_Hb7. zenon_intro zenon_H179. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H179). zenon_intro zenon_H90. zenon_intro zenon_H17a. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 10.03/10.24 apply (zenon_L505_); trivial. % 10.03/10.24 (* end of lemma zenon_L515_ *) % 10.03/10.24 assert (zenon_L516_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.24 do 0 intro. intros zenon_H17b zenon_H2a zenon_H2b. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H68. zenon_intro zenon_H17c. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H17c). zenon_intro zenon_H5e. zenon_intro zenon_H6f. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H20. zenon_intro zenon_H20. % 10.03/10.24 apply (zenon_L7_); trivial. % 10.03/10.24 (* end of lemma zenon_L516_ *) % 10.03/10.24 assert (zenon_L517_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 10.03/10.24 do 0 intro. intros zenon_H110 zenon_H26 zenon_H106. % 10.03/10.24 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e1) (e3)))). % 10.03/10.24 intro zenon_D_pnotp. % 10.03/10.24 apply zenon_H110. % 10.03/10.24 rewrite <- zenon_D_pnotp. % 10.03/10.24 exact zenon_H26. % 10.03/10.24 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 10.03/10.24 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 10.03/10.24 congruence. % 10.03/10.24 apply zenon_H61. apply refl_equal. % 10.03/10.24 apply zenon_H107. apply sym_equal. exact zenon_H106. % 10.03/10.24 (* end of lemma zenon_L517_ *) % 10.03/10.24 assert (zenon_L518_ : (((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 (e3) (e3)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H10d zenon_Hb7 zenon_H105 zenon_Hfe zenon_H11b zenon_H26 zenon_H110 zenon_H112 zenon_H101. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hfd | zenon_intro zenon_H10e ]. % 10.03/10.24 apply (zenon_L235_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H10f ]. % 10.03/10.24 apply (zenon_L510_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H106 | zenon_intro zenon_H109 ]. % 10.03/10.24 apply (zenon_L517_); trivial. % 10.03/10.24 apply (zenon_L80_); trivial. % 10.03/10.24 (* end of lemma zenon_L518_ *) % 10.03/10.24 assert (zenon_L519_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((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 (e3) (e3)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H2ee zenon_H64 zenon_H187 zenon_H2c zenon_H1ec zenon_H1d4 zenon_H83 zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_H1b9 zenon_H1f0 zenon_H10d zenon_Hb7 zenon_H105 zenon_Hfe zenon_H11b zenon_H26 zenon_H110 zenon_H101. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.03/10.24 apply (zenon_L22_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.03/10.24 apply (zenon_L401_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.03/10.24 apply (zenon_L506_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.03/10.24 apply (zenon_L406_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.03/10.24 apply (zenon_L403_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.03/10.24 apply (zenon_L174_); trivial. % 10.03/10.24 apply (zenon_L518_); trivial. % 10.03/10.24 (* end of lemma zenon_L519_ *) % 10.03/10.24 assert (zenon_L520_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.03/10.24 do 0 intro. intros zenon_H14c zenon_H90 zenon_H1d9 zenon_H5e zenon_H7a zenon_H26 zenon_H93 zenon_H14b zenon_H7f. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H94 | zenon_intro zenon_H14d ]. % 10.03/10.24 apply (zenon_L334_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 10.03/10.24 apply (zenon_L428_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H149 | zenon_intro zenon_H79 ]. % 10.03/10.24 apply (zenon_L124_); trivial. % 10.03/10.24 apply (zenon_L95_); trivial. % 10.03/10.24 (* end of lemma zenon_L520_ *) % 10.03/10.24 assert (zenon_L521_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H11b zenon_H82 zenon_H25. % 10.03/10.24 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H6a | zenon_intro zenon_H22 ]. % 10.03/10.24 cut (((e2) = (e2)) = ((e1) = (e2))). % 10.03/10.24 intro zenon_D_pnotp. % 10.03/10.24 apply zenon_H25. % 10.03/10.24 rewrite <- zenon_D_pnotp. % 10.03/10.24 exact zenon_H6a. % 10.03/10.24 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.24 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 10.03/10.24 congruence. % 10.03/10.24 cut (((op (e3) (e3)) = (e1)) = ((e2) = (e1))). % 10.03/10.24 intro zenon_D_pnotp. % 10.03/10.24 apply zenon_H6b. % 10.03/10.24 rewrite <- zenon_D_pnotp. % 10.03/10.24 exact zenon_H11b. % 10.03/10.24 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.24 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 10.03/10.24 congruence. % 10.03/10.24 exact (zenon_H191 zenon_H82). % 10.03/10.24 apply zenon_H1d. apply refl_equal. % 10.03/10.24 apply zenon_H22. apply refl_equal. % 10.03/10.24 apply zenon_H22. apply refl_equal. % 10.03/10.24 (* end of lemma zenon_L521_ *) % 10.03/10.24 assert (zenon_L522_ : (((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) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H192 zenon_H86 zenon_H11f zenon_H26 zenon_H93 zenon_Hd0 zenon_H96 zenon_H11b zenon_H25. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.03/10.24 apply (zenon_L123_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.03/10.24 apply (zenon_L124_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.03/10.24 apply (zenon_L104_); trivial. % 10.03/10.24 apply (zenon_L521_); trivial. % 10.03/10.24 (* end of lemma zenon_L522_ *) % 10.03/10.24 assert (zenon_L523_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H195 zenon_H192 zenon_H11f zenon_H26 zenon_H93 zenon_H96 zenon_H11b zenon_H25. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H188. zenon_intro zenon_H196. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H196). zenon_intro zenon_H18c. zenon_intro zenon_Hcf. % 10.03/10.24 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd0. zenon_intro zenon_H86. % 10.03/10.24 apply (zenon_L522_); trivial. % 10.03/10.24 (* end of lemma zenon_L523_ *) % 10.03/10.24 assert (zenon_L524_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H19b zenon_H155 zenon_H2b zenon_H30 zenon_H5f zenon_H26 zenon_H96 zenon_H12a. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H19b). zenon_intro zenon_H188. zenon_intro zenon_H19c. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H19c). zenon_intro zenon_H18c. zenon_intro zenon_H16b. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.03/10.24 apply (zenon_L477_); trivial. % 10.03/10.24 (* end of lemma zenon_L524_ *) % 10.03/10.24 assert (zenon_L525_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H1a5 zenon_H11b zenon_H2c. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_Hf7. zenon_intro zenon_H1a6. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1a6). zenon_intro zenon_H143. zenon_intro zenon_H17a. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 10.03/10.24 apply (zenon_L505_); trivial. % 10.03/10.24 (* end of lemma zenon_L525_ *) % 10.03/10.24 assert (zenon_L526_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.24 do 0 intro. intros zenon_H1a7 zenon_H2a zenon_H2b. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H86. zenon_intro zenon_H1a8. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hd0. zenon_intro zenon_H6f. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H20. zenon_intro zenon_H20. % 10.03/10.24 apply (zenon_L7_); trivial. % 10.03/10.24 (* end of lemma zenon_L526_ *) % 10.03/10.24 assert (zenon_L527_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H1a9 zenon_H192 zenon_H11f zenon_H26 zenon_H93 zenon_H96 zenon_H11b zenon_H25. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1a9). zenon_intro zenon_H86. zenon_intro zenon_H1aa. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_Hd0. zenon_intro zenon_Hb3. % 10.03/10.24 apply (zenon_L522_); trivial. % 10.03/10.24 (* end of lemma zenon_L527_ *) % 10.03/10.24 assert (zenon_L528_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H1ad zenon_H192 zenon_H11f zenon_H26 zenon_H93 zenon_H96 zenon_H11b zenon_H25. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H86. zenon_intro zenon_H1ae. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_Hd0. zenon_intro zenon_Hbd. % 10.03/10.24 apply (zenon_L522_); trivial. % 10.03/10.24 (* end of lemma zenon_L528_ *) % 10.03/10.24 assert (zenon_L529_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H21c zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_Ha5 zenon_H2a zenon_H101. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H21c). zenon_intro zenon_H128. zenon_intro zenon_H21d. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H166. zenon_intro zenon_H174. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.03/10.24 apply (zenon_L509_); trivial. % 10.03/10.24 (* end of lemma zenon_L529_ *) % 10.03/10.24 assert (zenon_L530_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H1e4 zenon_H11b zenon_H2c. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1e4). zenon_intro zenon_H128. zenon_intro zenon_H1e5. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1e5). zenon_intro zenon_H166. zenon_intro zenon_H17a. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 10.03/10.24 apply (zenon_L505_); trivial. % 10.03/10.24 (* end of lemma zenon_L530_ *) % 10.03/10.24 assert (zenon_L531_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.24 do 0 intro. intros zenon_H1fb zenon_H1c9 zenon_H2b. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H72. zenon_intro zenon_H1fc. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_He2. zenon_intro zenon_Hbd. % 10.03/10.24 apply (zenon_L370_); trivial. % 10.03/10.24 (* end of lemma zenon_L531_ *) % 10.03/10.24 assert (zenon_L532_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H1fd zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_Ha5 zenon_H2a zenon_H101. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H79. zenon_intro zenon_H1fe. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H109. zenon_intro zenon_Hc2. % 10.03/10.24 apply (zenon_L509_); trivial. % 10.03/10.24 (* end of lemma zenon_L532_ *) % 10.03/10.24 assert (zenon_L533_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H223 zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_Ha5 zenon_H2a zenon_H101. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H79. zenon_intro zenon_H224. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H109. zenon_intro zenon_Hc8. % 10.03/10.24 apply (zenon_L509_); trivial. % 10.03/10.24 (* end of lemma zenon_L533_ *) % 10.03/10.24 assert (zenon_L534_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H203 zenon_H22e zenon_H2b zenon_Hbe zenon_H30 zenon_H26 zenon_H1ec zenon_H101. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H203). zenon_intro zenon_H7f. zenon_intro zenon_H204. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H204). zenon_intro zenon_H112. zenon_intro zenon_Hcf. % 10.03/10.24 apply (zenon_L513_); trivial. % 10.03/10.24 (* end of lemma zenon_L534_ *) % 10.03/10.24 assert (zenon_L535_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.24 do 0 intro. intros zenon_H20b zenon_H1d4 zenon_H2b. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_H52. zenon_intro zenon_H20c. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H20c). zenon_intro zenon_H52. zenon_intro zenon_H171. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.24 apply (zenon_L402_); trivial. % 10.03/10.24 (* end of lemma zenon_L535_ *) % 10.03/10.24 assert (zenon_L536_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H20d zenon_H11b zenon_H2c. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H52. zenon_intro zenon_H20e. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H20e). zenon_intro zenon_H52. zenon_intro zenon_H174. % 10.03/10.24 apply (zenon_L505_); trivial. % 10.03/10.24 (* end of lemma zenon_L536_ *) % 10.03/10.24 assert (zenon_L537_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H20f zenon_H11b zenon_H2c. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H20f). zenon_intro zenon_H52. zenon_intro zenon_H210. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H210). zenon_intro zenon_H52. zenon_intro zenon_H177. % 10.03/10.24 apply (zenon_L505_); trivial. % 10.03/10.24 (* end of lemma zenon_L537_ *) % 10.03/10.24 assert (zenon_L538_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H211 zenon_H11b zenon_H2c. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H211). zenon_intro zenon_H52. zenon_intro zenon_H212. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H212). zenon_intro zenon_H52. zenon_intro zenon_H17a. % 10.03/10.24 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 10.03/10.24 apply (zenon_L505_); trivial. % 10.03/10.24 (* end of lemma zenon_L538_ *) % 10.03/10.24 assert (zenon_L539_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.03/10.24 do 0 intro. intros zenon_H13d zenon_H43 zenon_H26 zenon_H23 zenon_H1b9 zenon_Ha5 zenon_H105 zenon_Hb7. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.03/10.24 apply (zenon_L88_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.03/10.24 apply (zenon_L31_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.03/10.24 apply (zenon_L341_); trivial. % 10.03/10.24 apply (zenon_L235_); trivial. % 10.03/10.24 (* end of lemma zenon_L539_ *) % 10.03/10.24 assert (zenon_L540_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H2c7 zenon_H2ac zenon_Ha5 zenon_H4f zenon_H26 zenon_Hd1 zenon_H79 zenon_H2c4. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H2c8 ]. % 10.03/10.24 apply (zenon_L333_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2c8); [ zenon_intro zenon_H18c | zenon_intro zenon_H2c9 ]. % 10.03/10.24 apply (zenon_L205_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2c9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H121 ]. % 10.03/10.24 apply (zenon_L56_); trivial. % 10.03/10.24 apply (zenon_L403_); trivial. % 10.03/10.24 (* end of lemma zenon_L540_ *) % 10.03/10.24 assert (zenon_L541_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 10.03/10.24 do 0 intro. intros zenon_H2ee zenon_H64 zenon_H30 zenon_H2c zenon_H11b zenon_H1f0 zenon_H1ec zenon_H1d4 zenon_H2b zenon_H83 zenon_H2c7 zenon_H2ac zenon_Ha5 zenon_H4f zenon_H26 zenon_Hd1 zenon_H2c4. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.03/10.24 apply (zenon_L22_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.03/10.24 apply (zenon_L38_); trivial. % 10.03/10.24 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.03/10.24 apply (zenon_L506_); trivial. % 10.03/10.24 apply (zenon_L540_); trivial. % 10.03/10.24 (* end of lemma zenon_L541_ *) % 10.03/10.24 assert (zenon_L542_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> False). % 10.03/10.25 do 0 intro. intros zenon_H272 zenon_H7f zenon_H26 zenon_H5e zenon_H89 zenon_Ha5 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2c zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.03/10.25 apply (zenon_L520_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.03/10.25 apply (zenon_L382_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.03/10.25 apply (zenon_L383_); trivial. % 10.03/10.25 apply (zenon_L500_); trivial. % 10.03/10.25 (* end of lemma zenon_L542_ *) % 10.03/10.25 assert (zenon_L543_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.03/10.25 do 0 intro. intros zenon_H83 zenon_H1d4 zenon_H101 zenon_H109 zenon_H2a zenon_Ha5 zenon_H2c4 zenon_H2dd zenon_H2b zenon_H12f zenon_H1ec zenon_H1f0 zenon_H11b zenon_H2c. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.03/10.25 apply (zenon_L402_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.03/10.25 apply (zenon_L509_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.03/10.25 apply (zenon_L404_); trivial. % 10.03/10.25 apply (zenon_L505_); trivial. % 10.03/10.25 (* end of lemma zenon_L543_ *) % 10.03/10.25 assert (zenon_L544_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 10.03/10.25 do 0 intro. intros zenon_H127 zenon_Ha5 zenon_Ha8. % 10.03/10.25 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e2) (e3)))). % 10.03/10.25 intro zenon_D_pnotp. % 10.03/10.25 apply zenon_H127. % 10.03/10.25 rewrite <- zenon_D_pnotp. % 10.03/10.25 exact zenon_Ha5. % 10.03/10.25 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 10.03/10.25 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.03/10.25 congruence. % 10.03/10.25 apply zenon_H81. apply refl_equal. % 10.03/10.25 apply zenon_Had. apply sym_equal. exact zenon_Ha8. % 10.03/10.25 (* end of lemma zenon_L544_ *) % 10.03/10.25 assert (zenon_L545_ : ((op (e3) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.25 do 0 intro. intros zenon_H11b zenon_H102 zenon_Ha9. % 10.03/10.25 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.03/10.25 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 10.03/10.25 intro zenon_D_pnotp. % 10.03/10.25 apply zenon_Ha9. % 10.03/10.25 rewrite <- zenon_D_pnotp. % 10.03/10.25 exact zenon_Haa. % 10.03/10.25 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.25 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 10.03/10.25 congruence. % 10.03/10.25 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 10.03/10.25 intro zenon_D_pnotp. % 10.03/10.25 apply zenon_Hac. % 10.03/10.25 rewrite <- zenon_D_pnotp. % 10.03/10.25 exact zenon_H11b. % 10.03/10.25 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 10.03/10.25 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.03/10.25 congruence. % 10.03/10.25 apply zenon_Hab. apply refl_equal. % 10.03/10.25 apply zenon_H103. apply sym_equal. exact zenon_H102. % 10.03/10.25 apply zenon_Hab. apply refl_equal. % 10.03/10.25 apply zenon_Hab. apply refl_equal. % 10.03/10.25 (* end of lemma zenon_L545_ *) % 10.03/10.25 assert (zenon_L546_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.25 do 0 intro. intros zenon_H2ee zenon_H64 zenon_H110 zenon_H1ec zenon_H26 zenon_H30 zenon_Hbe zenon_H22e zenon_Hf4 zenon_H12a zenon_H11b zenon_Ha9 zenon_H127 zenon_H12c zenon_H2ac zenon_H83 zenon_H1d4 zenon_H2c zenon_Hef zenon_H2f7 zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_Ha5 zenon_H2a zenon_H109 zenon_H101. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.03/10.25 apply (zenon_L22_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.03/10.25 apply (zenon_L73_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.03/10.25 apply (zenon_L64_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.03/10.25 apply (zenon_L543_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.03/10.25 apply (zenon_L389_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.03/10.25 apply (zenon_L544_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.03/10.25 apply (zenon_L545_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.03/10.25 apply (zenon_L105_); trivial. % 10.03/10.25 apply (zenon_L513_); trivial. % 10.03/10.25 apply (zenon_L509_); trivial. % 10.03/10.25 (* end of lemma zenon_L546_ *) % 10.03/10.25 assert (zenon_L547_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.25 do 0 intro. intros zenon_Hd1 zenon_H4f zenon_H2c7 zenon_H2ee zenon_H64 zenon_H110 zenon_H1ec zenon_H26 zenon_H30 zenon_Hbe zenon_H22e zenon_Hf4 zenon_H12a zenon_H11b zenon_Ha9 zenon_H127 zenon_H12c zenon_H2ac zenon_H83 zenon_H1d4 zenon_H2c zenon_Hef zenon_H2f7 zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_Ha5 zenon_H2a zenon_H101. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.25 apply (zenon_L316_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.25 apply (zenon_L38_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.25 apply (zenon_L541_); trivial. % 10.03/10.25 apply (zenon_L546_); trivial. % 10.03/10.25 (* end of lemma zenon_L547_ *) % 10.03/10.25 assert (zenon_L548_ : (~((op (e2) (op (e2) (e3))) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.25 do 0 intro. intros zenon_H50 zenon_H272 zenon_H5e zenon_H89 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H16c zenon_H155 zenon_H5f zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H187 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e zenon_H9d zenon_Hd1 zenon_H4f zenon_H2c7 zenon_H2ee zenon_H64 zenon_H110 zenon_H1ec zenon_H26 zenon_H30 zenon_Hbe zenon_H22e zenon_H12a zenon_H11b zenon_Ha9 zenon_H127 zenon_H12c zenon_H2ac zenon_H83 zenon_H1d4 zenon_H2c zenon_Hef zenon_H2f7 zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_Ha5 zenon_H2a zenon_H101. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.03/10.25 apply (zenon_L384_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.03/10.25 apply (zenon_L29_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.03/10.25 apply (zenon_L152_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.03/10.25 apply (zenon_L153_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.03/10.25 apply (zenon_L522_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.25 apply (zenon_L316_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.25 apply (zenon_L38_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.25 apply (zenon_L541_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.03/10.25 apply (zenon_L22_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.03/10.25 apply (zenon_L73_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.03/10.25 apply (zenon_L123_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.03/10.25 apply (zenon_L56_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.03/10.25 apply (zenon_L63_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.03/10.25 apply (zenon_L64_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.03/10.25 apply (zenon_L506_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.03/10.25 apply (zenon_L199_); trivial. % 10.03/10.25 apply (zenon_L542_); trivial. % 10.03/10.25 apply (zenon_L540_); trivial. % 10.03/10.25 apply (zenon_L547_); trivial. % 10.03/10.25 (* end of lemma zenon_L548_ *) % 10.03/10.25 assert (zenon_L549_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.03/10.25 do 0 intro. intros zenon_H272 zenon_H5a zenon_H89 zenon_H7a zenon_Ha5 zenon_H7e zenon_H11b zenon_H1e. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.03/10.25 apply (zenon_L381_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.03/10.25 apply (zenon_L382_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.03/10.25 apply (zenon_L383_); trivial. % 10.03/10.25 apply (zenon_L77_); trivial. % 10.03/10.25 (* end of lemma zenon_L549_ *) % 10.03/10.25 assert (zenon_L550_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.03/10.25 do 0 intro. intros zenon_Hc0 zenon_H272 zenon_H5a zenon_H7a zenon_Ha5 zenon_H7e zenon_H11b zenon_H1e. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_H89. zenon_intro zenon_Hc1. % 10.03/10.25 apply (zenon_L549_); trivial. % 10.03/10.25 (* end of lemma zenon_L550_ *) % 10.03/10.25 assert (zenon_L551_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.03/10.25 do 0 intro. intros zenon_Hc6 zenon_H272 zenon_H5a zenon_H7a zenon_Ha5 zenon_H7e zenon_H11b zenon_H1e. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_H89. zenon_intro zenon_Hc7. % 10.03/10.25 apply (zenon_L549_); trivial. % 10.03/10.25 (* end of lemma zenon_L551_ *) % 10.03/10.25 assert (zenon_L552_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.03/10.25 do 0 intro. intros zenon_H17d zenon_H272 zenon_H5a zenon_H7a zenon_Ha5 zenon_H7e zenon_H11b zenon_H1e. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H68. zenon_intro zenon_H17e. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H17e). zenon_intro zenon_H5e. zenon_intro zenon_Hb3. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.03/10.25 apply (zenon_L549_); trivial. % 10.03/10.25 (* end of lemma zenon_L552_ *) % 10.03/10.25 assert (zenon_L553_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> False). % 10.03/10.25 do 0 intro. intros zenon_H181 zenon_H5a. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_H5e. zenon_intro zenon_Hbd. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.03/10.25 apply (zenon_L381_); trivial. % 10.03/10.25 (* end of lemma zenon_L553_ *) % 10.03/10.25 assert (zenon_L554_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.03/10.25 do 0 intro. intros zenon_H1f6 zenon_Ha5 zenon_H7e zenon_H188 zenon_H1ec zenon_H5d zenon_H14b zenon_H79. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.03/10.25 apply (zenon_L383_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.03/10.25 apply (zenon_L172_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.03/10.25 apply (zenon_L208_); trivial. % 10.03/10.25 apply (zenon_L95_); trivial. % 10.03/10.25 (* end of lemma zenon_L554_ *) % 10.03/10.25 assert (zenon_L555_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 10.03/10.25 do 0 intro. intros zenon_H223 zenon_H1f6 zenon_Ha5 zenon_H7e zenon_H1ec zenon_H5d zenon_H14b. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H79. zenon_intro zenon_H224. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H109. zenon_intro zenon_Hc8. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.03/10.25 apply (zenon_L554_); trivial. % 10.03/10.25 (* end of lemma zenon_L555_ *) % 10.03/10.25 assert (zenon_L556_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (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) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.03/10.25 do 0 intro. intros zenon_H1d4 zenon_H23 zenon_Hd1 zenon_H22e zenon_Hbe zenon_H1ec zenon_H101 zenon_H1f6 zenon_H7e zenon_H14b zenon_H25 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_Heb zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H105 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H110 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H12a zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H26 zenon_Ha5 zenon_H2a zenon_H11b zenon_H2c. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_Hd8. zenon_intro zenon_H15b. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_H15c. zenon_intro zenon_He1. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.25 apply (zenon_L21_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.25 apply (zenon_L473_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.25 apply (zenon_L474_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.25 apply (zenon_L504_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.25 apply (zenon_L246_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.25 apply (zenon_L51_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_H89. zenon_intro zenon_Hc7. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_H9d. zenon_intro zenon_Hc8. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.25 apply (zenon_L316_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.25 apply (zenon_L38_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.25 apply (zenon_L315_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.03/10.25 apply (zenon_L22_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.03/10.25 apply (zenon_L73_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.03/10.25 apply (zenon_L64_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.03/10.25 apply (zenon_L506_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.03/10.25 apply (zenon_L389_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.03/10.25 apply (zenon_L508_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.03/10.25 apply (zenon_L382_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.03/10.25 apply (zenon_L383_); trivial. % 10.03/10.25 apply (zenon_L77_); trivial. % 10.03/10.25 apply (zenon_L509_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.25 apply (zenon_L511_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.25 apply (zenon_L55_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.25 apply (zenon_L57_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.25 apply (zenon_L325_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.25 apply (zenon_L478_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.25 apply (zenon_L479_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.25 apply (zenon_L512_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.25 apply (zenon_L514_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.25 apply (zenon_L515_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.25 apply (zenon_L516_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.25 apply (zenon_L264_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.25 apply (zenon_L332_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_H5e. zenon_intro zenon_Hbd. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.25 apply (zenon_L316_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.25 apply (zenon_L38_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.25 apply (zenon_L519_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.03/10.25 apply (zenon_L22_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.03/10.25 apply (zenon_L73_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.03/10.25 apply (zenon_L64_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.03/10.25 apply (zenon_L519_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.03/10.25 apply (zenon_L389_); trivial. % 10.03/10.25 apply (zenon_L520_); trivial. % 10.03/10.25 apply (zenon_L509_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.25 apply (zenon_L117_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.25 apply (zenon_L118_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.25 apply (zenon_L121_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.25 apply (zenon_L122_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.25 apply (zenon_L523_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.25 apply (zenon_L128_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.25 apply (zenon_L337_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.25 apply (zenon_L524_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.25 apply (zenon_L131_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.25 apply (zenon_L133_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.25 apply (zenon_L482_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.25 apply (zenon_L525_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.25 apply (zenon_L526_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.25 apply (zenon_L527_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.25 apply (zenon_L138_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.25 apply (zenon_L528_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.25 apply (zenon_L140_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.25 apply (zenon_L141_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.25 apply (zenon_L142_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.25 apply (zenon_L143_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.25 apply (zenon_L284_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.25 apply (zenon_L146_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.25 apply (zenon_L345_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.25 apply (zenon_L149_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.25 apply (zenon_L150_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.25 apply (zenon_L529_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.25 apply (zenon_L167_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.25 apply (zenon_L530_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.25 apply (zenon_L486_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.25 apply (zenon_L487_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.25 apply (zenon_L488_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.25 apply (zenon_L531_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.25 apply (zenon_L532_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.25 apply (zenon_L182_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.25 apply (zenon_L533_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.25 apply (zenon_L183_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.25 apply (zenon_L534_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.25 apply (zenon_L185_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.25 apply (zenon_L355_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.25 apply (zenon_L187_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.25 apply (zenon_L535_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.25 apply (zenon_L536_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.25 apply (zenon_L537_); trivial. % 10.03/10.25 apply (zenon_L538_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.25 apply (zenon_L21_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.25 apply (zenon_L473_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.25 apply (zenon_L474_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.25 apply (zenon_L504_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.25 apply (zenon_L302_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.25 apply (zenon_L51_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.25 apply (zenon_L303_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.25 apply (zenon_L304_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.25 apply (zenon_L55_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.25 apply (zenon_L57_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.25 apply (zenon_L325_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.25 apply (zenon_L478_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.25 apply (zenon_L479_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.25 apply (zenon_L512_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.25 apply (zenon_L514_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.25 apply (zenon_L515_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.25 apply (zenon_L516_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.25 apply (zenon_L309_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.25 apply (zenon_L332_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_H5e. zenon_intro zenon_Hbd. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.03/10.25 apply (zenon_L539_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.25 apply (zenon_L117_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.25 apply (zenon_L118_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.25 apply (zenon_L121_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.25 apply (zenon_L122_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.25 apply (zenon_L523_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.25 apply (zenon_L128_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.25 apply (zenon_L337_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.25 apply (zenon_L524_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.25 apply (zenon_L480_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.25 apply (zenon_L133_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.25 apply (zenon_L482_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.25 apply (zenon_L525_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.25 apply (zenon_L526_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.25 apply (zenon_L527_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.25 apply (zenon_L138_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.25 apply (zenon_L528_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.25 apply (zenon_L140_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.25 apply (zenon_L141_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.25 apply (zenon_L142_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.25 apply (zenon_L143_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.25 apply (zenon_L284_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.25 apply (zenon_L193_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.25 apply (zenon_L345_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.25 apply (zenon_L149_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.25 apply (zenon_L483_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.25 apply (zenon_L529_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.25 apply (zenon_L167_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.25 apply (zenon_L530_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.25 apply (zenon_L486_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.25 apply (zenon_L195_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.25 apply (zenon_L488_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.25 apply (zenon_L531_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.25 apply (zenon_L532_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.25 apply (zenon_L182_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.25 apply (zenon_L533_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.25 apply (zenon_L183_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.25 apply (zenon_L534_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.25 apply (zenon_L185_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.25 apply (zenon_L355_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.25 apply (zenon_L187_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.25 apply (zenon_L535_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.25 apply (zenon_L536_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.25 apply (zenon_L537_); trivial. % 10.03/10.25 apply (zenon_L538_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.25 apply (zenon_L21_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.25 apply (zenon_L473_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.25 apply (zenon_L474_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.25 apply (zenon_L504_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_H89. zenon_intro zenon_Hc1. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H9d. zenon_intro zenon_Hc2. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.03/10.25 apply (zenon_L548_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.25 apply (zenon_L51_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.25 apply (zenon_L364_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H89. zenon_intro zenon_Hca. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_H9d. zenon_intro zenon_Hcb. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.25 apply (zenon_L316_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.25 apply (zenon_L38_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.25 apply (zenon_L541_); trivial. % 10.03/10.25 apply (zenon_L132_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.25 apply (zenon_L55_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.25 apply (zenon_L57_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.25 apply (zenon_L325_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.25 apply (zenon_L198_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.25 apply (zenon_L479_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.25 apply (zenon_L512_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.25 apply (zenon_L514_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.25 apply (zenon_L515_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.25 apply (zenon_L516_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H68. zenon_intro zenon_H17e. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H17e). zenon_intro zenon_H5e. zenon_intro zenon_Hb3. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.03/10.25 apply (zenon_L548_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.25 apply (zenon_L332_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_H5e. zenon_intro zenon_Hbd. % 10.03/10.25 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.03/10.25 apply (zenon_L384_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.03/10.25 apply (zenon_L103_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.03/10.25 apply (zenon_L522_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.03/10.25 apply (zenon_L56_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.03/10.25 apply (zenon_L324_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.03/10.25 apply (zenon_L64_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.03/10.25 apply (zenon_L541_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.03/10.25 apply (zenon_L199_); trivial. % 10.03/10.25 apply (zenon_L520_); trivial. % 10.03/10.25 apply (zenon_L547_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.25 apply (zenon_L117_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.25 apply (zenon_L118_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.25 apply (zenon_L121_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.25 apply (zenon_L122_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.25 apply (zenon_L523_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.25 apply (zenon_L128_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.25 apply (zenon_L337_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.25 apply (zenon_L524_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.25 apply (zenon_L480_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.25 apply (zenon_L133_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.25 apply (zenon_L482_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.25 apply (zenon_L525_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.25 apply (zenon_L526_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.25 apply (zenon_L527_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.25 apply (zenon_L138_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.25 apply (zenon_L528_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.25 apply (zenon_L140_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.25 apply (zenon_L141_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.25 apply (zenon_L142_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.25 apply (zenon_L143_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.25 apply (zenon_L284_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.25 apply (zenon_L146_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.25 apply (zenon_L345_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.25 apply (zenon_L149_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.25 apply (zenon_L483_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.25 apply (zenon_L529_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.25 apply (zenon_L167_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.25 apply (zenon_L530_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.25 apply (zenon_L486_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.25 apply (zenon_L487_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.25 apply (zenon_L204_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.25 apply (zenon_L531_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.25 apply (zenon_L532_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.25 apply (zenon_L182_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.25 apply (zenon_L206_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.25 apply (zenon_L183_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.25 apply (zenon_L534_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.25 apply (zenon_L185_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.25 apply (zenon_L355_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.25 apply (zenon_L187_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.25 apply (zenon_L535_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.25 apply (zenon_L536_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.25 apply (zenon_L537_); trivial. % 10.03/10.25 apply (zenon_L538_); trivial. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 10.03/10.25 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H51. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.25 apply (zenon_L21_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.25 apply (zenon_L473_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.25 apply (zenon_L474_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.25 apply (zenon_L502_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.25 apply (zenon_L550_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.25 apply (zenon_L51_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.25 apply (zenon_L551_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.25 apply (zenon_L207_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.25 apply (zenon_L55_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.25 apply (zenon_L57_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.25 apply (zenon_L325_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.25 apply (zenon_L209_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.25 apply (zenon_L479_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.25 apply (zenon_L512_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.25 apply (zenon_L514_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.25 apply (zenon_L515_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.25 apply (zenon_L516_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.25 apply (zenon_L552_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.25 apply (zenon_L332_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.25 apply (zenon_L553_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.25 apply (zenon_L117_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.25 apply (zenon_L118_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.25 apply (zenon_L121_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.25 apply (zenon_L122_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.25 apply (zenon_L523_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.25 apply (zenon_L128_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.25 apply (zenon_L337_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.25 apply (zenon_L211_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.25 apply (zenon_L480_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.25 apply (zenon_L133_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.25 apply (zenon_L482_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.25 apply (zenon_L525_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.25 apply (zenon_L526_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.25 apply (zenon_L527_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.25 apply (zenon_L138_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.25 apply (zenon_L528_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.25 apply (zenon_L140_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.25 apply (zenon_L141_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.25 apply (zenon_L142_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.25 apply (zenon_L143_); trivial. % 10.03/10.25 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.26 apply (zenon_L284_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.26 apply (zenon_L193_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.26 apply (zenon_L345_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.26 apply (zenon_L213_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.26 apply (zenon_L483_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.26 apply (zenon_L529_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.26 apply (zenon_L167_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.26 apply (zenon_L530_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.26 apply (zenon_L486_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.26 apply (zenon_L487_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.26 apply (zenon_L488_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.26 apply (zenon_L531_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.26 apply (zenon_L532_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.26 apply (zenon_L182_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.26 apply (zenon_L555_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.26 apply (zenon_L183_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.26 apply (zenon_L534_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.26 apply (zenon_L185_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.26 apply (zenon_L355_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.26 apply (zenon_L187_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.26 apply (zenon_L535_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.26 apply (zenon_L536_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.26 apply (zenon_L537_); trivial. % 10.03/10.26 apply (zenon_L538_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.03/10.26 apply (zenon_L38_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.03/10.26 apply (zenon_L42_); trivial. % 10.03/10.26 apply (zenon_L505_); trivial. % 10.03/10.26 (* end of lemma zenon_L556_ *) % 10.03/10.26 assert (zenon_L557_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H192 zenon_H24 zenon_H1d4 zenon_Hd2 zenon_H2c4 zenon_Hd7 zenon_H1ec zenon_H11b zenon_H25. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.03/10.26 apply (zenon_L217_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.03/10.26 apply (zenon_L386_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.03/10.26 apply (zenon_L219_); trivial. % 10.03/10.26 apply (zenon_L521_); trivial. % 10.03/10.26 (* end of lemma zenon_L557_ *) % 10.03/10.26 assert (zenon_L558_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H12f zenon_H11f zenon_H72 zenon_H2d zenon_Hd1 zenon_Heb zenon_Hde zenon_H128 zenon_H30. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.03/10.26 apply (zenon_L78_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.03/10.26 apply (zenon_L79_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.03/10.26 apply (zenon_L259_); trivial. % 10.03/10.26 apply (zenon_L166_); trivial. % 10.03/10.26 (* end of lemma zenon_L558_ *) % 10.03/10.26 assert (zenon_L559_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (op (e0) (e3))) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H118 zenon_He1 zenon_H110 zenon_H7f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_Hde zenon_H130 zenon_H11b zenon_H2c. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_He2 | zenon_intro zenon_H119 ]. % 10.03/10.26 apply (zenon_L61_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H109 | zenon_intro zenon_H11a ]. % 10.03/10.26 apply (zenon_L73_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H112 | zenon_intro zenon_H52 ]. % 10.03/10.26 apply (zenon_L329_); trivial. % 10.03/10.26 apply (zenon_L505_); trivial. % 10.03/10.26 (* end of lemma zenon_L559_ *) % 10.03/10.26 assert (zenon_L560_ : (((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 (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.03/10.26 do 0 intro. intros zenon_H14c zenon_H89 zenon_H7a zenon_H141 zenon_H11b zenon_Hd2 zenon_H2c4 zenon_H1d9 zenon_H72. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H94 | zenon_intro zenon_H14d ]. % 10.03/10.26 apply (zenon_L382_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 10.03/10.26 apply (zenon_L507_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H149 | zenon_intro zenon_H79 ]. % 10.03/10.26 apply (zenon_L386_); trivial. % 10.03/10.26 apply (zenon_L162_); trivial. % 10.03/10.26 (* end of lemma zenon_L560_ *) % 10.03/10.26 assert (zenon_L561_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H1cb zenon_H24 zenon_H2dd zenon_H149 zenon_H2c4 zenon_H23 zenon_Ha5 zenon_H106 zenon_H101. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.03/10.26 apply (zenon_L399_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.03/10.26 apply (zenon_L386_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.03/10.26 apply (zenon_L324_); trivial. % 10.03/10.26 apply (zenon_L241_); trivial. % 10.03/10.26 (* end of lemma zenon_L561_ *) % 10.03/10.26 assert (zenon_L562_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H2ca zenon_H110 zenon_H72 zenon_H1d9 zenon_H11b zenon_H141 zenon_H7a zenon_H89 zenon_H14c zenon_H1cb zenon_H24 zenon_H2dd zenon_H2c4 zenon_H23 zenon_Ha5 zenon_H106 zenon_H101. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.03/10.26 apply (zenon_L29_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.03/10.26 apply (zenon_L517_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.03/10.26 apply (zenon_L560_); trivial. % 10.03/10.26 apply (zenon_L561_); trivial. % 10.03/10.26 (* end of lemma zenon_L562_ *) % 10.03/10.26 assert (zenon_L563_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.26 do 0 intro. intros zenon_Hd4 zenon_H192 zenon_H24 zenon_H1d4 zenon_H2c4 zenon_H1ec zenon_H11b zenon_H25. % 10.03/10.26 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_H97. zenon_intro zenon_Hd5. % 10.03/10.26 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_H9e. zenon_intro zenon_Hd6. % 10.03/10.26 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.03/10.26 apply (zenon_L557_); trivial. % 10.03/10.26 (* end of lemma zenon_L563_ *) % 10.03/10.26 assert (zenon_L564_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H2a8 zenon_H24 zenon_Hbe zenon_H30 zenon_H2d zenon_H166 zenon_H1ec zenon_H128 zenon_H101. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.03/10.26 apply (zenon_L385_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.03/10.26 apply (zenon_L38_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.03/10.26 apply (zenon_L219_); trivial. % 10.03/10.26 apply (zenon_L241_); trivial. % 10.03/10.26 (* end of lemma zenon_L564_ *) % 10.03/10.26 assert (zenon_L565_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H169 zenon_H2a8 zenon_H24 zenon_Hbe zenon_H30 zenon_H2d zenon_H1ec zenon_H101. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H169). zenon_intro zenon_H97. zenon_intro zenon_H16a. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H16a). zenon_intro zenon_H9e. zenon_intro zenon_H16b. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.03/10.26 apply (zenon_L564_); trivial. % 10.03/10.26 (* end of lemma zenon_L565_ *) % 10.03/10.26 assert (zenon_L566_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.26 do 0 intro. intros zenon_He8 zenon_H24 zenon_H30 zenon_H5f zenon_H7f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H112 zenon_H12a. % 10.03/10.26 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.03/10.26 apply (zenon_L384_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.03/10.26 apply (zenon_L59_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.03/10.26 apply (zenon_L329_); trivial. % 10.03/10.26 apply (zenon_L84_); trivial. % 10.03/10.26 (* end of lemma zenon_L566_ *) % 10.03/10.26 assert (zenon_L567_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H175 zenon_He8 zenon_H24 zenon_H30 zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H175). zenon_intro zenon_Hb7. zenon_intro zenon_H176. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H176). zenon_intro zenon_H90. zenon_intro zenon_H177. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.03/10.26 apply (zenon_L566_); trivial. % 10.03/10.26 (* end of lemma zenon_L567_ *) % 10.03/10.26 assert (zenon_L568_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.26 do 0 intro. intros zenon_H17b zenon_H23 zenon_H24. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H68. zenon_intro zenon_H17c. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H17c). zenon_intro zenon_H5e. zenon_intro zenon_H6f. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H20. zenon_intro zenon_H20. % 10.03/10.26 apply (zenon_L4_); trivial. % 10.03/10.26 (* end of lemma zenon_L568_ *) % 10.03/10.26 assert (zenon_L569_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H18d zenon_H11b zenon_Hfe. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H18d). zenon_intro zenon_H27. zenon_intro zenon_H18e. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H18e). zenon_intro zenon_H27. zenon_intro zenon_Hcb. % 10.03/10.26 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.26 apply (zenon_L510_); trivial. % 10.03/10.26 (* end of lemma zenon_L569_ *) % 10.03/10.26 assert (zenon_L570_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H197 zenon_H192 zenon_H24 zenon_H1d4 zenon_H2c4 zenon_H1ec zenon_H11b zenon_H25. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H197). zenon_intro zenon_H188. zenon_intro zenon_H198. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H198). zenon_intro zenon_H18c. zenon_intro zenon_Hd6. % 10.03/10.26 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.03/10.26 apply (zenon_L557_); trivial. % 10.03/10.26 (* end of lemma zenon_L570_ *) % 10.03/10.26 assert (zenon_L571_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H19b zenon_H2a8 zenon_H24 zenon_Hbe zenon_H30 zenon_H2d zenon_H1ec zenon_H101. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H19b). zenon_intro zenon_H188. zenon_intro zenon_H19c. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H19c). zenon_intro zenon_H18c. zenon_intro zenon_H16b. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.03/10.26 apply (zenon_L564_); trivial. % 10.03/10.26 (* end of lemma zenon_L571_ *) % 10.03/10.26 assert (zenon_L572_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H1a3 zenon_He8 zenon_H24 zenon_H30 zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_Hf7. zenon_intro zenon_H1a4. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1a4). zenon_intro zenon_H143. zenon_intro zenon_H177. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.03/10.26 apply (zenon_L566_); trivial. % 10.03/10.26 (* end of lemma zenon_L572_ *) % 10.03/10.26 assert (zenon_L573_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.26 do 0 intro. intros zenon_H1ad zenon_Hef zenon_H24. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H86. zenon_intro zenon_H1ae. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_Hd0. zenon_intro zenon_Hbd. % 10.03/10.26 apply (zenon_L152_); trivial. % 10.03/10.26 (* end of lemma zenon_L573_ *) % 10.03/10.26 assert (zenon_L574_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H1af zenon_H192 zenon_H24 zenon_H1d4 zenon_H2c4 zenon_H1ec zenon_H11b zenon_H25. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_Hd2. zenon_intro zenon_H1b0. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hd7. zenon_intro zenon_Hc2. % 10.03/10.26 apply (zenon_L557_); trivial. % 10.03/10.26 (* end of lemma zenon_L574_ *) % 10.03/10.26 assert (zenon_L575_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H1b3 zenon_H192 zenon_H24 zenon_H1d4 zenon_H2c4 zenon_H1ec zenon_H11b zenon_H25. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_Hd2. zenon_intro zenon_H1b4. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1b4). zenon_intro zenon_Hd7. zenon_intro zenon_Hc8. % 10.03/10.26 apply (zenon_L557_); trivial. % 10.03/10.26 (* end of lemma zenon_L575_ *) % 10.03/10.26 assert (zenon_L576_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H1b5 zenon_H11b zenon_Hfe. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_Hd2. zenon_intro zenon_H1b6. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_Hd7. zenon_intro zenon_Hcb. % 10.03/10.26 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.26 apply (zenon_L510_); trivial. % 10.03/10.26 (* end of lemma zenon_L576_ *) % 10.03/10.26 assert (zenon_L577_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H205 zenon_He8 zenon_H24 zenon_H30 zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H7f. zenon_intro zenon_H206. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H112. zenon_intro zenon_Hd6. % 10.03/10.26 apply (zenon_L566_); trivial. % 10.03/10.26 (* end of lemma zenon_L577_ *) % 10.03/10.26 assert (zenon_L578_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H1ad zenon_H5a. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H86. zenon_intro zenon_H1ae. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_Hd0. zenon_intro zenon_Hbd. % 10.03/10.26 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.03/10.26 apply (zenon_L381_); trivial. % 10.03/10.26 (* end of lemma zenon_L578_ *) % 10.03/10.26 assert (zenon_L579_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H1fb zenon_H5a. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H72. zenon_intro zenon_H1fc. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_He2. zenon_intro zenon_Hbd. % 10.03/10.26 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.03/10.26 apply (zenon_L381_); trivial. % 10.03/10.26 (* end of lemma zenon_L579_ *) % 10.03/10.26 assert (zenon_L580_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((((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)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((~((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) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_H30 zenon_H23 zenon_He8 zenon_H24 zenon_H5f zenon_H1f5 zenon_H113 zenon_Hf1 zenon_Hef zenon_H130 zenon_H2dd zenon_H1f6 zenon_H7e zenon_H1ec zenon_H14b zenon_H110 zenon_Heb zenon_H272 zenon_H7a zenon_H1e zenon_H1b9 zenon_Hfe zenon_H192 zenon_H1d4 zenon_H2c4 zenon_H25 zenon_H187 zenon_H93 zenon_H22f zenon_H1d9 zenon_H2ac zenon_H2ae zenon_H127 zenon_H101 zenon_Hbe zenon_H2a8 zenon_H155 zenon_H2c7 zenon_H2ee zenon_H64 zenon_Ha9 zenon_H12c zenon_H2f7 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H124 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H105 zenon_H1db zenon_H301 zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H96 zenon_H1c9 zenon_H22e zenon_H83 zenon_H1cb zenon_H14c zenon_H141 zenon_H2ca zenon_H118 zenon_Ha5 zenon_H2a zenon_H11b zenon_H2c. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.03/10.26 apply (zenon_L384_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_Hd8. zenon_intro zenon_H15b. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_H15c. zenon_intro zenon_He1. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.26 apply (zenon_L424_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.26 apply (zenon_L425_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.26 apply (zenon_L426_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.26 apply (zenon_L503_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.26 apply (zenon_L246_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.26 apply (zenon_L321_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.26 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_H89. zenon_intro zenon_Hc7. % 10.03/10.26 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.03/10.26 apply (zenon_L384_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.03/10.26 apply (zenon_L59_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.03/10.26 apply (zenon_L385_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.03/10.26 apply (zenon_L556_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.03/10.26 apply (zenon_L29_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.03/10.26 apply (zenon_L173_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.03/10.26 apply (zenon_L557_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.03/10.26 apply (zenon_L399_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.03/10.26 apply (zenon_L386_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.03/10.26 apply (zenon_L145_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.03/10.26 apply (zenon_L558_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.03/10.26 apply (zenon_L91_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.03/10.26 apply (zenon_L559_); trivial. % 10.03/10.26 apply (zenon_L505_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.03/10.26 apply (zenon_L562_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.03/10.26 apply (zenon_L91_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.03/10.26 apply (zenon_L559_); trivial. % 10.03/10.26 apply (zenon_L505_); trivial. % 10.03/10.26 apply (zenon_L61_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.26 apply (zenon_L511_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.26 apply (zenon_L55_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.26 apply (zenon_L563_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.26 apply (zenon_L325_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.26 apply (zenon_L565_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.26 apply (zenon_L327_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.26 apply (zenon_L328_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.26 apply (zenon_L567_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.26 apply (zenon_L515_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.26 apply (zenon_L568_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.26 apply (zenon_L264_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.26 apply (zenon_L332_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.26 apply (zenon_L335_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.26 apply (zenon_L117_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.26 apply (zenon_L336_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.26 apply (zenon_L121_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.26 apply (zenon_L569_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.26 apply (zenon_L454_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.26 apply (zenon_L570_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.26 apply (zenon_L337_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.26 apply (zenon_L571_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.26 apply (zenon_L131_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.26 apply (zenon_L133_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.26 apply (zenon_L572_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.26 apply (zenon_L525_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.26 apply (zenon_L461_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.26 apply (zenon_L462_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.26 apply (zenon_L138_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.26 apply (zenon_L573_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.26 apply (zenon_L574_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.26 apply (zenon_L340_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.26 apply (zenon_L575_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.26 apply (zenon_L576_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.26 apply (zenon_L284_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.26 apply (zenon_L146_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.26 apply (zenon_L345_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.26 apply (zenon_L149_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.26 apply (zenon_L150_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.26 apply (zenon_L346_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.26 apply (zenon_L167_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.26 apply (zenon_L530_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.26 apply (zenon_L472_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.26 apply (zenon_L347_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.26 apply (zenon_L348_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.26 apply (zenon_L349_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.26 apply (zenon_L350_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.26 apply (zenon_L351_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.26 apply (zenon_L352_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.26 apply (zenon_L183_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.26 apply (zenon_L496_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.26 apply (zenon_L577_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.26 apply (zenon_L355_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.26 apply (zenon_L187_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.26 apply (zenon_L356_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.26 apply (zenon_L536_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.26 apply (zenon_L537_); trivial. % 10.03/10.26 apply (zenon_L538_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.26 apply (zenon_L424_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.26 apply (zenon_L425_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.26 apply (zenon_L426_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.26 apply (zenon_L503_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.26 apply (zenon_L302_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.26 apply (zenon_L321_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.26 apply (zenon_L303_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.26 apply (zenon_L304_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.26 apply (zenon_L55_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.26 apply (zenon_L563_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.26 apply (zenon_L325_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.26 apply (zenon_L565_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.26 apply (zenon_L327_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.26 apply (zenon_L328_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.26 apply (zenon_L567_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.26 apply (zenon_L515_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.26 apply (zenon_L568_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.26 apply (zenon_L309_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.26 apply (zenon_L332_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.26 apply (zenon_L335_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.26 apply (zenon_L117_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.26 apply (zenon_L336_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.26 apply (zenon_L121_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.26 apply (zenon_L569_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.26 apply (zenon_L454_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.26 apply (zenon_L570_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.26 apply (zenon_L337_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.26 apply (zenon_L571_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.26 apply (zenon_L360_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.26 apply (zenon_L133_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.26 apply (zenon_L572_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.26 apply (zenon_L525_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.26 apply (zenon_L461_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.26 apply (zenon_L462_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.26 apply (zenon_L138_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.26 apply (zenon_L573_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.26 apply (zenon_L574_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.26 apply (zenon_L340_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.26 apply (zenon_L575_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.26 apply (zenon_L576_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.26 apply (zenon_L466_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.26 apply (zenon_L146_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.26 apply (zenon_L345_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.26 apply (zenon_L149_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.26 apply (zenon_L362_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.26 apply (zenon_L346_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.26 apply (zenon_L167_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.26 apply (zenon_L530_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.26 apply (zenon_L472_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.26 apply (zenon_L195_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.26 apply (zenon_L348_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.26 apply (zenon_L349_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.26 apply (zenon_L350_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.26 apply (zenon_L351_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.26 apply (zenon_L352_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.26 apply (zenon_L183_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.26 apply (zenon_L496_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.26 apply (zenon_L577_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.26 apply (zenon_L355_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.26 apply (zenon_L187_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.26 apply (zenon_L356_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.26 apply (zenon_L536_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.26 apply (zenon_L537_); trivial. % 10.03/10.26 apply (zenon_L538_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.26 apply (zenon_L424_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.26 apply (zenon_L425_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.26 apply (zenon_L426_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.26 apply (zenon_L503_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.26 apply (zenon_L246_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.26 apply (zenon_L321_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.26 apply (zenon_L364_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.26 apply (zenon_L511_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.26 apply (zenon_L55_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.26 apply (zenon_L563_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.26 apply (zenon_L325_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.26 apply (zenon_L198_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.26 apply (zenon_L327_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.26 apply (zenon_L328_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.26 apply (zenon_L567_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.26 apply (zenon_L515_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.26 apply (zenon_L568_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.26 apply (zenon_L264_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.26 apply (zenon_L332_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.26 apply (zenon_L335_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.26 apply (zenon_L117_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.26 apply (zenon_L336_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.26 apply (zenon_L121_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.26 apply (zenon_L569_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.26 apply (zenon_L454_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.26 apply (zenon_L570_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.26 apply (zenon_L337_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.26 apply (zenon_L375_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.26 apply (zenon_L360_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.26 apply (zenon_L133_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.26 apply (zenon_L572_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.26 apply (zenon_L525_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.26 apply (zenon_L461_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.26 apply (zenon_L462_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.26 apply (zenon_L138_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.26 apply (zenon_L573_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.26 apply (zenon_L574_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.26 apply (zenon_L340_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.26 apply (zenon_L575_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.26 apply (zenon_L576_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.26 apply (zenon_L284_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.26 apply (zenon_L146_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.26 apply (zenon_L345_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.26 apply (zenon_L149_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.26 apply (zenon_L362_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.26 apply (zenon_L346_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.26 apply (zenon_L167_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.26 apply (zenon_L530_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.26 apply (zenon_L472_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.26 apply (zenon_L347_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.26 apply (zenon_L204_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.26 apply (zenon_L349_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.26 apply (zenon_L350_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.26 apply (zenon_L351_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.26 apply (zenon_L206_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.26 apply (zenon_L183_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.26 apply (zenon_L496_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.26 apply (zenon_L577_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.26 apply (zenon_L355_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.26 apply (zenon_L187_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.26 apply (zenon_L356_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.26 apply (zenon_L536_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.26 apply (zenon_L537_); trivial. % 10.03/10.26 apply (zenon_L538_); trivial. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H51. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.26 apply (zenon_L424_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.26 apply (zenon_L425_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.26 apply (zenon_L426_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.26 apply (zenon_L502_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.26 apply (zenon_L550_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.26 apply (zenon_L321_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.26 apply (zenon_L551_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.26 apply (zenon_L207_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.26 apply (zenon_L55_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.26 apply (zenon_L563_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.26 apply (zenon_L325_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.26 apply (zenon_L209_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.26 apply (zenon_L327_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.26 apply (zenon_L328_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.26 apply (zenon_L567_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.26 apply (zenon_L515_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.26 apply (zenon_L568_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.26 apply (zenon_L552_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.26 apply (zenon_L332_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.26 apply (zenon_L553_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.26 apply (zenon_L117_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.26 apply (zenon_L336_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.26 apply (zenon_L121_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.26 apply (zenon_L569_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.26 apply (zenon_L454_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.26 apply (zenon_L570_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.26 apply (zenon_L337_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.26 apply (zenon_L211_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.26 apply (zenon_L360_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.26 apply (zenon_L133_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.26 apply (zenon_L572_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.26 apply (zenon_L525_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.26 apply (zenon_L461_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.26 apply (zenon_L462_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.26 apply (zenon_L138_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.26 apply (zenon_L578_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.26 apply (zenon_L574_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.26 apply (zenon_L340_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.26 apply (zenon_L575_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.26 apply (zenon_L576_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.26 apply (zenon_L466_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.26 apply (zenon_L146_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.26 apply (zenon_L345_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.26 apply (zenon_L213_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.26 apply (zenon_L362_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.26 apply (zenon_L346_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.26 apply (zenon_L167_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.26 apply (zenon_L530_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.26 apply (zenon_L472_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1e8). zenon_intro zenon_H72. zenon_intro zenon_H1e9. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1e9). zenon_intro zenon_He2. zenon_intro zenon_Hb3. % 10.03/10.26 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.03/10.26 apply (zenon_L549_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.26 apply (zenon_L348_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.26 apply (zenon_L579_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.26 apply (zenon_L350_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.26 apply (zenon_L351_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.26 apply (zenon_L555_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.26 apply (zenon_L183_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.26 apply (zenon_L496_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.26 apply (zenon_L577_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.26 apply (zenon_L355_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.26 apply (zenon_L187_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.26 apply (zenon_L356_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.26 apply (zenon_L536_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.26 apply (zenon_L537_); trivial. % 10.03/10.26 apply (zenon_L538_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.03/10.26 apply (zenon_L42_); trivial. % 10.03/10.26 apply (zenon_L505_); trivial. % 10.03/10.26 (* end of lemma zenon_L580_ *) % 10.03/10.26 assert (zenon_L581_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (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)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H2ae zenon_H2c zenon_H2a zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H12a zenon_H1d9 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H64 zenon_H110 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H105 zenon_H141 zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H1e zenon_H7a zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Heb zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H14b zenon_H7e zenon_H1f6 zenon_H101 zenon_H1ec zenon_Hbe zenon_H22e zenon_Hd1 zenon_H1d4 zenon_H23 zenon_Ha5 zenon_H11b zenon_H25. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H24 | zenon_intro zenon_H230 ]. % 10.03/10.26 apply (zenon_L580_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H26 | zenon_intro zenon_H231 ]. % 10.03/10.26 apply (zenon_L556_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H2e | zenon_intro zenon_H82 ]. % 10.03/10.26 apply (zenon_L324_); trivial. % 10.03/10.26 apply (zenon_L521_); trivial. % 10.03/10.26 (* end of lemma zenon_L581_ *) % 10.03/10.26 assert (zenon_L582_ : ((op (e0) (e0)) = (e1)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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)) 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(e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (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)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H1f zenon_H5c zenon_H188 zenon_H2ae zenon_H2c zenon_H2a zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H12a zenon_H1d9 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H64 zenon_H110 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H105 zenon_H141 zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H1e zenon_H7a zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Heb zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H14b zenon_H7e zenon_H1f6 zenon_H101 zenon_H1ec zenon_Hbe zenon_H22e zenon_Hd1 zenon_H1d4 zenon_H23 zenon_Ha5 zenon_H25. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.03/10.26 apply (zenon_L160_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.03/10.26 apply (zenon_L93_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.03/10.26 apply (zenon_L172_); trivial. % 10.03/10.26 apply (zenon_L581_); trivial. % 10.03/10.26 (* end of lemma zenon_L582_ *) % 10.03/10.26 assert (zenon_L583_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H18d zenon_H5c. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H18d). zenon_intro zenon_H27. zenon_intro zenon_H18e. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H18e). zenon_intro zenon_H27. zenon_intro zenon_Hcb. % 10.03/10.26 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.26 apply (zenon_L93_); trivial. % 10.03/10.26 (* end of lemma zenon_L583_ *) % 10.03/10.26 assert (zenon_L584_ : (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> False). % 10.03/10.26 do 0 intro. intros zenon_H5d zenon_H82 zenon_H7f. % 10.03/10.26 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (op (e3) (e2))) = (e2))). % 10.03/10.26 intro zenon_D_pnotp. % 10.03/10.26 apply zenon_H5d. % 10.03/10.26 rewrite <- zenon_D_pnotp. % 10.03/10.26 exact zenon_H82. % 10.03/10.26 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.26 cut (((op (e3) (e3)) = (op (e3) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H308]. % 10.03/10.26 congruence. % 10.03/10.26 elim (classic ((op (e3) (op (e3) (e2))) = (op (e3) (op (e3) (e2))))); [ zenon_intro zenon_H226 | zenon_intro zenon_H227 ]. % 10.03/10.26 cut (((op (e3) (op (e3) (e2))) = (op (e3) (op (e3) (e2)))) = ((op (e3) (e3)) = (op (e3) (op (e3) (e2))))). % 10.03/10.26 intro zenon_D_pnotp. % 10.03/10.26 apply zenon_H308. % 10.03/10.26 rewrite <- zenon_D_pnotp. % 10.03/10.26 exact zenon_H226. % 10.03/10.26 cut (((op (e3) (op (e3) (e2))) = (op (e3) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H227]. % 10.03/10.26 cut (((op (e3) (op (e3) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H309]. % 10.03/10.26 congruence. % 10.03/10.26 cut (((op (e3) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H30a]. % 10.03/10.26 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.26 congruence. % 10.03/10.26 apply zenon_H29. apply refl_equal. % 10.03/10.26 exact (zenon_H30a zenon_H7f). % 10.03/10.26 apply zenon_H227. apply refl_equal. % 10.03/10.26 apply zenon_H227. apply refl_equal. % 10.03/10.26 apply zenon_H22. apply refl_equal. % 10.03/10.26 (* end of lemma zenon_L584_ *) % 10.03/10.26 assert (zenon_L585_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.03/10.26 do 0 intro. intros zenon_H1a3 zenon_H5d zenon_H82. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_Hf7. zenon_intro zenon_H1a4. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1a4). zenon_intro zenon_H143. zenon_intro zenon_H177. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.03/10.26 apply (zenon_L584_); trivial. % 10.03/10.26 (* end of lemma zenon_L585_ *) % 10.03/10.26 assert (zenon_L586_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H1b5 zenon_H5c. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_Hd2. zenon_intro zenon_H1b6. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_Hd7. zenon_intro zenon_Hcb. % 10.03/10.26 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.26 apply (zenon_L93_); trivial. % 10.03/10.26 (* end of lemma zenon_L586_ *) % 10.03/10.26 assert (zenon_L587_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.03/10.26 do 0 intro. intros zenon_H1ea zenon_H93 zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_He8 zenon_H1f zenon_H2c zenon_H5f zenon_H1f5 zenon_H113 zenon_Hf1 zenon_Hef zenon_H130 zenon_H1f6 zenon_H7e zenon_H1ec zenon_H14b zenon_Hbe zenon_Heb zenon_H1e zenon_H110 zenon_H23 zenon_H1b9 zenon_H2ae zenon_H127 zenon_H155 zenon_H1d9 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H64 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_H2f7 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H105 zenon_H141 zenon_H1db zenon_H301 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H7a zenon_H272 zenon_H187 zenon_H96 zenon_H192 zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H101 zenon_H22e zenon_H1d4 zenon_H25 zenon_H2b4 zenon_H2b1 zenon_Ha5 zenon_H2a zenon_H82 zenon_H30. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.03/10.26 apply (zenon_L32_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_Hd8. zenon_intro zenon_H15b. % 10.03/10.26 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_H15c. zenon_intro zenon_He1. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.26 apply (zenon_L39_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.26 apply (zenon_L243_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.26 apply (zenon_L46_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.26 apply (zenon_L244_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.26 apply (zenon_L246_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.26 apply (zenon_L321_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.26 apply (zenon_L248_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.26 apply (zenon_L249_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.26 apply (zenon_L55_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.26 apply (zenon_L323_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.26 apply (zenon_L325_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.26 apply (zenon_L256_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.26 apply (zenon_L327_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.26 apply (zenon_L328_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.26 apply (zenon_L331_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.26 apply (zenon_L263_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.26 apply (zenon_L113_); trivial. % 10.03/10.26 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.27 apply (zenon_L264_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.27 apply (zenon_L332_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.27 apply (zenon_L335_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.27 apply (zenon_L117_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.27 apply (zenon_L336_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.27 apply (zenon_L121_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.27 apply (zenon_L271_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.27 apply (zenon_L273_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.27 apply (zenon_L274_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.27 apply (zenon_L337_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.27 apply (zenon_L275_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.27 apply (zenon_L131_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.27 apply (zenon_L133_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.27 apply (zenon_L338_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.27 apply (zenon_L276_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.27 apply (zenon_L277_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.27 apply (zenon_L278_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.27 apply (zenon_L138_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.27 apply (zenon_L279_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.27 apply (zenon_L339_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.27 apply (zenon_L340_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.27 apply (zenon_L282_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_Hd2. zenon_intro zenon_H1b6. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.03/10.27 apply (zenon_L2_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.03/10.27 apply (zenon_L58_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.03/10.27 apply (zenon_L62_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.03/10.27 apply (zenon_L30_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.03/10.27 apply (zenon_L19_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.03/10.27 apply (zenon_L153_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.03/10.27 apply (zenon_L33_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.03/10.27 apply (zenon_L341_); trivial. % 10.03/10.27 apply (zenon_L235_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.03/10.27 apply (zenon_L342_); trivial. % 10.03/10.27 apply (zenon_L343_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.03/10.27 apply (zenon_L272_); trivial. % 10.03/10.27 apply (zenon_L344_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.27 apply (zenon_L284_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.27 apply (zenon_L146_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.27 apply (zenon_L345_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.27 apply (zenon_L149_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.27 apply (zenon_L150_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.27 apply (zenon_L346_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.27 apply (zenon_L167_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.27 apply (zenon_L286_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.27 apply (zenon_L169_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.27 apply (zenon_L347_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.27 apply (zenon_L348_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.27 apply (zenon_L349_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.27 apply (zenon_L350_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.27 apply (zenon_L351_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.27 apply (zenon_L352_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.27 apply (zenon_L183_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.27 apply (zenon_L353_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.27 apply (zenon_L354_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.27 apply (zenon_L355_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.27 apply (zenon_L187_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.27 apply (zenon_L356_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.27 apply (zenon_L357_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.27 apply (zenon_L300_); trivial. % 10.03/10.27 apply (zenon_L301_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H3c. zenon_intro zenon_H44. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H160. zenon_intro zenon_Hf6. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.27 apply (zenon_L39_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.27 apply (zenon_L243_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.27 apply (zenon_L46_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.27 apply (zenon_L244_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.27 apply (zenon_L302_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.27 apply (zenon_L321_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.27 apply (zenon_L303_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.27 apply (zenon_L304_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.27 apply (zenon_L55_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.27 apply (zenon_L323_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.27 apply (zenon_L325_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.27 apply (zenon_L256_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.27 apply (zenon_L327_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.27 apply (zenon_L328_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.27 apply (zenon_L331_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.27 apply (zenon_L263_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.27 apply (zenon_L113_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.27 apply (zenon_L309_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.27 apply (zenon_L115_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.27 apply (zenon_L335_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.27 apply (zenon_L117_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.27 apply (zenon_L336_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.27 apply (zenon_L121_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.27 apply (zenon_L271_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H188. zenon_intro zenon_H196. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H196). zenon_intro zenon_H18c. zenon_intro zenon_Hcf. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd0. zenon_intro zenon_H86. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.03/10.27 apply (zenon_L2_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.03/10.27 apply (zenon_L29_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.03/10.27 apply (zenon_L163_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.03/10.27 apply (zenon_L342_); trivial. % 10.03/10.27 apply (zenon_L358_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.03/10.27 apply (zenon_L38_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.03/10.27 apply (zenon_L250_); trivial. % 10.03/10.27 apply (zenon_L313_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.03/10.27 apply (zenon_L322_); trivial. % 10.03/10.27 apply (zenon_L359_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.27 apply (zenon_L274_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.27 apply (zenon_L337_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.27 apply (zenon_L275_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.27 apply (zenon_L360_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.27 apply (zenon_L133_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.27 apply (zenon_L338_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.27 apply (zenon_L276_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.27 apply (zenon_L277_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.27 apply (zenon_L361_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.27 apply (zenon_L138_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H86. zenon_intro zenon_H1ae. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_Hd0. zenon_intro zenon_Hbd. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.03/10.27 apply (zenon_L359_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.27 apply (zenon_L339_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.27 apply (zenon_L340_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.27 apply (zenon_L282_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_Hd2. zenon_intro zenon_H1b6. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_Hd7. zenon_intro zenon_Hcb. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.27 apply (zenon_L67_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.27 apply (zenon_L284_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.27 apply (zenon_L146_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.27 apply (zenon_L345_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.27 apply (zenon_L149_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.27 apply (zenon_L362_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.27 apply (zenon_L346_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.27 apply (zenon_L167_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.27 apply (zenon_L286_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.27 apply (zenon_L169_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.27 apply (zenon_L195_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.27 apply (zenon_L348_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.27 apply (zenon_L349_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.27 apply (zenon_L181_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.27 apply (zenon_L351_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.27 apply (zenon_L352_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.27 apply (zenon_L183_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.27 apply (zenon_L353_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.27 apply (zenon_L354_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.27 apply (zenon_L363_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.27 apply (zenon_L187_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.27 apply (zenon_L356_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.27 apply (zenon_L357_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.27 apply (zenon_L300_); trivial. % 10.03/10.27 apply (zenon_L301_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.27 apply (zenon_L39_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.27 apply (zenon_L243_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.27 apply (zenon_L46_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.27 apply (zenon_L244_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.27 apply (zenon_L246_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.27 apply (zenon_L321_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.27 apply (zenon_L364_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H89. zenon_intro zenon_Hca. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_H9d. zenon_intro zenon_Hcb. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.27 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.03/10.27 apply (zenon_L32_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.03/10.27 apply (zenon_L59_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.03/10.27 apply (zenon_L32_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.03/10.27 apply (zenon_L65_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.03/10.27 apply (zenon_L367_); trivial. % 10.03/10.27 apply (zenon_L369_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.03/10.27 apply (zenon_L370_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.03/10.27 apply (zenon_L371_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.03/10.27 apply (zenon_L367_); trivial. % 10.03/10.27 apply (zenon_L326_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.27 apply (zenon_L55_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.27 apply (zenon_L372_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.27 apply (zenon_L325_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.27 apply (zenon_L198_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.27 apply (zenon_L327_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.27 apply (zenon_L328_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.27 apply (zenon_L331_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.27 apply (zenon_L263_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.27 apply (zenon_L113_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.27 apply (zenon_L264_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.27 apply (zenon_L332_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.27 apply (zenon_L335_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.27 apply (zenon_L117_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.27 apply (zenon_L336_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.27 apply (zenon_L121_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.27 apply (zenon_L271_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H188. zenon_intro zenon_H196. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H196). zenon_intro zenon_H18c. zenon_intro zenon_Hcf. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd0. zenon_intro zenon_H86. % 10.03/10.27 apply (zenon_L373_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.27 apply (zenon_L374_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.27 apply (zenon_L337_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.27 apply (zenon_L375_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.27 apply (zenon_L360_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.27 apply (zenon_L133_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.27 apply (zenon_L338_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.27 apply (zenon_L276_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.27 apply (zenon_L277_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1a9). zenon_intro zenon_H86. zenon_intro zenon_H1aa. % 10.03/10.27 apply (zenon_L373_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.27 apply (zenon_L138_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.27 apply (zenon_L376_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.27 apply (zenon_L339_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.27 apply (zenon_L340_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.27 apply (zenon_L377_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_Hd2. zenon_intro zenon_H1b6. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_Hd7. zenon_intro zenon_Hcb. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.27 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.03/10.27 apply (zenon_L32_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.03/10.27 apply (zenon_L59_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.03/10.27 apply (zenon_L32_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.03/10.27 apply (zenon_L65_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.03/10.27 apply (zenon_L379_); trivial. % 10.03/10.27 apply (zenon_L369_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.03/10.27 apply (zenon_L370_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.03/10.27 apply (zenon_L65_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.03/10.27 apply (zenon_L379_); trivial. % 10.03/10.27 apply (zenon_L380_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.27 apply (zenon_L284_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.27 apply (zenon_L146_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.27 apply (zenon_L345_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.27 apply (zenon_L149_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.27 apply (zenon_L362_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.27 apply (zenon_L346_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.27 apply (zenon_L167_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.27 apply (zenon_L286_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.27 apply (zenon_L169_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.27 apply (zenon_L347_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.27 apply (zenon_L204_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.27 apply (zenon_L349_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.27 apply (zenon_L350_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.27 apply (zenon_L351_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.27 apply (zenon_L206_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.27 apply (zenon_L183_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.27 apply (zenon_L353_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.27 apply (zenon_L354_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.27 apply (zenon_L355_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.27 apply (zenon_L187_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.27 apply (zenon_L356_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.27 apply (zenon_L357_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.27 apply (zenon_L300_); trivial. % 10.03/10.27 apply (zenon_L301_); trivial. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H51. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.03/10.27 apply (zenon_L39_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_H20. zenon_intro zenon_Hb2. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hb2). zenon_intro zenon_H20. zenon_intro zenon_Hb3. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.03/10.27 apply (zenon_L501_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.03/10.27 apply (zenon_L46_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.03/10.27 apply (zenon_L502_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.03/10.27 apply (zenon_L50_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.03/10.27 apply (zenon_L321_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_H89. zenon_intro zenon_Hc7. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_H9d. zenon_intro zenon_Hc8. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.03/10.27 apply (zenon_L582_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.03/10.27 apply (zenon_L207_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.03/10.27 apply (zenon_L55_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.03/10.27 apply (zenon_L323_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.03/10.27 apply (zenon_L325_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.03/10.27 apply (zenon_L209_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.03/10.27 apply (zenon_L327_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.03/10.27 apply (zenon_L328_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.03/10.27 apply (zenon_L331_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.03/10.27 apply (zenon_L263_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.03/10.27 apply (zenon_L113_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.03/10.27 apply (zenon_L264_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.03/10.27 apply (zenon_L115_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.03/10.27 apply (zenon_L553_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.03/10.27 apply (zenon_L117_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.03/10.27 apply (zenon_L336_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.03/10.27 apply (zenon_L121_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.03/10.27 apply (zenon_L583_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H188. zenon_intro zenon_H196. % 10.03/10.27 apply (zenon_L582_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H197). zenon_intro zenon_H188. zenon_intro zenon_H198. % 10.03/10.27 apply (zenon_L582_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.03/10.27 apply (zenon_L337_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.03/10.27 apply (zenon_L211_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.03/10.27 apply (zenon_L360_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.03/10.27 apply (zenon_L133_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.03/10.27 apply (zenon_L585_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.03/10.27 apply (zenon_L276_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.03/10.27 apply (zenon_L277_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1a9). zenon_intro zenon_H86. zenon_intro zenon_H1aa. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_Hd0. zenon_intro zenon_Hb3. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.03/10.27 apply (zenon_L501_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.03/10.27 apply (zenon_L138_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.03/10.27 apply (zenon_L578_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.03/10.27 apply (zenon_L339_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.03/10.27 apply (zenon_L340_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_Hd2. zenon_intro zenon_H1b4. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1b4). zenon_intro zenon_Hd7. zenon_intro zenon_Hc8. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.03/10.27 apply (zenon_L582_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.03/10.27 apply (zenon_L586_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.03/10.27 apply (zenon_L284_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.03/10.27 apply (zenon_L146_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.03/10.27 apply (zenon_L345_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.03/10.27 apply (zenon_L213_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.03/10.27 apply (zenon_L362_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.03/10.27 apply (zenon_L346_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.03/10.27 apply (zenon_L167_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.03/10.27 apply (zenon_L286_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.03/10.27 apply (zenon_L169_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.03/10.27 apply (zenon_L347_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.03/10.27 apply (zenon_L348_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.03/10.27 apply (zenon_L579_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.03/10.27 apply (zenon_L181_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.03/10.27 apply (zenon_L351_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.03/10.27 apply (zenon_L555_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.03/10.27 apply (zenon_L183_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.03/10.27 apply (zenon_L353_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.03/10.27 apply (zenon_L354_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.03/10.27 apply (zenon_L363_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.03/10.27 apply (zenon_L187_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.03/10.27 apply (zenon_L356_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.03/10.27 apply (zenon_L357_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.03/10.27 apply (zenon_L300_); trivial. % 10.03/10.27 apply (zenon_L301_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.03/10.27 apply (zenon_L42_); trivial. % 10.03/10.27 apply (zenon_L26_); trivial. % 10.03/10.27 (* end of lemma zenon_L587_ *) % 10.03/10.27 assert (zenon_L588_ : ((op (e2) (e0)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (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 (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.03/10.27 do 0 intro. intros zenon_H86 zenon_H8d zenon_H30 zenon_H82 zenon_H2a zenon_H2b1 zenon_H2b4 zenon_H25 zenon_H1d4 zenon_H22e zenon_H101 zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_H192 zenon_H96 zenon_H187 zenon_H272 zenon_H7a zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H301 zenon_H1db zenon_H141 zenon_H105 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H10d zenon_H304 zenon_H2f7 zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H155 zenon_H127 zenon_H2ae zenon_H1b9 zenon_H23 zenon_H110 zenon_H1e zenon_Heb zenon_Hbe zenon_H14b zenon_H1ec zenon_H7e zenon_H1f6 zenon_H130 zenon_Hef zenon_Hf1 zenon_H113 zenon_H1f5 zenon_H5f zenon_H2c zenon_H1f zenon_He8 zenon_Hd1 zenon_H11f zenon_H12f zenon_H93 zenon_H1ea zenon_H12a zenon_Hb7. % 10.03/10.27 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.03/10.27 apply (zenon_L54_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.03/10.27 apply (zenon_L320_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.03/10.27 apply (zenon_L587_); trivial. % 10.03/10.27 apply (zenon_L232_); trivial. % 10.03/10.27 (* end of lemma zenon_L588_ *) % 10.03/10.27 assert (zenon_L589_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H19d zenon_H22e zenon_H74 zenon_H8d zenon_H2a zenon_H1b9 zenon_H2f zenon_H105. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_Hf7. zenon_intro zenon_H19e. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H171. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.27 apply (zenon_L257_); trivial. % 10.03/10.27 (* end of lemma zenon_L589_ *) % 10.03/10.27 assert (zenon_L590_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> ((op (e1) (e1)) = (e0)) -> False). % 10.03/10.27 do 0 intro. intros zenon_H1af zenon_H43 zenon_H8d. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_Hd2. zenon_intro zenon_H1b0. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hd7. zenon_intro zenon_Hc2. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.03/10.27 apply (zenon_L310_); trivial. % 10.03/10.27 (* end of lemma zenon_L590_ *) % 10.03/10.27 assert (zenon_L591_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H1b5 zenon_H160. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_Hd2. zenon_intro zenon_H1b6. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_Hd7. zenon_intro zenon_Hcb. % 10.03/10.27 apply (zenon_L305_); trivial. % 10.03/10.27 (* end of lemma zenon_L591_ *) % 10.03/10.27 assert (zenon_L592_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H1c2 zenon_H22e zenon_H74 zenon_H8d zenon_H2a zenon_H1b9 zenon_H2f zenon_H105. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H128. zenon_intro zenon_H1c3. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1c3). zenon_intro zenon_H166. zenon_intro zenon_H171. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.03/10.27 apply (zenon_L257_); trivial. % 10.03/10.27 (* end of lemma zenon_L592_ *) % 10.03/10.27 assert (zenon_L593_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H21c zenon_Hf6. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H21c). zenon_intro zenon_H128. zenon_intro zenon_H21d. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H166. zenon_intro zenon_H174. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.03/10.27 apply (zenon_L307_); trivial. % 10.03/10.27 (* end of lemma zenon_L593_ *) % 10.03/10.27 assert (zenon_L594_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> ((op (e1) (e1)) = (e0)) -> False). % 10.03/10.27 do 0 intro. intros zenon_H1fd zenon_H43 zenon_H8d. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H79. zenon_intro zenon_H1fe. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H109. zenon_intro zenon_Hc2. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.03/10.27 apply (zenon_L310_); trivial. % 10.03/10.27 (* end of lemma zenon_L594_ *) % 10.03/10.27 assert (zenon_L595_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H223 zenon_Hf6. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H79. zenon_intro zenon_H224. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H109. zenon_intro zenon_Hc8. % 10.03/10.27 apply (zenon_L307_); trivial. % 10.03/10.27 (* end of lemma zenon_L595_ *) % 10.03/10.27 assert (zenon_L596_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H175 zenon_H50. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H175). zenon_intro zenon_Hb7. zenon_intro zenon_H176. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H176). zenon_intro zenon_H90. zenon_intro zenon_H177. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.03/10.27 apply (zenon_L368_); trivial. % 10.03/10.27 (* end of lemma zenon_L596_ *) % 10.03/10.27 assert (zenon_L597_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H17f zenon_H4d. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H68. zenon_intro zenon_H180. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H5e. zenon_intro zenon_Hb6. % 10.03/10.27 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 10.03/10.27 apply (zenon_L197_); trivial. % 10.03/10.27 (* end of lemma zenon_L597_ *) % 10.03/10.27 assert (zenon_L598_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.03/10.27 do 0 intro. intros zenon_H13d zenon_H2a zenon_H73 zenon_H26 zenon_H23 zenon_H1b9 zenon_Ha5 zenon_H105 zenon_Hb7. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.03/10.27 apply (zenon_L371_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.03/10.27 apply (zenon_L31_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.03/10.27 apply (zenon_L341_); trivial. % 10.03/10.27 apply (zenon_L235_); trivial. % 10.03/10.27 (* end of lemma zenon_L598_ *) % 10.03/10.27 assert (zenon_L599_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H2d4 zenon_Hde zenon_H2c. % 10.03/10.27 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 10.03/10.27 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H2c. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H31. % 10.03/10.27 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.27 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 10.03/10.27 congruence. % 10.03/10.27 cut (((op (e0) (e2)) = (e1)) = ((e3) = (e1))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H19f. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H2d4. % 10.03/10.27 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.27 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_He0]. % 10.03/10.27 congruence. % 10.03/10.27 exact (zenon_He0 zenon_Hde). % 10.03/10.27 apply zenon_H1d. apply refl_equal. % 10.03/10.27 apply zenon_H29. apply refl_equal. % 10.03/10.27 apply zenon_H29. apply refl_equal. % 10.03/10.27 (* end of lemma zenon_L599_ *) % 10.03/10.27 assert (zenon_L600_ : (((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 (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H14c zenon_H89 zenon_H7a zenon_H27 zenon_H93 zenon_Hd2 zenon_H2c4 zenon_H52 zenon_H141. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H94 | zenon_intro zenon_H14d ]. % 10.03/10.27 apply (zenon_L382_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 10.03/10.27 apply (zenon_L269_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H149 | zenon_intro zenon_H79 ]. % 10.03/10.27 apply (zenon_L386_); trivial. % 10.03/10.27 apply (zenon_L297_); trivial. % 10.03/10.27 (* end of lemma zenon_L600_ *) % 10.03/10.27 assert (zenon_L601_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H2ca zenon_H110 zenon_H141 zenon_H52 zenon_H93 zenon_H27 zenon_H7a zenon_H89 zenon_H14c zenon_H1cb zenon_H24 zenon_H2dd zenon_H2c4 zenon_H23 zenon_Ha5 zenon_H106 zenon_H101. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.03/10.27 apply (zenon_L29_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.03/10.27 apply (zenon_L517_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.03/10.27 apply (zenon_L600_); trivial. % 10.03/10.27 apply (zenon_L561_); trivial. % 10.03/10.27 (* end of lemma zenon_L601_ *) % 10.03/10.27 assert (zenon_L602_ : (~((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))) -> ((op (e2) (e2)) = (e0)) -> False). % 10.03/10.27 do 0 intro. intros zenon_H30b zenon_Ha5. % 10.03/10.27 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.27 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 10.03/10.27 congruence. % 10.03/10.27 exact (zenon_Ha6 zenon_Ha5). % 10.03/10.27 apply zenon_H22. apply refl_equal. % 10.03/10.27 (* end of lemma zenon_L602_ *) % 10.03/10.27 assert (zenon_L603_ : ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((e3) = (op (op (e2) (e2)) (e2)))) -> False). % 10.03/10.27 do 0 intro. intros zenon_Hde zenon_Ha5 zenon_H30c. % 10.03/10.27 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H30d | zenon_intro zenon_H30e ]. % 10.03/10.27 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e3) = (op (op (e2) (e2)) (e2)))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H30c. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H30d. % 10.03/10.27 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H30e]. % 10.03/10.27 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H30f]. % 10.03/10.27 congruence. % 10.03/10.27 cut (((op (e0) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H30f. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_Hde. % 10.03/10.27 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.27 cut (((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H310]. % 10.03/10.27 congruence. % 10.03/10.27 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H30d | zenon_intro zenon_H30e ]. % 10.03/10.27 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H310. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H30d. % 10.03/10.27 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H30e]. % 10.03/10.27 cut (((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H30b]. % 10.03/10.27 congruence. % 10.03/10.27 apply (zenon_L602_); trivial. % 10.03/10.27 apply zenon_H30e. apply refl_equal. % 10.03/10.27 apply zenon_H30e. apply refl_equal. % 10.03/10.27 apply zenon_H29. apply refl_equal. % 10.03/10.27 apply zenon_H30e. apply refl_equal. % 10.03/10.27 apply zenon_H30e. apply refl_equal. % 10.03/10.27 (* end of lemma zenon_L603_ *) % 10.03/10.27 assert (zenon_L604_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> False). % 10.03/10.27 do 0 intro. intros zenon_Hf3 zenon_Hde zenon_Ha5. % 10.03/10.27 apply (zenon_notand_s _ _ ax13); [ zenon_intro zenon_H312 | zenon_intro zenon_H311 ]. % 10.03/10.27 elim (classic ((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))); [ zenon_intro zenon_H313 | zenon_intro zenon_H314 ]. % 10.03/10.27 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2)))) = ((e1) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H312. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H313. % 10.03/10.27 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H314]. % 10.03/10.27 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H315]. % 10.03/10.27 congruence. % 10.03/10.27 cut (((op (e0) (e3)) = (e1)) = ((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (e1))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H315. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_Hf3. % 10.03/10.27 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.27 cut (((op (e0) (e3)) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H316]. % 10.03/10.27 congruence. % 10.03/10.27 elim (classic ((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))); [ zenon_intro zenon_H313 | zenon_intro zenon_H314 ]. % 10.03/10.27 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2)))) = ((op (e0) (e3)) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H316. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H313. % 10.03/10.27 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H314]. % 10.03/10.27 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H317]. % 10.03/10.27 congruence. % 10.03/10.27 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H30f]. % 10.03/10.27 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 10.03/10.27 congruence. % 10.03/10.27 exact (zenon_Ha6 zenon_Ha5). % 10.03/10.27 cut (((op (e0) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H30f. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_Hde. % 10.03/10.27 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.27 cut (((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H310]. % 10.03/10.27 congruence. % 10.03/10.27 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H30d | zenon_intro zenon_H30e ]. % 10.03/10.27 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H310. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H30d. % 10.03/10.27 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H30e]. % 10.03/10.27 cut (((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H30b]. % 10.03/10.27 congruence. % 10.03/10.27 apply (zenon_L602_); trivial. % 10.03/10.27 apply zenon_H30e. apply refl_equal. % 10.03/10.27 apply zenon_H30e. apply refl_equal. % 10.03/10.27 apply zenon_H29. apply refl_equal. % 10.03/10.27 apply zenon_H314. apply refl_equal. % 10.03/10.27 apply zenon_H314. apply refl_equal. % 10.03/10.27 apply zenon_H1d. apply refl_equal. % 10.03/10.27 apply zenon_H314. apply refl_equal. % 10.03/10.27 apply zenon_H314. apply refl_equal. % 10.03/10.27 apply (zenon_notand_s _ _ zenon_H311); [ zenon_intro zenon_H318 | zenon_intro zenon_H30c ]. % 10.03/10.27 apply zenon_H318. apply sym_equal. exact zenon_Ha5. % 10.03/10.27 apply (zenon_L603_); trivial. % 10.03/10.27 (* end of lemma zenon_L604_ *) % 10.03/10.27 assert (zenon_L605_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H2f7 zenon_Hf3 zenon_H30 zenon_Hd7 zenon_Ha5 zenon_H2a zenon_H52 zenon_H1ea. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.03/10.27 apply (zenon_L604_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.03/10.27 apply (zenon_L251_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.03/10.27 apply (zenon_L42_); trivial. % 10.03/10.27 apply (zenon_L299_); trivial. % 10.03/10.27 (* end of lemma zenon_L605_ *) % 10.03/10.27 assert (zenon_L606_ : (~((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.27 do 0 intro. intros zenon_H319 zenon_H24. % 10.03/10.27 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.03/10.27 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2c3]. % 10.03/10.27 congruence. % 10.03/10.27 exact (zenon_H2c3 zenon_H24). % 10.03/10.27 apply zenon_H34. apply refl_equal. % 10.03/10.27 (* end of lemma zenon_L606_ *) % 10.03/10.27 assert (zenon_L607_ : ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> (~((e3) = (op (op (e0) (e0)) (e0)))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H87 zenon_H24 zenon_H285. % 10.03/10.27 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H286 | zenon_intro zenon_H287 ]. % 10.03/10.27 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e3) = (op (op (e0) (e0)) (e0)))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H285. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H286. % 10.03/10.27 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 10.03/10.27 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H288]. % 10.03/10.27 congruence. % 10.03/10.27 cut (((op (e2) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H288. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H87. % 10.03/10.27 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.27 cut (((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H31a]. % 10.03/10.27 congruence. % 10.03/10.27 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H286 | zenon_intro zenon_H287 ]. % 10.03/10.27 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H31a. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H286. % 10.03/10.27 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 10.03/10.27 cut (((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H319]. % 10.03/10.27 congruence. % 10.03/10.27 apply (zenon_L606_); trivial. % 10.03/10.27 apply zenon_H287. apply refl_equal. % 10.03/10.27 apply zenon_H287. apply refl_equal. % 10.03/10.27 apply zenon_H29. apply refl_equal. % 10.03/10.27 apply zenon_H287. apply refl_equal. % 10.03/10.27 apply zenon_H287. apply refl_equal. % 10.03/10.27 (* end of lemma zenon_L607_ *) % 10.03/10.27 assert (zenon_L608_ : ((op (e2) (e3)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.27 do 0 intro. intros zenon_H102 zenon_H87 zenon_H24. % 10.03/10.27 apply (zenon_notand_s _ _ ax15); [ zenon_intro zenon_H2e9 | zenon_intro zenon_H31b ]. % 10.03/10.27 elim (classic ((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))); [ zenon_intro zenon_H28c | zenon_intro zenon_H28d ]. % 10.03/10.27 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0)))) = ((e1) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H2e9. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H28c. % 10.03/10.27 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 10.03/10.27 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2ea]. % 10.03/10.27 congruence. % 10.03/10.27 cut (((op (e2) (e3)) = (e1)) = ((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (e1))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H2ea. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H102. % 10.03/10.27 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.27 cut (((op (e2) (e3)) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H31c]. % 10.03/10.27 congruence. % 10.03/10.27 elim (classic ((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))); [ zenon_intro zenon_H28c | zenon_intro zenon_H28d ]. % 10.03/10.27 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0)))) = ((op (e2) (e3)) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H31c. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H28c. % 10.03/10.27 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (op (e0) (e0)) (op (op (e0) (e0)) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 10.03/10.27 cut (((op (op (e0) (e0)) (op (op (e0) (e0)) (e0))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H31d]. % 10.03/10.27 congruence. % 10.03/10.27 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H288]. % 10.03/10.27 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2c3]. % 10.03/10.27 congruence. % 10.03/10.27 exact (zenon_H2c3 zenon_H24). % 10.03/10.27 cut (((op (e2) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H288. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H87. % 10.03/10.27 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.03/10.27 cut (((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H31a]. % 10.03/10.27 congruence. % 10.03/10.27 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H286 | zenon_intro zenon_H287 ]. % 10.03/10.27 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H31a. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H286. % 10.03/10.27 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 10.03/10.27 cut (((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H319]. % 10.03/10.27 congruence. % 10.03/10.27 apply (zenon_L606_); trivial. % 10.03/10.27 apply zenon_H287. apply refl_equal. % 10.03/10.27 apply zenon_H287. apply refl_equal. % 10.03/10.27 apply zenon_H29. apply refl_equal. % 10.03/10.27 apply zenon_H28d. apply refl_equal. % 10.03/10.27 apply zenon_H28d. apply refl_equal. % 10.03/10.27 apply zenon_H1d. apply refl_equal. % 10.03/10.27 apply zenon_H28d. apply refl_equal. % 10.03/10.27 apply zenon_H28d. apply refl_equal. % 10.03/10.27 apply (zenon_notand_s _ _ zenon_H31b); [ zenon_intro zenon_H31e | zenon_intro zenon_H285 ]. % 10.03/10.27 apply zenon_H31e. apply sym_equal. exact zenon_H24. % 10.03/10.27 apply (zenon_L607_); trivial. % 10.03/10.27 (* end of lemma zenon_L608_ *) % 10.03/10.27 assert (zenon_L609_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False). % 10.03/10.27 do 0 intro. intros zenon_H2b4 zenon_H2c zenon_H27 zenon_Hd1 zenon_Heb zenon_H2d4 zenon_H87 zenon_H24. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b5 ]. % 10.03/10.27 apply (zenon_L365_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H18c | zenon_intro zenon_H2b6 ]. % 10.03/10.27 apply (zenon_L388_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H102 ]. % 10.03/10.27 apply (zenon_L434_); trivial. % 10.03/10.27 apply (zenon_L608_); trivial. % 10.03/10.27 (* end of lemma zenon_L609_ *) % 10.03/10.27 assert (zenon_L610_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.03/10.27 do 0 intro. intros zenon_H13d zenon_H23 zenon_H69 zenon_H27 zenon_H1e zenon_H1b9 zenon_Ha5 zenon_H105 zenon_Hb7. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.03/10.27 apply (zenon_L153_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.03/10.27 apply (zenon_L231_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.03/10.27 apply (zenon_L341_); trivial. % 10.03/10.27 apply (zenon_L235_); trivial. % 10.03/10.27 (* end of lemma zenon_L610_ *) % 10.03/10.27 assert (zenon_L611_ : (((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 (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H10d zenon_Hb7 zenon_H105 zenon_Hf3 zenon_H101 zenon_H128 zenon_H52 zenon_Hfe. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hfd | zenon_intro zenon_H10e ]. % 10.03/10.27 apply (zenon_L235_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H10f ]. % 10.03/10.27 apply (zenon_L435_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H106 | zenon_intro zenon_H109 ]. % 10.03/10.27 apply (zenon_L241_); trivial. % 10.03/10.27 apply (zenon_L236_); trivial. % 10.03/10.27 (* end of lemma zenon_L611_ *) % 10.03/10.27 assert (zenon_L612_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((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 (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H1cb zenon_H24 zenon_H2dd zenon_H149 zenon_H2c4 zenon_H1b9 zenon_Hd7 zenon_H10d zenon_Hb7 zenon_H105 zenon_Hf3 zenon_H101 zenon_H52 zenon_Hfe. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.03/10.27 apply (zenon_L399_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.03/10.27 apply (zenon_L386_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.03/10.27 apply (zenon_L145_); trivial. % 10.03/10.27 apply (zenon_L611_); trivial. % 10.03/10.27 (* end of lemma zenon_L612_ *) % 10.03/10.27 assert (zenon_L613_ : ((op (e3) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H1d5 zenon_H91 zenon_H25. % 10.03/10.27 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H6a | zenon_intro zenon_H22 ]. % 10.03/10.27 cut (((e2) = (e2)) = ((e1) = (e2))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H25. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H6a. % 10.03/10.27 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.03/10.27 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 10.03/10.27 congruence. % 10.03/10.27 cut (((op (e3) (e0)) = (e1)) = ((e2) = (e1))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H6b. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H1d5. % 10.03/10.27 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.03/10.27 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H92]. % 10.03/10.27 congruence. % 10.03/10.27 exact (zenon_H92 zenon_H91). % 10.03/10.27 apply zenon_H1d. apply refl_equal. % 10.03/10.27 apply zenon_H22. apply refl_equal. % 10.03/10.27 apply zenon_H22. apply refl_equal. % 10.03/10.27 (* end of lemma zenon_L613_ *) % 10.03/10.27 assert (zenon_L614_ : ((op (e1) (e1)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (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)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H27 zenon_H2b zenon_H91 zenon_H2ae zenon_H2c zenon_H2a zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H12a zenon_H1d9 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H64 zenon_H110 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H105 zenon_H141 zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H1e zenon_H7a zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Heb zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H14b zenon_H7e zenon_H1f6 zenon_H101 zenon_H1ec zenon_Hbe zenon_H22e zenon_Hd1 zenon_H1d4 zenon_H23 zenon_Ha5 zenon_H25. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.03/10.27 apply (zenon_L613_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.03/10.27 apply (zenon_L269_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.03/10.27 apply (zenon_L411_); trivial. % 10.03/10.27 apply (zenon_L581_); trivial. % 10.03/10.27 (* end of lemma zenon_L614_ *) % 10.03/10.27 assert (zenon_L615_ : ((op (e1) (e0)) = (e0)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (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)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H9d zenon_H4d zenon_H27 zenon_H2b zenon_H2ae zenon_H2c zenon_H2a zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H12a zenon_H1d9 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H64 zenon_H110 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H105 zenon_H141 zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H1e zenon_H7a zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Heb zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H14b zenon_H7e zenon_H1f6 zenon_H101 zenon_H1ec zenon_Hbe zenon_H22e zenon_Hd1 zenon_H1d4 zenon_H23 zenon_Ha5 zenon_H25. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.03/10.27 apply (zenon_L384_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.03/10.27 apply (zenon_L153_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.03/10.27 apply (zenon_L373_); trivial. % 10.03/10.27 apply (zenon_L614_); trivial. % 10.03/10.27 (* end of lemma zenon_L615_ *) % 10.03/10.27 assert (zenon_L616_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 10.03/10.27 do 0 intro. intros zenon_H110 zenon_H27 zenon_Hf7. % 10.03/10.27 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e3)))). % 10.03/10.27 intro zenon_D_pnotp. % 10.03/10.27 apply zenon_H110. % 10.03/10.27 rewrite <- zenon_D_pnotp. % 10.03/10.27 exact zenon_H27. % 10.03/10.27 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H307]. % 10.03/10.27 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 10.03/10.27 congruence. % 10.03/10.27 apply zenon_H61. apply refl_equal. % 10.03/10.27 apply zenon_H307. apply sym_equal. exact zenon_Hf7. % 10.03/10.27 (* end of lemma zenon_L616_ *) % 10.03/10.27 assert (zenon_L617_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H175 zenon_H22e zenon_H2b zenon_Hbe zenon_H27 zenon_H2c zenon_H1ec zenon_H101. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H175). zenon_intro zenon_Hb7. zenon_intro zenon_H176. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H176). zenon_intro zenon_H90. zenon_intro zenon_H177. % 10.03/10.27 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.03/10.27 apply (zenon_L407_); trivial. % 10.03/10.27 (* end of lemma zenon_L617_ *) % 10.03/10.27 assert (zenon_L618_ : ((op (e0) (e3)) = (e0)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) 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(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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (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)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 10.03/10.27 do 0 intro. intros zenon_Hb7 zenon_H4d zenon_H27 zenon_H2b zenon_H2ae zenon_H2c zenon_H2a zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H12a zenon_H1d9 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H64 zenon_H110 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H105 zenon_H141 zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H1e zenon_H7a zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Heb zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H14b zenon_H7e zenon_H1f6 zenon_H101 zenon_H1ec zenon_Hbe zenon_H22e zenon_Hd1 zenon_H1d4 zenon_H23 zenon_Ha5 zenon_H25. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.03/10.27 apply (zenon_L384_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.03/10.27 apply (zenon_L610_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.03/10.27 apply (zenon_L373_); trivial. % 10.03/10.27 apply (zenon_L614_); trivial. % 10.03/10.27 (* end of lemma zenon_L618_ *) % 10.03/10.27 assert (zenon_L619_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H83 zenon_H2b zenon_H1d4 zenon_H2c4 zenon_H121 zenon_H1ec zenon_H1f0 zenon_H82 zenon_H30. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.03/10.27 apply (zenon_L402_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.03/10.27 apply (zenon_L403_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.03/10.27 apply (zenon_L404_); trivial. % 10.03/10.27 apply (zenon_L26_); trivial. % 10.03/10.27 (* end of lemma zenon_L619_ *) % 10.03/10.27 assert (zenon_L620_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.03/10.27 do 0 intro. intros zenon_H14c zenon_H90 zenon_H1d9 zenon_H27 zenon_H93 zenon_Hd2 zenon_H2c4 zenon_H14b zenon_H7f. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H94 | zenon_intro zenon_H14d ]. % 10.03/10.27 apply (zenon_L334_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 10.03/10.27 apply (zenon_L269_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H149 | zenon_intro zenon_H79 ]. % 10.03/10.27 apply (zenon_L386_); trivial. % 10.03/10.27 apply (zenon_L95_); trivial. % 10.03/10.27 (* end of lemma zenon_L620_ *) % 10.03/10.27 assert (zenon_L621_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H2ee zenon_H64 zenon_H110 zenon_H14b zenon_Hd2 zenon_H93 zenon_H27 zenon_H1d9 zenon_H90 zenon_H14c zenon_H2ac zenon_H83 zenon_H1d4 zenon_H1ec zenon_H82 zenon_H30 zenon_Hef zenon_H2f7 zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_Ha5 zenon_H2a zenon_H109 zenon_H101. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.03/10.27 apply (zenon_L22_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.03/10.27 apply (zenon_L73_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.03/10.27 apply (zenon_L64_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.03/10.27 apply (zenon_L619_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.03/10.27 apply (zenon_L389_); trivial. % 10.03/10.27 apply (zenon_L620_); trivial. % 10.03/10.27 apply (zenon_L509_); trivial. % 10.03/10.27 (* end of lemma zenon_L621_ *) % 10.03/10.27 assert (zenon_L622_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e3))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.27 do 0 intro. intros zenon_H22e zenon_Hbe zenon_H2c zenon_H50 zenon_H1b9 zenon_H187 zenon_H2ee zenon_H64 zenon_H110 zenon_H14b zenon_Hd2 zenon_H93 zenon_H27 zenon_H1d9 zenon_H90 zenon_H14c zenon_H2ac zenon_H83 zenon_H1d4 zenon_H1ec zenon_H82 zenon_H30 zenon_Hef zenon_H2f7 zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_Ha5 zenon_H2a zenon_H101. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.27 apply (zenon_L316_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.27 apply (zenon_L8_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.03/10.27 apply (zenon_L22_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.03/10.27 apply (zenon_L401_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.03/10.27 apply (zenon_L619_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.03/10.27 apply (zenon_L406_); trivial. % 10.03/10.27 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.03/10.28 apply (zenon_L403_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.03/10.28 apply (zenon_L174_); trivial. % 10.03/10.28 apply (zenon_L368_); trivial. % 10.03/10.28 apply (zenon_L621_); trivial. % 10.03/10.28 (* end of lemma zenon_L622_ *) % 10.03/10.28 assert (zenon_L623_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H2c7 zenon_H2ac zenon_Ha5 zenon_H27 zenon_Hd1 zenon_H149 zenon_H79 zenon_H2c4. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H2c8 ]. % 10.03/10.28 apply (zenon_L333_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2c8); [ zenon_intro zenon_H18c | zenon_intro zenon_H2c9 ]. % 10.03/10.28 apply (zenon_L388_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2c9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H121 ]. % 10.03/10.28 apply (zenon_L386_); trivial. % 10.03/10.28 apply (zenon_L403_); trivial. % 10.03/10.28 (* end of lemma zenon_L623_ *) % 10.03/10.28 assert (zenon_L624_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H2ee zenon_H64 zenon_H187 zenon_H30 zenon_H82 zenon_H1f0 zenon_H1ec zenon_H1d4 zenon_H2b zenon_H83 zenon_H2c7 zenon_H2ac zenon_Ha5 zenon_H27 zenon_Hd1 zenon_H149 zenon_H2c4. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.03/10.28 apply (zenon_L22_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.03/10.28 apply (zenon_L401_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.03/10.28 apply (zenon_L619_); trivial. % 10.03/10.28 apply (zenon_L623_); trivial. % 10.03/10.28 (* end of lemma zenon_L624_ *) % 10.03/10.28 assert (zenon_L625_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H2ca zenon_H23 zenon_H89 zenon_Hf1 zenon_H69 zenon_H1b9 zenon_H50 zenon_H22e zenon_Hbe zenon_H2c zenon_H185 zenon_Hd1 zenon_H2c7 zenon_H187 zenon_H1cb zenon_H4d zenon_H101 zenon_H2a zenon_Ha5 zenon_H2c4 zenon_H2dd zenon_H2b zenon_H12f zenon_H2f7 zenon_Hef zenon_H30 zenon_H1ec zenon_H1d4 zenon_H83 zenon_H2ac zenon_H14c zenon_H90 zenon_H1d9 zenon_H27 zenon_H93 zenon_H14b zenon_H110 zenon_H64 zenon_H2ee zenon_H45 zenon_H82 zenon_Ha9. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.03/10.28 apply (zenon_L29_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.03/10.28 apply (zenon_L163_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.03/10.28 apply (zenon_L622_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.28 apply (zenon_L316_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.28 apply (zenon_L336_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.28 apply (zenon_L624_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.03/10.28 apply (zenon_L373_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.03/10.28 apply (zenon_L621_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.03/10.28 apply (zenon_L14_); trivial. % 10.03/10.28 apply (zenon_L255_); trivial. % 10.03/10.28 (* end of lemma zenon_L625_ *) % 10.03/10.28 assert (zenon_L626_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> False). % 10.03/10.28 do 0 intro. intros zenon_H195 zenon_Hd1 zenon_H27. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H188. zenon_intro zenon_H196. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H196). zenon_intro zenon_H18c. zenon_intro zenon_Hcf. % 10.03/10.28 apply (zenon_L388_); trivial. % 10.03/10.28 (* end of lemma zenon_L626_ *) % 10.03/10.28 assert (zenon_L627_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H1a3 zenon_H22e zenon_H2b zenon_Hbe zenon_H27 zenon_H2c zenon_H1ec zenon_H101. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_Hf7. zenon_intro zenon_H1a4. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H1a4). zenon_intro zenon_H143. zenon_intro zenon_H177. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.03/10.28 apply (zenon_L407_); trivial. % 10.03/10.28 (* end of lemma zenon_L627_ *) % 10.03/10.28 assert (zenon_L628_ : ((op (e0) (e2)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (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)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 10.03/10.28 do 0 intro. intros zenon_Hd0 zenon_H9d zenon_H4d zenon_H27 zenon_H2b zenon_H2ae zenon_H2c zenon_H2a zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H12a zenon_H1d9 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H64 zenon_H110 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H105 zenon_H141 zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H1e zenon_H7a zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Heb zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H14b zenon_H7e zenon_H1f6 zenon_H101 zenon_H1ec zenon_Hbe zenon_H22e zenon_Hd1 zenon_H1d4 zenon_H23 zenon_Ha5 zenon_H25. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.03/10.28 apply (zenon_L152_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.03/10.28 apply (zenon_L153_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.03/10.28 apply (zenon_L373_); trivial. % 10.03/10.28 apply (zenon_L614_); trivial. % 10.03/10.28 (* end of lemma zenon_L628_ *) % 10.03/10.28 assert (zenon_L629_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H1af zenon_H27 zenon_H5f. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_Hd2. zenon_intro zenon_H1b0. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hd7. zenon_intro zenon_Hc2. % 10.03/10.28 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.03/10.28 apply (zenon_L18_); trivial. % 10.03/10.28 (* end of lemma zenon_L629_ *) % 10.03/10.28 assert (zenon_L630_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H22e zenon_Hbe zenon_H2c zenon_H1b1 zenon_Hd7 zenon_H2ee zenon_H64 zenon_H110 zenon_H14b zenon_Hd2 zenon_H93 zenon_H27 zenon_H1d9 zenon_H90 zenon_H14c zenon_H2ac zenon_H83 zenon_H1d4 zenon_H1ec zenon_H82 zenon_H30 zenon_Hef zenon_H2f7 zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_Ha5 zenon_H2a zenon_H101. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.28 apply (zenon_L316_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.28 apply (zenon_L340_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.28 apply (zenon_L251_); trivial. % 10.03/10.28 apply (zenon_L621_); trivial. % 10.03/10.28 (* end of lemma zenon_L630_ *) % 10.03/10.28 assert (zenon_L631_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> False). % 10.03/10.28 do 0 intro. intros zenon_H1b3 zenon_H187 zenon_H27. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_Hd2. zenon_intro zenon_H1b4. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H1b4). zenon_intro zenon_Hd7. zenon_intro zenon_Hc8. % 10.03/10.28 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.03/10.28 apply (zenon_L119_); trivial. % 10.03/10.28 (* end of lemma zenon_L631_ *) % 10.03/10.28 assert (zenon_L632_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> False). % 10.03/10.28 do 0 intro. intros zenon_H1b5 zenon_H93 zenon_H27. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_Hd2. zenon_intro zenon_H1b6. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_Hd7. zenon_intro zenon_Hcb. % 10.03/10.28 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.03/10.28 apply (zenon_L269_); trivial. % 10.03/10.28 (* end of lemma zenon_L632_ *) % 10.03/10.28 assert (zenon_L633_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H1fd zenon_H27 zenon_H5f. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H79. zenon_intro zenon_H1fe. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H109. zenon_intro zenon_Hc2. % 10.03/10.28 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.03/10.28 apply (zenon_L18_); trivial. % 10.03/10.28 (* end of lemma zenon_L633_ *) % 10.03/10.28 assert (zenon_L634_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H1ff zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_Ha5 zenon_H2a zenon_H101. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H1ff). zenon_intro zenon_H79. zenon_intro zenon_H200. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H200). zenon_intro zenon_H109. zenon_intro zenon_Hc5. % 10.03/10.28 apply (zenon_L509_); trivial. % 10.03/10.28 (* end of lemma zenon_L634_ *) % 10.03/10.28 assert (zenon_L635_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H203 zenon_H22e zenon_H2b zenon_Hbe zenon_H27 zenon_H2c zenon_H1ec zenon_H101. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H203). zenon_intro zenon_H7f. zenon_intro zenon_H204. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H204). zenon_intro zenon_H112. zenon_intro zenon_Hcf. % 10.03/10.28 apply (zenon_L407_); trivial. % 10.03/10.28 (* end of lemma zenon_L635_ *) % 10.03/10.28 assert (zenon_L636_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H205 zenon_H22e zenon_H2b zenon_Hbe zenon_H27 zenon_H2c zenon_H1ec zenon_H101. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H7f. zenon_intro zenon_H206. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H112. zenon_intro zenon_Hd6. % 10.03/10.28 apply (zenon_L407_); trivial. % 10.03/10.28 (* end of lemma zenon_L636_ *) % 10.03/10.28 assert (zenon_L637_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H20d zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_Ha5 zenon_H2a zenon_H101. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H52. zenon_intro zenon_H20e. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H20e). zenon_intro zenon_H52. zenon_intro zenon_H174. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.03/10.28 apply (zenon_L509_); trivial. % 10.03/10.28 (* end of lemma zenon_L637_ *) % 10.03/10.28 assert (zenon_L638_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H20f zenon_H22e zenon_H2b zenon_Hbe zenon_H27 zenon_H2c zenon_H1ec zenon_H101. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H20f). zenon_intro zenon_H52. zenon_intro zenon_H210. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H210). zenon_intro zenon_H52. zenon_intro zenon_H177. % 10.03/10.28 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.03/10.28 apply (zenon_L407_); trivial. % 10.03/10.28 (* end of lemma zenon_L638_ *) % 10.03/10.28 assert (zenon_L639_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H1f6 zenon_H1ea zenon_Ha7 zenon_H1d5 zenon_H1f5 zenon_H5d zenon_H22e zenon_H2b zenon_Hbe zenon_H27 zenon_H2c zenon_H1ec zenon_H112 zenon_H101. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.03/10.28 apply (zenon_L171_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.03/10.28 apply (zenon_L215_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.03/10.28 apply (zenon_L208_); trivial. % 10.03/10.28 apply (zenon_L407_); trivial. % 10.03/10.28 (* end of lemma zenon_L639_ *) % 10.03/10.28 assert (zenon_L640_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H1f6 zenon_H1ea zenon_Ha7 zenon_H91 zenon_H5d zenon_H22e zenon_H2b zenon_Hbe zenon_H27 zenon_H2c zenon_H1ec zenon_H112 zenon_H101. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.03/10.28 apply (zenon_L171_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.03/10.28 apply (zenon_L411_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.03/10.28 apply (zenon_L208_); trivial. % 10.03/10.28 apply (zenon_L407_); trivial. % 10.03/10.28 (* end of lemma zenon_L640_ *) % 10.03/10.28 assert (zenon_L641_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.28 do 0 intro. intros zenon_H1db zenon_H16c zenon_H1f5 zenon_H101 zenon_H112 zenon_H1ec zenon_H2c zenon_H27 zenon_Hbe zenon_H22e zenon_H5d zenon_Ha7 zenon_H1ea zenon_H1f6 zenon_H1d4 zenon_H2b. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1db); [ zenon_intro zenon_H90 | zenon_intro zenon_H1df ]. % 10.03/10.28 apply (zenon_L108_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H1e0 ]. % 10.03/10.28 apply (zenon_L639_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H91 | zenon_intro zenon_H72 ]. % 10.03/10.28 apply (zenon_L640_); trivial. % 10.03/10.28 apply (zenon_L402_); trivial. % 10.03/10.28 (* end of lemma zenon_L641_ *) % 10.03/10.28 assert (zenon_L642_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.28 do 0 intro. intros zenon_H272 zenon_H5a zenon_H89 zenon_H7a zenon_Ha5 zenon_H7e zenon_H1db zenon_H16c zenon_H1f5 zenon_H101 zenon_H112 zenon_H1ec zenon_H2c zenon_H27 zenon_Hbe zenon_H22e zenon_H5d zenon_H1ea zenon_H1f6 zenon_H1d4 zenon_H2b. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.03/10.28 apply (zenon_L381_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.03/10.28 apply (zenon_L382_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.03/10.28 apply (zenon_L383_); trivial. % 10.03/10.28 apply (zenon_L641_); trivial. % 10.03/10.28 (* end of lemma zenon_L642_ *) % 10.03/10.28 assert (zenon_L643_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.03/10.28 do 0 intro. intros zenon_H2f7 zenon_Hef zenon_H30 zenon_H1ec zenon_H2c4 zenon_H1d4 zenon_H2b zenon_H83 zenon_H2ac zenon_H121 zenon_H5d zenon_H82. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.03/10.28 apply (zenon_L64_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.03/10.28 apply (zenon_L619_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.03/10.28 apply (zenon_L389_); trivial. % 10.03/10.28 apply (zenon_L584_); trivial. % 10.03/10.28 (* end of lemma zenon_L643_ *) % 10.03/10.28 assert (zenon_L644_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H2ee zenon_H64 zenon_H110 zenon_H82 zenon_H5d zenon_H2ac zenon_H83 zenon_H1d4 zenon_H1ec zenon_H30 zenon_Hef zenon_H2f7 zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_Ha5 zenon_H2a zenon_H109 zenon_H101. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.03/10.28 apply (zenon_L22_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.03/10.28 apply (zenon_L73_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.03/10.28 apply (zenon_L643_); trivial. % 10.03/10.28 apply (zenon_L509_); trivial. % 10.03/10.28 (* end of lemma zenon_L644_ *) % 10.03/10.28 assert (zenon_L645_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((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 (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H1f6 zenon_H1ea zenon_H22e zenon_Hbe zenon_H27 zenon_H2c zenon_H1f5 zenon_H16c zenon_H1db zenon_H7e zenon_H7a zenon_H89 zenon_H5a zenon_H272 zenon_H1b9 zenon_H187 zenon_H2ee zenon_H64 zenon_H110 zenon_H82 zenon_H5d zenon_H2ac zenon_H83 zenon_H1d4 zenon_H1ec zenon_H30 zenon_Hef zenon_H2f7 zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_Ha5 zenon_H2a zenon_H101. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.28 apply (zenon_L316_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.28 apply (zenon_L8_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.03/10.28 apply (zenon_L22_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.03/10.28 apply (zenon_L401_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.03/10.28 apply (zenon_L619_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.03/10.28 apply (zenon_L406_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.03/10.28 apply (zenon_L403_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.03/10.28 apply (zenon_L174_); trivial. % 10.03/10.28 apply (zenon_L642_); trivial. % 10.03/10.28 apply (zenon_L644_); trivial. % 10.03/10.28 (* end of lemma zenon_L645_ *) % 10.03/10.28 assert (zenon_L646_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> False). % 10.03/10.28 do 0 intro. intros zenon_Hc6 zenon_H187 zenon_H27. % 10.03/10.28 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_H89. zenon_intro zenon_Hc7. % 10.03/10.28 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_H9d. zenon_intro zenon_Hc8. % 10.03/10.28 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.03/10.28 apply (zenon_L119_); trivial. % 10.03/10.28 (* end of lemma zenon_L646_ *) % 10.03/10.28 assert (zenon_L647_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.28 do 0 intro. intros zenon_H1f6 zenon_Ha5 zenon_H7e zenon_H1d5 zenon_H1f5 zenon_Hd7 zenon_H22e zenon_H2b zenon_Hbe zenon_H27 zenon_H2c zenon_H1ec zenon_H112 zenon_H101. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.03/10.28 apply (zenon_L383_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.03/10.28 apply (zenon_L215_); trivial. % 10.03/10.28 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.03/10.28 apply (zenon_L219_); trivial. % 10.03/10.28 apply (zenon_L407_); trivial. % 10.03/10.28 (* end of lemma zenon_L647_ *) % 10.03/10.28 assert (zenon_L648_ : ((op (e3) (e1)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (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)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 10.03/10.29 do 0 intro. intros zenon_H79 zenon_H1f0 zenon_Hd7 zenon_H27 zenon_H2b zenon_H91 zenon_H2ae zenon_H2c zenon_H2a zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H12a zenon_H1d9 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H64 zenon_H110 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H105 zenon_H141 zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H1e zenon_H7a zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Heb zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H14b zenon_H7e zenon_H1f6 zenon_H101 zenon_H1ec zenon_Hbe zenon_H22e zenon_Hd1 zenon_H1d4 zenon_H23 zenon_Ha5 zenon_H25. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.03/10.29 apply (zenon_L406_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.03/10.29 apply (zenon_L403_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.03/10.29 apply (zenon_L174_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.03/10.29 apply (zenon_L647_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.03/10.29 apply (zenon_L269_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.03/10.29 apply (zenon_L411_); trivial. % 10.03/10.29 apply (zenon_L581_); trivial. % 10.03/10.29 (* end of lemma zenon_L648_ *) % 10.03/10.29 assert (zenon_L649_ : ((op (e3) (e1)) = (e0)) -> ((op (e2) (e3)) = (e3)) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (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) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.03/10.29 do 0 intro. intros zenon_H94 zenon_H112 zenon_H25 zenon_Ha5 zenon_H23 zenon_H1d4 zenon_Hd1 zenon_H22e zenon_Hbe zenon_H1ec zenon_H101 zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_Heb zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H105 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H110 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H12a zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2a zenon_H2c zenon_H2ae zenon_H2b zenon_H27 zenon_Hd7 zenon_H1f0 zenon_H1d9 zenon_H79. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H1db); [ zenon_intro zenon_H90 | zenon_intro zenon_H1df ]. % 10.03/10.29 apply (zenon_L334_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H1e0 ]. % 10.03/10.29 apply (zenon_L647_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H91 | zenon_intro zenon_H72 ]. % 10.03/10.29 apply (zenon_L648_); trivial. % 10.03/10.29 apply (zenon_L162_); trivial. % 10.03/10.29 (* end of lemma zenon_L649_ *) % 10.03/10.29 assert (zenon_L650_ : (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = 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(e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.03/10.29 do 0 intro. intros zenon_H5a zenon_H79 zenon_H1d9 zenon_H1f0 zenon_Hd7 zenon_H2ae zenon_H2a zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H12a zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H64 zenon_H110 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H2fe zenon_H105 zenon_H141 zenon_H301 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H1e zenon_H7a zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Heb zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H14b zenon_Hd1 zenon_H23 zenon_H25 zenon_Ha5 zenon_H7e zenon_H1db zenon_H16c zenon_H1f5 zenon_H101 zenon_H1ec zenon_H2c zenon_H27 zenon_Hbe zenon_H22e zenon_H5d zenon_H1ea zenon_H1f6 zenon_H1d4 zenon_H2b. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.03/10.29 apply (zenon_L406_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.03/10.29 apply (zenon_L403_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.03/10.29 apply (zenon_L174_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.03/10.29 apply (zenon_L381_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.03/10.29 apply (zenon_L649_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.03/10.29 apply (zenon_L383_); trivial. % 10.03/10.29 apply (zenon_L641_); trivial. % 10.03/10.29 (* end of lemma zenon_L650_ *) % 10.03/10.29 assert (zenon_L651_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (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) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.29 do 0 intro. intros zenon_H1f6 zenon_H1ea zenon_H22e zenon_Hbe zenon_H27 zenon_H2c zenon_H1f5 zenon_H16c zenon_H1db zenon_H7e zenon_H25 zenon_H23 zenon_Hd1 zenon_H14b zenon_H1c9 zenon_Heb zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H301 zenon_H141 zenon_H105 zenon_H2fe zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H12c zenon_Ha9 zenon_H2c7 zenon_H1cb zenon_H14c zenon_H12a zenon_H155 zenon_H1b9 zenon_H127 zenon_H2ae zenon_Hd7 zenon_H1d9 zenon_H5a zenon_H2ee zenon_H64 zenon_H110 zenon_H82 zenon_H5d zenon_H2ac zenon_H83 zenon_H1d4 zenon_H1ec zenon_H30 zenon_Hef zenon_H2f7 zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_Ha5 zenon_H2a zenon_H101. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.03/10.29 apply (zenon_L316_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.03/10.29 apply (zenon_L8_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.03/10.29 apply (zenon_L22_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.03/10.29 apply (zenon_L401_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.03/10.29 apply (zenon_L619_); trivial. % 10.03/10.29 apply (zenon_L650_); trivial. % 10.03/10.29 apply (zenon_L644_); trivial. % 10.03/10.29 (* end of lemma zenon_L651_ *) % 10.03/10.29 assert (zenon_L652_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 10.03/10.29 do 0 intro. intros zenon_H1f6 zenon_Ha5 zenon_H7e zenon_H1d5 zenon_H1f5 zenon_Hd0 zenon_H96 zenon_H1f0 zenon_H1ec. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.03/10.29 apply (zenon_L383_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.03/10.29 apply (zenon_L215_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.03/10.29 apply (zenon_L104_); trivial. % 10.03/10.29 apply (zenon_L404_); trivial. % 10.03/10.29 (* end of lemma zenon_L652_ *) % 10.03/10.29 assert (zenon_L653_ : ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (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 (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (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) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> False). % 10.03/10.29 do 0 intro. intros zenon_H1d5 zenon_H2b zenon_H1d4 zenon_H1f6 zenon_H1ea zenon_H22e zenon_Hbe zenon_H27 zenon_H2c zenon_H1ec zenon_H101 zenon_H1f5 zenon_H16c zenon_H1db zenon_H7e zenon_H25 zenon_Hd1 zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_Heb zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H301 zenon_H141 zenon_H105 zenon_H2fe zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H110 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H12a zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2a zenon_H2ae zenon_H1f0 zenon_H1d9 zenon_H79 zenon_H5a zenon_H23 zenon_Ha5 zenon_H5d. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.03/10.29 apply (zenon_L652_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.03/10.29 apply (zenon_L650_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.03/10.29 apply (zenon_L324_); trivial. % 10.03/10.29 apply (zenon_L208_); trivial. % 10.03/10.29 (* end of lemma zenon_L653_ *) % 10.03/10.29 assert (zenon_L654_ : (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (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)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.03/10.29 do 0 intro. intros zenon_H5d zenon_Ha5 zenon_H23 zenon_H5a zenon_H1d9 zenon_H1f0 zenon_H2ae zenon_H2a zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H12a zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H64 zenon_H110 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H2fe zenon_H105 zenon_H141 zenon_H301 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H1e zenon_H7a zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Heb zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H14b zenon_Hd1 zenon_H7e zenon_H1db zenon_H16c zenon_H1f5 zenon_H101 zenon_H1ec zenon_H2c zenon_H27 zenon_Hbe zenon_H22e zenon_H1ea zenon_H1f6 zenon_H1d4 zenon_H5c zenon_H2b zenon_H91 zenon_H82 zenon_H25. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.03/10.29 apply (zenon_L22_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.03/10.29 apply (zenon_L401_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.03/10.29 apply (zenon_L619_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.03/10.29 apply (zenon_L653_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.03/10.29 apply (zenon_L93_); trivial. % 10.03/10.29 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.03/10.29 apply (zenon_L411_); trivial. % 10.03/10.29 apply (zenon_L521_); trivial. % 10.03/10.29 (* end of lemma zenon_L654_ *) % 10.03/10.29 assert (zenon_L655_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> False). % 10.03/10.29 do 0 intro. intros zenon_H19d zenon_H93 zenon_H27. % 10.03/10.29 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_Hf7. zenon_intro zenon_H19e. % 10.03/10.29 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H171. % 10.03/10.29 apply (zenon_L269_); trivial. % 10.03/10.29 (* end of lemma zenon_L655_ *) % 10.03/10.29 assert (zenon_L656_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.03/10.29 do 0 intro. intros zenon_H207 zenon_H22e zenon_H2b zenon_Hbe zenon_H27 zenon_H2c zenon_H1ec zenon_H101. % 10.03/10.29 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H7f. zenon_intro zenon_H208. % 10.03/10.29 apply (zenon_and_s _ _ zenon_H208). zenon_intro zenon_H112. zenon_intro zenon_H165. % 10.03/10.29 apply (zenon_L407_); trivial. % 10.03/10.29 (* end of lemma zenon_L656_ *) % 10.03/10.29 assert (zenon_L657_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.15/10.29 do 0 intro. intros zenon_H22e zenon_Hbe zenon_H1ec zenon_H101 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1d4 zenon_H1f6 zenon_H7e zenon_H14b zenon_H23 zenon_H1b9 zenon_Heb zenon_H93 zenon_H187 zenon_H1ea zenon_H1f5 zenon_H16c zenon_H1db zenon_H25 zenon_Hd1 zenon_H1c9 zenon_H192 zenon_H11f zenon_H96 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H301 zenon_H141 zenon_H105 zenon_H2fe zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H12c zenon_Ha9 zenon_H2c7 zenon_H1cb zenon_H14c zenon_H12a zenon_H155 zenon_H127 zenon_H2ae zenon_H1d9 zenon_H2ee zenon_H64 zenon_H110 zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H27 zenon_H2c zenon_Ha5 zenon_H2a zenon_H82 zenon_H30. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_Hd8. zenon_intro zenon_H15b. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_H15c. zenon_intro zenon_He1. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.15/10.29 apply (zenon_L7_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.15/10.29 apply (zenon_L384_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.15/10.29 apply (zenon_L29_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.15/10.29 apply (zenon_L272_); trivial. % 10.15/10.29 apply (zenon_L344_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.15/10.29 apply (zenon_L322_); trivial. % 10.15/10.29 apply (zenon_L283_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.15/10.29 apply (zenon_L13_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.15/10.29 apply (zenon_L21_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.15/10.29 apply (zenon_L473_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.15/10.29 apply (zenon_L474_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.15/10.29 apply (zenon_L504_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.15/10.29 apply (zenon_L246_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_H89. zenon_intro zenon_Hc4. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_H9d. zenon_intro zenon_Hc5. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 10.15/10.29 apply (zenon_L615_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.15/10.29 apply (zenon_L364_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H89. zenon_intro zenon_Hca. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_H9d. zenon_intro zenon_Hcb. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.15/10.29 apply (zenon_L616_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.15/10.29 apply (zenon_L55_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.15/10.29 apply (zenon_L372_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.15/10.29 apply (zenon_L325_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.15/10.29 apply (zenon_L198_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.15/10.29 apply (zenon_L479_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.15/10.29 apply (zenon_L512_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.15/10.29 apply (zenon_L617_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.15/10.29 apply (zenon_L263_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.15/10.29 apply (zenon_L516_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.15/10.29 apply (zenon_L264_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.15/10.29 apply (zenon_L332_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_H5e. zenon_intro zenon_Hbd. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.15/10.29 apply (zenon_L618_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.15/10.29 apply (zenon_L117_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.15/10.29 apply (zenon_L7_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H20 | zenon_intro zenon_H1dd ]. % 10.15/10.29 apply (zenon_L7_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 10.15/10.29 apply (zenon_L615_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H9e | zenon_intro zenon_H90 ]. % 10.15/10.29 apply (zenon_L197_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.15/10.29 apply (zenon_L384_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.15/10.29 apply (zenon_L29_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.15/10.29 apply (zenon_L152_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.15/10.29 apply (zenon_L625_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.15/10.29 apply (zenon_L373_); trivial. % 10.15/10.29 apply (zenon_L614_); trivial. % 10.15/10.29 apply (zenon_L344_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.15/10.29 apply (zenon_L322_); trivial. % 10.15/10.29 apply (zenon_L618_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.15/10.29 apply (zenon_L121_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.15/10.29 apply (zenon_L270_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.15/10.29 apply (zenon_L626_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.15/10.29 apply (zenon_L374_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.15/10.29 apply (zenon_L337_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.15/10.29 apply (zenon_L375_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.15/10.29 apply (zenon_L480_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.15/10.29 apply (zenon_L133_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.15/10.29 apply (zenon_L627_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.15/10.29 apply (zenon_L276_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.15/10.29 apply (zenon_L526_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H1a9). zenon_intro zenon_H86. zenon_intro zenon_H1aa. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_Hd0. zenon_intro zenon_Hb3. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.15/10.29 apply (zenon_L628_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.15/10.29 apply (zenon_L138_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.15/10.29 apply (zenon_L376_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.15/10.29 apply (zenon_L629_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_Hd2. zenon_intro zenon_H1b2. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_Hd7. zenon_intro zenon_Hc5. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H20 | zenon_intro zenon_H1dd ]. % 10.15/10.29 apply (zenon_L7_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 10.15/10.29 apply (zenon_L615_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H9e | zenon_intro zenon_H90 ]. % 10.15/10.29 apply (zenon_L197_); trivial. % 10.15/10.29 apply (zenon_L630_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.15/10.29 apply (zenon_L631_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.15/10.29 apply (zenon_L632_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.15/10.29 apply (zenon_L284_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.15/10.29 apply (zenon_L146_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.15/10.29 apply (zenon_L345_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.15/10.29 apply (zenon_L149_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.15/10.29 apply (zenon_L483_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.15/10.29 apply (zenon_L529_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.15/10.29 apply (zenon_L167_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.15/10.29 apply (zenon_L286_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.15/10.29 apply (zenon_L486_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.15/10.29 apply (zenon_L487_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.15/10.29 apply (zenon_L204_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.15/10.29 apply (zenon_L531_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.15/10.29 apply (zenon_L633_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.15/10.29 apply (zenon_L634_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.15/10.29 apply (zenon_L206_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.15/10.29 apply (zenon_L183_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.15/10.29 apply (zenon_L635_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.15/10.29 apply (zenon_L636_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.15/10.29 apply (zenon_L355_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.15/10.29 apply (zenon_L187_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.15/10.29 apply (zenon_L535_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.15/10.29 apply (zenon_L637_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.15/10.29 apply (zenon_L638_); trivial. % 10.15/10.29 apply (zenon_L301_); trivial. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H51. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.15/10.29 apply (zenon_L21_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.15/10.29 apply (zenon_L473_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.15/10.29 apply (zenon_L474_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.15/10.29 apply (zenon_L502_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.15/10.29 apply (zenon_L246_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_H89. zenon_intro zenon_Hc4. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_H9d. zenon_intro zenon_Hc5. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 10.15/10.29 apply (zenon_L645_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.15/10.29 apply (zenon_L646_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.15/10.29 apply (zenon_L207_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.15/10.29 apply (zenon_L55_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_H97. zenon_intro zenon_Hd5. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_H9e. zenon_intro zenon_Hd6. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.15/10.29 apply (zenon_L651_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.15/10.29 apply (zenon_L325_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.15/10.29 apply (zenon_L209_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.15/10.29 apply (zenon_L479_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.15/10.29 apply (zenon_L512_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.15/10.29 apply (zenon_L617_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.15/10.29 apply (zenon_L263_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.15/10.29 apply (zenon_L516_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.15/10.29 apply (zenon_L264_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.15/10.29 apply (zenon_L332_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.15/10.29 apply (zenon_L553_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.15/10.29 apply (zenon_L117_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.15/10.29 apply (zenon_L316_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.15/10.29 apply (zenon_L336_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.15/10.29 apply (zenon_L22_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.15/10.29 apply (zenon_L401_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.15/10.29 apply (zenon_L619_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H1db); [ zenon_intro zenon_H90 | zenon_intro zenon_H1df ]. % 10.15/10.29 apply (zenon_L381_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H1e0 ]. % 10.15/10.29 apply (zenon_L653_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H91 | zenon_intro zenon_H72 ]. % 10.15/10.29 apply (zenon_L654_); trivial. % 10.15/10.29 apply (zenon_L402_); trivial. % 10.15/10.29 apply (zenon_L644_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.15/10.29 apply (zenon_L120_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.15/10.29 apply (zenon_L270_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.15/10.29 apply (zenon_L626_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H197). zenon_intro zenon_H188. zenon_intro zenon_H198. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H198). zenon_intro zenon_H18c. zenon_intro zenon_Hd6. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.15/10.29 apply (zenon_L651_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.15/10.29 apply (zenon_L337_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.15/10.29 apply (zenon_L211_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.15/10.29 apply (zenon_L655_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.15/10.29 apply (zenon_L133_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.15/10.29 apply (zenon_L627_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.15/10.29 apply (zenon_L276_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.15/10.29 apply (zenon_L526_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H1a9). zenon_intro zenon_H86. zenon_intro zenon_H1aa. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_Hd0. zenon_intro zenon_Hb3. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.15/10.29 apply (zenon_L645_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.15/10.29 apply (zenon_L138_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.15/10.29 apply (zenon_L578_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.15/10.29 apply (zenon_L629_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_Hd2. zenon_intro zenon_H1b2. % 10.15/10.29 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_Hd7. zenon_intro zenon_Hc5. % 10.15/10.29 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H27. zenon_intro zenon_H27. % 10.15/10.29 apply (zenon_L651_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.15/10.29 apply (zenon_L631_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.15/10.29 apply (zenon_L632_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.15/10.29 apply (zenon_L284_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.15/10.29 apply (zenon_L146_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.15/10.29 apply (zenon_L345_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.15/10.29 apply (zenon_L213_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.15/10.29 apply (zenon_L483_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.15/10.29 apply (zenon_L529_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.15/10.29 apply (zenon_L167_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.15/10.29 apply (zenon_L286_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.15/10.29 apply (zenon_L486_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.15/10.29 apply (zenon_L487_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.15/10.29 apply (zenon_L488_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.15/10.29 apply (zenon_L579_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.15/10.29 apply (zenon_L532_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.15/10.29 apply (zenon_L634_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.15/10.29 apply (zenon_L555_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.15/10.29 apply (zenon_L183_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.15/10.29 apply (zenon_L635_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.15/10.29 apply (zenon_L636_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.15/10.29 apply (zenon_L656_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.15/10.29 apply (zenon_L187_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.15/10.29 apply (zenon_L535_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.15/10.29 apply (zenon_L637_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.15/10.29 apply (zenon_L638_); trivial. % 10.15/10.29 apply (zenon_L301_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.15/10.29 apply (zenon_L8_); trivial. % 10.15/10.29 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.15/10.29 apply (zenon_L42_); trivial. % 10.15/10.29 apply (zenon_L26_); trivial. % 10.15/10.29 (* end of lemma zenon_L657_ *) % 10.15/10.29 assert (zenon_L658_ : ((op (e3) (e3)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> False). % 10.16/10.30 do 0 intro. intros zenon_H52 zenon_Hf3 zenon_Hb7 zenon_H24 zenon_Hd7 zenon_H22e zenon_Hbe zenon_H1ec zenon_H101 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1d4 zenon_H1f6 zenon_H7e zenon_H14b zenon_H23 zenon_H1b9 zenon_Heb zenon_H93 zenon_H187 zenon_H1ea zenon_H1f5 zenon_H16c zenon_H1db zenon_H25 zenon_Hd1 zenon_H1c9 zenon_H192 zenon_H11f zenon_H96 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H301 zenon_H141 zenon_H105 zenon_H2fe zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H12c zenon_Ha9 zenon_H2c7 zenon_H1cb zenon_H14c zenon_H12a zenon_H155 zenon_H127 zenon_H2ae zenon_H1d9 zenon_H2ee zenon_H64 zenon_H110 zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H27 zenon_H2c zenon_Ha5 zenon_H2a zenon_H30. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.16/10.30 apply (zenon_L217_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.16/10.30 apply (zenon_L612_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.16/10.30 apply (zenon_L219_); trivial. % 10.16/10.30 apply (zenon_L657_); trivial. % 10.16/10.30 (* end of lemma zenon_L658_ *) % 10.16/10.30 assert (zenon_L659_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((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) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.30 do 0 intro. intros zenon_H1cb zenon_H24 zenon_H2dd zenon_H149 zenon_H2c4 zenon_H1b9 zenon_Hd7 zenon_H10d zenon_Hb7 zenon_H105 zenon_H102 zenon_H101 zenon_H52 zenon_Hfe. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.16/10.30 apply (zenon_L399_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.16/10.30 apply (zenon_L386_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.16/10.30 apply (zenon_L145_); trivial. % 10.16/10.30 apply (zenon_L242_); trivial. % 10.16/10.30 (* end of lemma zenon_L659_ *) % 10.16/10.30 assert (zenon_L660_ : ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> False). % 10.16/10.30 do 0 intro. intros zenon_H52 zenon_H102 zenon_Hb7 zenon_H24 zenon_Hd7 zenon_H22e zenon_Hbe zenon_H1ec zenon_H101 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1d4 zenon_H1f6 zenon_H7e zenon_H14b zenon_H23 zenon_H1b9 zenon_Heb zenon_H93 zenon_H187 zenon_H1ea zenon_H1f5 zenon_H16c zenon_H1db zenon_H25 zenon_Hd1 zenon_H1c9 zenon_H192 zenon_H11f zenon_H96 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H301 zenon_H141 zenon_H105 zenon_H2fe zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H12c zenon_Ha9 zenon_H2c7 zenon_H1cb zenon_H14c zenon_H12a zenon_H155 zenon_H127 zenon_H2ae zenon_H1d9 zenon_H2ee zenon_H64 zenon_H110 zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H27 zenon_H2c zenon_Ha5 zenon_H2a zenon_H30. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.16/10.30 apply (zenon_L217_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.16/10.30 apply (zenon_L659_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.16/10.30 apply (zenon_L219_); trivial. % 10.16/10.30 apply (zenon_L657_); trivial. % 10.16/10.30 (* end of lemma zenon_L660_ *) % 10.16/10.30 assert (zenon_L661_ : ((op (e1) (e1)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((((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)) = 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(e3) (e3))) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 10.16/10.30 do 0 intro. intros zenon_H27 zenon_Hd7 zenon_Hb7 zenon_H52 zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_H30 zenon_H23 zenon_He8 zenon_H24 zenon_H5f zenon_H1f5 zenon_H113 zenon_Hf1 zenon_Hef zenon_H130 zenon_H2dd zenon_H1f6 zenon_H7e zenon_H1ec zenon_H14b zenon_H110 zenon_Heb zenon_H272 zenon_H7a zenon_H1e zenon_H1b9 zenon_Hfe zenon_H192 zenon_H1d4 zenon_H2c4 zenon_H25 zenon_H187 zenon_H93 zenon_H22f zenon_H1d9 zenon_H2ac zenon_H2ae zenon_H127 zenon_H101 zenon_Hbe zenon_H2a8 zenon_H155 zenon_H2c7 zenon_H2ee zenon_H64 zenon_Ha9 zenon_H12c zenon_H2f7 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H124 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H105 zenon_H1db zenon_H301 zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H96 zenon_H1c9 zenon_H22e zenon_H83 zenon_H1cb zenon_H14c zenon_H141 zenon_H2ca zenon_H118 zenon_Ha5 zenon_H2a zenon_H2c. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.16/10.30 apply (zenon_L658_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.16/10.30 apply (zenon_L616_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.16/10.30 apply (zenon_L660_); trivial. % 10.16/10.30 apply (zenon_L580_); trivial. % 10.16/10.30 (* end of lemma zenon_L661_ *) % 10.16/10.30 assert (zenon_L662_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 10.16/10.30 do 0 intro. intros zenon_H12c zenon_Ha5 zenon_H127 zenon_Hf3 zenon_H12a zenon_H101 zenon_H106 zenon_H87 zenon_H113. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.16/10.30 apply (zenon_L544_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.16/10.30 apply (zenon_L155_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.16/10.30 apply (zenon_L241_); trivial. % 10.16/10.30 apply (zenon_L74_); trivial. % 10.16/10.30 (* end of lemma zenon_L662_ *) % 10.16/10.30 assert (zenon_L663_ : (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((((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) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (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) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 10.16/10.30 do 0 intro. intros zenon_H2c zenon_H2a zenon_H118 zenon_H2ca zenon_H141 zenon_H14c zenon_H1cb zenon_H83 zenon_H22e zenon_H1c9 zenon_H96 zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H301 zenon_H1db zenon_H105 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H124 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H10d zenon_H304 zenon_H2f7 zenon_Ha9 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H155 zenon_H2a8 zenon_Hbe zenon_H2ae zenon_H2ac zenon_H1d9 zenon_H22f zenon_H93 zenon_H187 zenon_H25 zenon_H2c4 zenon_H1d4 zenon_H192 zenon_Hfe zenon_H1b9 zenon_H1e zenon_H7a zenon_H272 zenon_Heb zenon_H110 zenon_H14b zenon_H1ec zenon_H7e zenon_H1f6 zenon_H2dd zenon_H130 zenon_Hef zenon_Hf1 zenon_H1f5 zenon_H5f zenon_H24 zenon_He8 zenon_H23 zenon_H30 zenon_Hd1 zenon_H11f zenon_H12f zenon_H52 zenon_Hb7 zenon_H27 zenon_H12c zenon_Ha5 zenon_H127 zenon_Hf3 zenon_H12a zenon_H101 zenon_H87 zenon_H113. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.30 apply (zenon_L610_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.30 apply (zenon_L5_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.30 apply (zenon_L661_); trivial. % 10.16/10.30 apply (zenon_L662_); trivial. % 10.16/10.30 (* end of lemma zenon_L663_ *) % 10.16/10.30 assert (zenon_L664_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.16/10.30 do 0 intro. intros zenon_H13d zenon_H9e zenon_H9c zenon_H27 zenon_H1e zenon_H1b9 zenon_Ha5 zenon_H105 zenon_Hb7. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.16/10.30 apply (zenon_L40_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.16/10.30 apply (zenon_L231_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.16/10.30 apply (zenon_L341_); trivial. % 10.16/10.30 apply (zenon_L235_); trivial. % 10.16/10.30 (* end of lemma zenon_L664_ *) % 10.16/10.30 assert (zenon_L665_ : ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) 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(e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.16/10.30 do 0 intro. intros zenon_H90 zenon_H1d9 zenon_H2ac zenon_H2c zenon_H2a zenon_H118 zenon_H83 zenon_H22e zenon_H1c9 zenon_H96 zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H301 zenon_H1db zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H124 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H10d zenon_H304 zenon_H2f7 zenon_H12c zenon_Ha9 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H155 zenon_H2a8 zenon_Hbe zenon_H127 zenon_H2ae zenon_H22f zenon_H187 zenon_H25 zenon_H1d4 zenon_H192 zenon_Hfe zenon_H272 zenon_Heb zenon_H14b zenon_H1ec zenon_H7e zenon_H1f6 zenon_H130 zenon_Hef zenon_Hf1 zenon_H113 zenon_H1f5 zenon_H5f zenon_He8 zenon_H30 zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_H2ca zenon_H110 zenon_H141 zenon_H52 zenon_H93 zenon_H7a zenon_H14c zenon_H1cb zenon_H24 zenon_H2dd zenon_H2c4 zenon_H23 zenon_H101 zenon_H27 zenon_H1e zenon_H1b9 zenon_Ha5 zenon_H105 zenon_Hb7. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.30 apply (zenon_L153_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.30 apply (zenon_L5_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.30 apply (zenon_L661_); trivial. % 10.16/10.30 apply (zenon_L601_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.16/10.30 apply (zenon_L231_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.16/10.30 apply (zenon_L333_); trivial. % 10.16/10.30 apply (zenon_L334_); trivial. % 10.16/10.30 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.16/10.31 apply (zenon_L231_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.16/10.31 apply (zenon_L341_); trivial. % 10.16/10.31 apply (zenon_L235_); trivial. % 10.16/10.31 (* end of lemma zenon_L665_ *) % 10.16/10.31 assert (zenon_L666_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.16/10.31 do 0 intro. intros zenon_H2f7 zenon_H2c zenon_H2d4 zenon_H30 zenon_Hd7 zenon_H128 zenon_H50 zenon_H52 zenon_H1ea. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.16/10.31 apply (zenon_L599_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.16/10.31 apply (zenon_L251_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.16/10.31 apply (zenon_L199_); trivial. % 10.16/10.31 apply (zenon_L299_); trivial. % 10.16/10.31 (* end of lemma zenon_L666_ *) % 10.16/10.31 assert (zenon_L667_ : ((op (e1) (e3)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> False). % 10.16/10.31 do 0 intro. intros zenon_H106 zenon_H24 zenon_Hd7 zenon_H22e zenon_Hbe zenon_H1ec zenon_H101 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1d4 zenon_H1f6 zenon_H7e zenon_H14b zenon_H23 zenon_H1b9 zenon_Heb zenon_H93 zenon_H187 zenon_H1ea zenon_H1f5 zenon_H16c zenon_H1db zenon_H25 zenon_Hd1 zenon_H1c9 zenon_H192 zenon_H11f zenon_H96 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H301 zenon_H141 zenon_H105 zenon_H2fe zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H12c zenon_Ha9 zenon_H2c7 zenon_H1cb zenon_H14c zenon_H12a zenon_H155 zenon_H127 zenon_H2ae zenon_H1d9 zenon_H2ee zenon_H64 zenon_H110 zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H27 zenon_H2c zenon_Ha5 zenon_H2a zenon_H30. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.16/10.31 apply (zenon_L217_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.16/10.31 apply (zenon_L561_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.16/10.31 apply (zenon_L219_); trivial. % 10.16/10.31 apply (zenon_L657_); trivial. % 10.16/10.31 (* end of lemma zenon_L667_ *) % 10.16/10.31 assert (zenon_L668_ : ((op (e2) (e2)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 10.16/10.31 do 0 intro. intros zenon_H2e zenon_Hd2 zenon_H2ac. % 10.16/10.31 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hec | zenon_intro zenon_H81 ]. % 10.16/10.31 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))). % 10.16/10.31 intro zenon_D_pnotp. % 10.16/10.31 apply zenon_H2ac. % 10.16/10.31 rewrite <- zenon_D_pnotp. % 10.16/10.31 exact zenon_Hec. % 10.16/10.31 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.16/10.31 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2ad]. % 10.16/10.31 congruence. % 10.16/10.31 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e1)))). % 10.16/10.31 intro zenon_D_pnotp. % 10.16/10.31 apply zenon_H2ad. % 10.16/10.31 rewrite <- zenon_D_pnotp. % 10.16/10.31 exact zenon_H2e. % 10.16/10.31 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 10.16/10.31 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.16/10.31 congruence. % 10.16/10.31 apply zenon_H81. apply refl_equal. % 10.16/10.31 apply zenon_Hd3. apply sym_equal. exact zenon_Hd2. % 10.16/10.31 apply zenon_H81. apply refl_equal. % 10.16/10.31 apply zenon_H81. apply refl_equal. % 10.16/10.31 (* end of lemma zenon_L668_ *) % 10.16/10.31 assert (zenon_L669_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.31 do 0 intro. intros zenon_H2a8 zenon_H24 zenon_Hbe zenon_H27 zenon_H25 zenon_H166 zenon_H1ec zenon_H128 zenon_H101. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.31 apply (zenon_L385_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.31 apply (zenon_L5_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.31 apply (zenon_L219_); trivial. % 10.16/10.31 apply (zenon_L241_); trivial. % 10.16/10.31 (* end of lemma zenon_L669_ *) % 10.16/10.31 assert (zenon_L670_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> False). % 10.16/10.31 do 0 intro. intros zenon_H12c zenon_Ha5 zenon_H127 zenon_Hf3 zenon_H12a zenon_H101 zenon_H1ec zenon_H166 zenon_H25 zenon_H27 zenon_Hbe zenon_H24 zenon_H2a8 zenon_H50. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.16/10.31 apply (zenon_L544_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.16/10.31 apply (zenon_L155_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.16/10.31 apply (zenon_L669_); trivial. % 10.16/10.31 apply (zenon_L368_); trivial. % 10.16/10.31 (* end of lemma zenon_L670_ *) % 10.16/10.31 assert (zenon_L671_ : (~((op (e2) (op (e2) (e3))) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.31 do 0 intro. intros zenon_H50 zenon_H2a8 zenon_Hbe zenon_H27 zenon_H25 zenon_H1ec zenon_H12a zenon_Hf3 zenon_H127 zenon_H12c zenon_H2ac zenon_H22e zenon_H12f zenon_H1d4 zenon_H1f6 zenon_H7e zenon_H14b zenon_H1b9 zenon_Heb zenon_H93 zenon_H187 zenon_H1ea zenon_H1f5 zenon_H16c zenon_H1db zenon_Hd1 zenon_H1c9 zenon_H192 zenon_H11f zenon_H96 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H301 zenon_H141 zenon_H105 zenon_H2fe zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_Ha9 zenon_H2c7 zenon_H14c zenon_H155 zenon_H2ae zenon_H1d9 zenon_H2ee zenon_H64 zenon_H110 zenon_H83 zenon_Hef zenon_H2f7 zenon_H2c zenon_H2a zenon_H30 zenon_H1cb zenon_H24 zenon_H2dd zenon_H2c4 zenon_H23 zenon_Ha5 zenon_H106 zenon_H101. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.16/10.31 apply (zenon_L19_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.16/10.31 apply (zenon_L517_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.16/10.31 apply (zenon_L152_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.16/10.31 apply (zenon_L667_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.16/10.31 apply (zenon_L668_); trivial. % 10.16/10.31 apply (zenon_L670_); trivial. % 10.16/10.31 apply (zenon_L561_); trivial. % 10.16/10.31 (* end of lemma zenon_L671_ *) % 10.16/10.31 assert (zenon_L672_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> False). % 10.16/10.31 do 0 intro. intros zenon_H22a zenon_Hef zenon_H30 zenon_H1f0 zenon_H2ac zenon_Hd2 zenon_H12c zenon_Ha5 zenon_H127 zenon_Hf3 zenon_H12a zenon_H101 zenon_H1ec zenon_H25 zenon_H27 zenon_Hbe zenon_H24 zenon_H2a8 zenon_H50. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.16/10.31 apply (zenon_L152_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.16/10.31 apply (zenon_L251_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.16/10.31 apply (zenon_L668_); trivial. % 10.16/10.31 apply (zenon_L670_); trivial. % 10.16/10.31 (* end of lemma zenon_L672_ *) % 10.16/10.31 assert (zenon_L673_ : ((op (e1) (e0)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.31 do 0 intro. intros zenon_H9d zenon_Hb7 zenon_H52 zenon_H50 zenon_H2a8 zenon_Hbe zenon_H27 zenon_H25 zenon_H1ec zenon_H12a zenon_Hf3 zenon_H127 zenon_H12c zenon_H2ac zenon_H22e zenon_H12f zenon_H1d4 zenon_H1f6 zenon_H7e zenon_H14b zenon_H1b9 zenon_Heb zenon_H93 zenon_H187 zenon_H1ea zenon_H1f5 zenon_H16c zenon_H1db zenon_Hd1 zenon_H1c9 zenon_H192 zenon_H11f zenon_H96 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H301 zenon_H141 zenon_H105 zenon_H2fe zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_Ha9 zenon_H2c7 zenon_H14c zenon_H155 zenon_H2ae zenon_H1d9 zenon_H2ee zenon_H64 zenon_H110 zenon_H83 zenon_Hef zenon_H2f7 zenon_H2c zenon_H2a zenon_H30 zenon_H1cb zenon_H24 zenon_H2dd zenon_H2c4 zenon_H23 zenon_Ha5 zenon_H101. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.31 apply (zenon_L153_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.31 apply (zenon_L5_); trivial. % 10.16/10.31 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.31 apply (zenon_L658_); trivial. % 10.16/10.31 apply (zenon_L671_); trivial. % 10.16/10.31 (* end of lemma zenon_L673_ *) % 10.16/10.31 assert (zenon_L674_ : (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (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)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (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)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> False). % 10.16/10.31 do 0 intro. intros zenon_H30 zenon_H2a zenon_H2c zenon_H27 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H110 zenon_H64 zenon_H2ee zenon_H1d9 zenon_H2ae zenon_H127 zenon_H155 zenon_H12a zenon_H14c zenon_H1cb zenon_H2c7 zenon_Ha9 zenon_H12c zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H2fe zenon_H105 zenon_H141 zenon_H301 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H1e zenon_H7a zenon_H272 zenon_H5f zenon_H96 zenon_H11f zenon_H192 zenon_H1c9 zenon_Hd1 zenon_H25 zenon_H1db zenon_H16c zenon_H1f5 zenon_H1ea zenon_H187 zenon_H93 zenon_Heb zenon_H1b9 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1d4 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H101 zenon_H1ec zenon_Hbe zenon_H22e zenon_H24 zenon_H106 zenon_H23 zenon_Ha5 zenon_H5d. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.16/10.32 apply (zenon_L152_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.16/10.32 apply (zenon_L667_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.16/10.32 apply (zenon_L324_); trivial. % 10.16/10.32 apply (zenon_L208_); trivial. % 10.16/10.32 (* end of lemma zenon_L674_ *) % 10.16/10.32 assert (zenon_L675_ : (((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) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H2b4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H101 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1d4 zenon_H1f6 zenon_H7e zenon_H14b zenon_H23 zenon_H1b9 zenon_Heb zenon_H93 zenon_H187 zenon_H1ea zenon_H1f5 zenon_H16c zenon_H1db zenon_H25 zenon_Hd1 zenon_H1c9 zenon_H192 zenon_H11f zenon_H96 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H301 zenon_H141 zenon_H105 zenon_H2fe zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H12c zenon_Ha9 zenon_H2c7 zenon_H1cb zenon_H14c zenon_H12a zenon_H155 zenon_H127 zenon_H2ae zenon_H1d9 zenon_H2ee zenon_H64 zenon_H110 zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H27 zenon_H2c zenon_Ha5 zenon_H2a zenon_H30. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H24 | zenon_intro zenon_H230 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.16/10.32 apply (zenon_L384_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.16/10.32 apply (zenon_L8_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.16/10.32 apply (zenon_L42_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_Hd8. zenon_intro zenon_H15b. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_H15c. zenon_intro zenon_He1. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.16/10.32 apply (zenon_L4_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.32 apply (zenon_L30_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.32 apply (zenon_L18_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.32 apply (zenon_L385_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.32 apply (zenon_L5_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.16/10.32 apply (zenon_L599_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.16/10.32 apply (zenon_L251_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.16/10.32 apply (zenon_L42_); trivial. % 10.16/10.32 apply (zenon_L299_); trivial. % 10.16/10.32 apply (zenon_L601_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.32 apply (zenon_L385_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.32 apply (zenon_L5_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.32 apply (zenon_L605_); trivial. % 10.16/10.32 apply (zenon_L601_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.16/10.32 apply (zenon_L151_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H20 | zenon_intro zenon_H1dd ]. % 10.16/10.32 apply (zenon_L4_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.32 apply (zenon_L30_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.32 apply (zenon_L18_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.32 apply (zenon_L384_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.32 apply (zenon_L22_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.32 apply (zenon_L371_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.32 apply (zenon_L609_); trivial. % 10.16/10.32 apply (zenon_L295_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.32 apply (zenon_L599_); trivial. % 10.16/10.32 apply (zenon_L229_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.32 apply (zenon_L283_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.32 apply (zenon_L371_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.32 apply (zenon_L663_); trivial. % 10.16/10.32 apply (zenon_L295_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H9e | zenon_intro zenon_H90 ]. % 10.16/10.32 apply (zenon_L664_); trivial. % 10.16/10.32 apply (zenon_L665_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.16/10.32 apply (zenon_L13_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.16/10.32 apply (zenon_L4_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.32 apply (zenon_L30_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.32 apply (zenon_L18_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.32 apply (zenon_L385_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.32 apply (zenon_L5_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.16/10.32 apply (zenon_L19_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.16/10.32 apply (zenon_L173_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.16/10.32 apply (zenon_L600_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.16/10.32 apply (zenon_L399_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.16/10.32 apply (zenon_L386_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.16/10.32 apply (zenon_L145_); trivial. % 10.16/10.32 apply (zenon_L666_); trivial. % 10.16/10.32 apply (zenon_L601_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.32 apply (zenon_L385_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.32 apply (zenon_L5_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.32 apply (zenon_L605_); trivial. % 10.16/10.32 apply (zenon_L671_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.16/10.32 apply (zenon_L322_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H20 | zenon_intro zenon_H1dd ]. % 10.16/10.32 apply (zenon_L4_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.32 apply (zenon_L30_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.32 apply (zenon_L18_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.32 apply (zenon_L384_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.32 apply (zenon_L22_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.32 apply (zenon_L371_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.32 apply (zenon_L385_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.32 apply (zenon_L5_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.32 apply (zenon_L661_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.16/10.32 apply (zenon_L19_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.16/10.32 apply (zenon_L517_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.16/10.32 apply (zenon_L371_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.16/10.32 apply (zenon_L8_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.16/10.32 apply (zenon_L672_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.16/10.32 apply (zenon_L616_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.16/10.32 apply (zenon_L608_); trivial. % 10.16/10.32 apply (zenon_L505_); trivial. % 10.16/10.32 apply (zenon_L236_); trivial. % 10.16/10.32 apply (zenon_L561_); trivial. % 10.16/10.32 apply (zenon_L295_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.32 apply (zenon_L599_); trivial. % 10.16/10.32 apply (zenon_L229_); trivial. % 10.16/10.32 apply (zenon_L673_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H9e | zenon_intro zenon_H90 ]. % 10.16/10.32 apply (zenon_L664_); trivial. % 10.16/10.32 apply (zenon_L665_); trivial. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H51. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.16/10.32 apply (zenon_L4_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.16/10.32 apply (zenon_L501_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.16/10.32 apply (zenon_L322_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.32 apply (zenon_L385_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.32 apply (zenon_L5_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.32 apply (zenon_L661_); trivial. % 10.16/10.32 apply (zenon_L674_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H26 | zenon_intro zenon_H231 ]. % 10.16/10.32 apply (zenon_L5_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H2e | zenon_intro zenon_H82 ]. % 10.16/10.32 apply (zenon_L324_); trivial. % 10.16/10.32 apply (zenon_L657_); trivial. % 10.16/10.32 (* end of lemma zenon_L675_ *) % 10.16/10.32 assert (zenon_L676_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H22e zenon_H2a zenon_H9d zenon_H30 zenon_H26 zenon_H2c zenon_H188 zenon_H52 zenon_Hfe. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.16/10.32 apply (zenon_L371_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.16/10.32 apply (zenon_L38_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.16/10.32 apply (zenon_L315_); trivial. % 10.16/10.32 apply (zenon_L236_); trivial. % 10.16/10.32 (* end of lemma zenon_L676_ *) % 10.16/10.32 assert (zenon_L677_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H1cb zenon_H91 zenon_H11f zenon_H26 zenon_Hd1 zenon_H23 zenon_Ha5 zenon_Hf4 zenon_H12a. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.16/10.32 apply (zenon_L123_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.16/10.32 apply (zenon_L56_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.16/10.32 apply (zenon_L324_); trivial. % 10.16/10.32 apply (zenon_L105_); trivial. % 10.16/10.32 (* end of lemma zenon_L677_ *) % 10.16/10.32 assert (zenon_L678_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H192 zenon_H12a zenon_Ha5 zenon_H23 zenon_Hd1 zenon_H11f zenon_H1cb zenon_H26 zenon_H93 zenon_Hd0 zenon_H96 zenon_Hf4 zenon_Hb8. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.16/10.32 apply (zenon_L677_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.16/10.32 apply (zenon_L124_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.16/10.32 apply (zenon_L104_); trivial. % 10.16/10.32 apply (zenon_L344_); trivial. % 10.16/10.32 (* end of lemma zenon_L678_ *) % 10.16/10.32 assert (zenon_L679_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H22a zenon_Hb8 zenon_Hf4 zenon_H93 zenon_H1cb zenon_H11f zenon_Hd1 zenon_H192 zenon_H187 zenon_H23 zenon_H12c zenon_Ha5 zenon_H127 zenon_Hf7 zenon_H101 zenon_H12a zenon_H96 zenon_H26 zenon_H5f zenon_H25 zenon_H1f zenon_H155 zenon_H87 zenon_H113. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.16/10.32 apply (zenon_L678_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.16/10.32 apply (zenon_L173_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.16/10.32 apply (zenon_L324_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.16/10.32 apply (zenon_L544_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.16/10.32 apply (zenon_L69_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.16/10.32 apply (zenon_L106_); trivial. % 10.16/10.32 apply (zenon_L74_); trivial. % 10.16/10.32 (* end of lemma zenon_L679_ *) % 10.16/10.32 assert (zenon_L680_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.16/10.32 do 0 intro. intros zenon_H13d zenon_H9e zenon_H9c zenon_H26 zenon_H23 zenon_H1b9 zenon_Ha5 zenon_H105 zenon_Hb7. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.16/10.32 apply (zenon_L40_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.16/10.32 apply (zenon_L31_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.16/10.32 apply (zenon_L341_); trivial. % 10.16/10.32 apply (zenon_L235_); trivial. % 10.16/10.32 (* end of lemma zenon_L680_ *) % 10.16/10.32 assert (zenon_L681_ : (~((op (e1) (op (e1) (e2))) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 10.16/10.32 do 0 intro. intros zenon_H160 zenon_H26 zenon_H188. % 10.16/10.32 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (op (e1) (e2))) = (e2))). % 10.16/10.32 intro zenon_D_pnotp. % 10.16/10.32 apply zenon_H160. % 10.16/10.32 rewrite <- zenon_D_pnotp. % 10.16/10.32 exact zenon_H26. % 10.16/10.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.16/10.32 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H31f]. % 10.16/10.32 congruence. % 10.16/10.32 elim (classic ((op (e1) (op (e1) (e2))) = (op (e1) (op (e1) (e2))))); [ zenon_intro zenon_H2a0 | zenon_intro zenon_H2a1 ]. % 10.16/10.32 cut (((op (e1) (op (e1) (e2))) = (op (e1) (op (e1) (e2)))) = ((op (e1) (e1)) = (op (e1) (op (e1) (e2))))). % 10.16/10.32 intro zenon_D_pnotp. % 10.16/10.32 apply zenon_H31f. % 10.16/10.32 rewrite <- zenon_D_pnotp. % 10.16/10.32 exact zenon_H2a0. % 10.16/10.32 cut (((op (e1) (op (e1) (e2))) = (op (e1) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2a1]. % 10.16/10.32 cut (((op (e1) (op (e1) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H320]. % 10.16/10.32 congruence. % 10.16/10.32 cut (((op (e1) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H321]. % 10.16/10.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.16/10.32 congruence. % 10.16/10.32 apply zenon_H1d. apply refl_equal. % 10.16/10.32 exact (zenon_H321 zenon_H188). % 10.16/10.32 apply zenon_H2a1. apply refl_equal. % 10.16/10.32 apply zenon_H2a1. apply refl_equal. % 10.16/10.32 apply zenon_H22. apply refl_equal. % 10.16/10.32 (* end of lemma zenon_L681_ *) % 10.16/10.32 assert (zenon_L682_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H1ce zenon_Hfd zenon_H105 zenon_Hf7 zenon_H12a zenon_H128 zenon_H52 zenon_Hb8. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H1cf ]. % 10.16/10.32 apply (zenon_L235_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1d0 ]. % 10.16/10.32 apply (zenon_L435_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hf4 | zenon_intro zenon_He2 ]. % 10.16/10.32 apply (zenon_L105_); trivial. % 10.16/10.32 apply (zenon_L229_); trivial. % 10.16/10.32 (* end of lemma zenon_L682_ *) % 10.16/10.32 assert (zenon_L683_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H12c zenon_Ha5 zenon_H127 zenon_H101 zenon_Hb8 zenon_H12a zenon_Hf7 zenon_H105 zenon_Hfd zenon_H1ce zenon_H52 zenon_Ha9. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.16/10.32 apply (zenon_L544_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.16/10.32 apply (zenon_L69_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.16/10.32 apply (zenon_L682_); trivial. % 10.16/10.32 apply (zenon_L233_); trivial. % 10.16/10.32 (* end of lemma zenon_L683_ *) % 10.16/10.32 assert (zenon_L684_ : ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H2b2 zenon_H86 zenon_H25. % 10.16/10.32 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H6a | zenon_intro zenon_H22 ]. % 10.16/10.32 cut (((e2) = (e2)) = ((e1) = (e2))). % 10.16/10.32 intro zenon_D_pnotp. % 10.16/10.32 apply zenon_H25. % 10.16/10.32 rewrite <- zenon_D_pnotp. % 10.16/10.32 exact zenon_H6a. % 10.16/10.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.16/10.32 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 10.16/10.32 congruence. % 10.16/10.32 cut (((op (e2) (e0)) = (e1)) = ((e2) = (e1))). % 10.16/10.32 intro zenon_D_pnotp. % 10.16/10.32 apply zenon_H6b. % 10.16/10.32 rewrite <- zenon_D_pnotp. % 10.16/10.32 exact zenon_H2b2. % 10.16/10.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.16/10.32 cut (((op (e2) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2bc]. % 10.16/10.32 congruence. % 10.16/10.32 exact (zenon_H2bc zenon_H86). % 10.16/10.32 apply zenon_H1d. apply refl_equal. % 10.16/10.32 apply zenon_H22. apply refl_equal. % 10.16/10.32 apply zenon_H22. apply refl_equal. % 10.16/10.32 (* end of lemma zenon_L684_ *) % 10.16/10.32 assert (zenon_L685_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((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))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H1ce zenon_Hfe zenon_H101 zenon_H102 zenon_H105 zenon_H10d zenon_H1f zenon_H1c9 zenon_H12a zenon_H128 zenon_H52 zenon_Hb8. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H1cf ]. % 10.16/10.32 apply (zenon_L242_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1d0 ]. % 10.16/10.32 apply (zenon_L154_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hf4 | zenon_intro zenon_He2 ]. % 10.16/10.32 apply (zenon_L105_); trivial. % 10.16/10.32 apply (zenon_L229_); trivial. % 10.16/10.32 (* end of lemma zenon_L685_ *) % 10.16/10.32 assert (zenon_L686_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((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))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H1cb zenon_H91 zenon_H11f zenon_H26 zenon_Hd1 zenon_H45 zenon_H1ce zenon_Hfe zenon_H101 zenon_H102 zenon_H105 zenon_H10d zenon_H1f zenon_H1c9 zenon_H12a zenon_H52 zenon_Hb8. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.16/10.32 apply (zenon_L123_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.16/10.32 apply (zenon_L56_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.16/10.32 apply (zenon_L14_); trivial. % 10.16/10.32 apply (zenon_L685_); trivial. % 10.16/10.32 (* end of lemma zenon_L686_ *) % 10.16/10.32 assert (zenon_L687_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (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 (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H13d zenon_H2a zenon_H73 zenon_H23 zenon_H301 zenon_Hbe zenon_H1c9 zenon_H1f zenon_H10d zenon_H101 zenon_Hfe zenon_H45 zenon_H11f zenon_H91 zenon_H1b9 zenon_H4f zenon_H25 zenon_H124 zenon_H2c zenon_H2b4 zenon_H1cb zenon_Ha5 zenon_H4d zenon_H26 zenon_Hd1 zenon_Heb zenon_Hd0 zenon_H1ce zenon_H105 zenon_H12a zenon_H52 zenon_Hb8. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.16/10.32 apply (zenon_L371_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.16/10.32 apply (zenon_L31_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.16/10.32 apply (zenon_L341_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.32 apply (zenon_L49_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.32 apply (zenon_L5_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b5 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.16/10.32 apply (zenon_L684_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.16/10.32 apply (zenon_L56_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.16/10.32 apply (zenon_L14_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.16/10.32 apply (zenon_L154_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.16/10.32 apply (zenon_L682_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.16/10.32 apply (zenon_L685_); trivial. % 10.16/10.32 apply (zenon_L505_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H18c | zenon_intro zenon_H2b6 ]. % 10.16/10.32 apply (zenon_L205_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H102 ]. % 10.16/10.32 apply (zenon_L432_); trivial. % 10.16/10.32 apply (zenon_L686_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.16/10.32 apply (zenon_L373_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.16/10.32 apply (zenon_L56_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.16/10.32 apply (zenon_L63_); trivial. % 10.16/10.32 apply (zenon_L682_); trivial. % 10.16/10.32 (* end of lemma zenon_L687_ *) % 10.16/10.32 assert (zenon_L688_ : (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (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) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H30 zenon_H2a zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H110 zenon_H64 zenon_H2ee zenon_H1d9 zenon_H2ae zenon_H127 zenon_H155 zenon_H14c zenon_H2c7 zenon_Ha9 zenon_H12c zenon_H304 zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_H2fe zenon_H141 zenon_H301 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H22f zenon_H7a zenon_H272 zenon_H5f zenon_H96 zenon_H192 zenon_H25 zenon_H1db zenon_H16c zenon_H1f5 zenon_H1ea zenon_H187 zenon_H93 zenon_Heb zenon_H23 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1d4 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1ec zenon_Hbe zenon_H22e zenon_Hb8 zenon_H52 zenon_H12a zenon_H1c9 zenon_H1f zenon_H10d zenon_H105 zenon_Hfe zenon_H1ce zenon_H45 zenon_Hd1 zenon_H26 zenon_H11f zenon_H91 zenon_H1cb zenon_H1b9 zenon_H2b4 zenon_H2c zenon_H87 zenon_H4f zenon_Ha5 zenon_H1e zenon_H101. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.32 apply (zenon_L49_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.32 apply (zenon_L675_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b5 ]. % 10.16/10.32 apply (zenon_L365_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H18c | zenon_intro zenon_H2b6 ]. % 10.16/10.32 apply (zenon_L205_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H102 ]. % 10.16/10.32 apply (zenon_L432_); trivial. % 10.16/10.32 apply (zenon_L686_); trivial. % 10.16/10.32 apply (zenon_L367_); trivial. % 10.16/10.32 (* end of lemma zenon_L688_ *) % 10.16/10.32 assert (zenon_L689_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H1d1 zenon_H1f zenon_H25 zenon_Hf1 zenon_H4d zenon_H1cb zenon_H11f zenon_H26 zenon_Hd1 zenon_H23 zenon_Ha5 zenon_Hf4 zenon_H12a. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.32 apply (zenon_L30_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.32 apply (zenon_L163_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.32 apply (zenon_L373_); trivial. % 10.16/10.32 apply (zenon_L677_); trivial. % 10.16/10.32 (* end of lemma zenon_L689_ *) % 10.16/10.32 assert (zenon_L690_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H1ea zenon_H93 zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_He8 zenon_H1f zenon_H2c zenon_H5f zenon_H1f5 zenon_H113 zenon_Hf1 zenon_Hef zenon_H130 zenon_H1f6 zenon_H7e zenon_H1ec zenon_H14b zenon_Hbe zenon_Heb zenon_H1e zenon_H110 zenon_H23 zenon_H1b9 zenon_H2ae zenon_H127 zenon_H155 zenon_H1d9 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H64 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_H2f7 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H105 zenon_H141 zenon_H1db zenon_H301 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H7a zenon_H272 zenon_H187 zenon_H96 zenon_H192 zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H101 zenon_H22e zenon_H1d4 zenon_H25 zenon_H2b4 zenon_H2b1 zenon_Ha5 zenon_H2a zenon_H30. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H24 | zenon_intro zenon_H230 ]. % 10.16/10.32 apply (zenon_L30_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H26 | zenon_intro zenon_H231 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.16/10.32 apply (zenon_L32_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.16/10.32 apply (zenon_L38_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.16/10.32 apply (zenon_L42_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_Hd8. zenon_intro zenon_H15b. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_H15c. zenon_intro zenon_He1. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.16/10.32 apply (zenon_L2_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.16/10.32 apply (zenon_L58_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.16/10.32 apply (zenon_L322_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H20 | zenon_intro zenon_H1dd ]. % 10.16/10.32 apply (zenon_L2_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.16/10.32 apply (zenon_L30_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.16/10.32 apply (zenon_L103_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.16/10.32 apply (zenon_L272_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.32 apply (zenon_L283_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.32 apply (zenon_L598_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.32 apply (zenon_L49_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.32 apply (zenon_L675_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.32 apply (zenon_L676_); trivial. % 10.16/10.32 apply (zenon_L679_); trivial. % 10.16/10.32 apply (zenon_L295_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H9e | zenon_intro zenon_H90 ]. % 10.16/10.32 apply (zenon_L680_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.16/10.32 apply (zenon_L58_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.16/10.32 apply (zenon_L31_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.16/10.32 apply (zenon_L333_); trivial. % 10.16/10.32 apply (zenon_L334_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H3c. zenon_intro zenon_H44. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H160. zenon_intro zenon_Hf6. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.16/10.32 apply (zenon_L88_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.16/10.32 apply (zenon_L31_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.16/10.32 apply (zenon_L341_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.32 apply (zenon_L49_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.32 apply (zenon_L5_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.32 apply (zenon_L681_); trivial. % 10.16/10.32 apply (zenon_L683_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.16/10.32 apply (zenon_L30_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.16/10.32 apply (zenon_L103_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.32 apply (zenon_L152_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.32 apply (zenon_L163_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.32 apply (zenon_L373_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.32 apply (zenon_L32_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.32 apply (zenon_L687_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.32 apply (zenon_L688_); trivial. % 10.16/10.32 apply (zenon_L295_); trivial. % 10.16/10.32 apply (zenon_L689_); trivial. % 10.16/10.32 apply (zenon_L17_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H2e | zenon_intro zenon_H82 ]. % 10.16/10.32 apply (zenon_L324_); trivial. % 10.16/10.32 apply (zenon_L587_); trivial. % 10.16/10.32 (* end of lemma zenon_L690_ *) % 10.16/10.32 assert (zenon_L691_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (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)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H2b1 zenon_H2b4 zenon_H2ae zenon_H2c zenon_H2a zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H12a zenon_H1d9 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H64 zenon_H110 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H105 zenon_H141 zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H1e zenon_H7a zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Heb zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H14b zenon_H7e zenon_H1f6 zenon_H101 zenon_H1ec zenon_Hbe zenon_H22e zenon_Hd1 zenon_H1d4 zenon_H23 zenon_Ha5 zenon_H25. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H1f | zenon_intro zenon_H305 ]. % 10.16/10.32 apply (zenon_L690_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H27 | zenon_intro zenon_H306 ]. % 10.16/10.32 apply (zenon_L675_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_H306); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H11b ]. % 10.16/10.32 apply (zenon_L366_); trivial. % 10.16/10.32 apply (zenon_L581_); trivial. % 10.16/10.32 (* end of lemma zenon_L691_ *) % 10.16/10.32 assert (zenon_L692_ : (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = 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= (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.16/10.32 do 0 intro. intros zenon_H4d zenon_H8d zenon_H25 zenon_H23 zenon_H1d4 zenon_Hd1 zenon_H22e zenon_Hbe zenon_H1ec zenon_H101 zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_Heb zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H105 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H110 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2a zenon_H2c zenon_H2ae zenon_H2b4 zenon_H2b1 zenon_H12a zenon_Hb7. % 10.16/10.32 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.16/10.32 apply (zenon_L197_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.16/10.32 apply (zenon_L320_); trivial. % 10.16/10.32 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.16/10.32 apply (zenon_L691_); trivial. % 10.16/10.32 apply (zenon_L232_); trivial. % 10.16/10.32 (* end of lemma zenon_L692_ *) % 10.16/10.32 assert (zenon_L693_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H181 zenon_H4d zenon_H8d zenon_H25 zenon_H23 zenon_H1d4 zenon_Hd1 zenon_H22e zenon_Hbe zenon_H1ec zenon_H101 zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_Heb zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H105 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H110 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2a zenon_H2c zenon_H2ae zenon_H2b4 zenon_H2b1 zenon_H12a. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_H5e. zenon_intro zenon_Hbd. % 10.16/10.32 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.16/10.32 apply (zenon_L692_); trivial. % 10.16/10.32 (* end of lemma zenon_L693_ *) % 10.16/10.32 assert (zenon_L694_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H195 zenon_H4f. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H188. zenon_intro zenon_H196. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H196). zenon_intro zenon_H18c. zenon_intro zenon_Hcf. % 10.16/10.32 apply (zenon_L205_); trivial. % 10.16/10.32 (* end of lemma zenon_L694_ *) % 10.16/10.32 assert (zenon_L695_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 10.16/10.32 do 0 intro. intros zenon_H1a9 zenon_H8d zenon_H5f. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H1a9). zenon_intro zenon_H86. zenon_intro zenon_H1aa. % 10.16/10.32 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_Hd0. zenon_intro zenon_Hb3. % 10.16/10.32 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.16/10.32 apply (zenon_L34_); trivial. % 10.16/10.32 (* end of lemma zenon_L695_ *) % 10.16/10.32 assert (zenon_L696_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.16/10.32 do 0 intro. intros zenon_Hae zenon_H23 zenon_H8d zenon_Hd1 zenon_H86 zenon_H4d zenon_H12a zenon_Hb7. % 10.16/10.32 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.16/10.32 apply (zenon_L54_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.16/10.33 apply (zenon_L320_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.16/10.33 apply (zenon_L373_); trivial. % 10.16/10.33 apply (zenon_L232_); trivial. % 10.16/10.33 (* end of lemma zenon_L696_ *) % 10.16/10.33 assert (zenon_L697_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.33 do 0 intro. intros zenon_H1ad zenon_Hae zenon_H23 zenon_H8d zenon_Hd1 zenon_H4d zenon_H12a. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H86. zenon_intro zenon_H1ae. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_Hd0. zenon_intro zenon_Hbd. % 10.16/10.33 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.16/10.33 apply (zenon_L696_); trivial. % 10.16/10.33 (* end of lemma zenon_L697_ *) % 10.16/10.33 assert (zenon_L698_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 10.16/10.33 do 0 intro. intros zenon_Hc6 zenon_H8d zenon_H5f. % 10.16/10.33 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_H89. zenon_intro zenon_Hc7. % 10.16/10.33 apply (zenon_L34_); trivial. % 10.16/10.33 (* end of lemma zenon_L698_ *) % 10.16/10.33 assert (zenon_L699_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = 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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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> False). % 10.16/10.33 do 0 intro. intros zenon_H272 zenon_H5a zenon_H8d zenon_H97 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2c zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.16/10.33 apply (zenon_L381_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.16/10.33 apply (zenon_L36_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.16/10.33 apply (zenon_L37_); trivial. % 10.16/10.33 apply (zenon_L500_); trivial. % 10.16/10.33 (* end of lemma zenon_L699_ *) % 10.16/10.33 assert (zenon_L700_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> False). % 10.16/10.33 do 0 intro. intros zenon_H16f zenon_H5a. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hb7. zenon_intro zenon_H170. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_H90. zenon_intro zenon_H171. % 10.16/10.33 apply (zenon_L381_); trivial. % 10.16/10.33 (* end of lemma zenon_L700_ *) % 10.16/10.33 assert (zenon_L701_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.16/10.33 do 0 intro. intros zenon_H175 zenon_H5d zenon_H82. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H175). zenon_intro zenon_Hb7. zenon_intro zenon_H176. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H176). zenon_intro zenon_H90. zenon_intro zenon_H177. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.16/10.33 apply (zenon_L584_); trivial. % 10.16/10.33 (* end of lemma zenon_L701_ *) % 10.16/10.33 assert (zenon_L702_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> False). % 10.16/10.33 do 0 intro. intros zenon_H17f zenon_H272 zenon_H5a zenon_H8d zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2c zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H68. zenon_intro zenon_H180. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H5e. zenon_intro zenon_Hb6. % 10.16/10.33 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 10.16/10.33 apply (zenon_L699_); trivial. % 10.16/10.33 (* end of lemma zenon_L702_ *) % 10.16/10.33 assert (zenon_L703_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> False). % 10.16/10.33 do 0 intro. intros zenon_H19d zenon_H5c. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_Hf7. zenon_intro zenon_H19e. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H171. % 10.16/10.33 apply (zenon_L93_); trivial. % 10.16/10.33 (* end of lemma zenon_L703_ *) % 10.16/10.33 assert (zenon_L704_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> False). % 10.16/10.33 do 0 intro. intros zenon_H1c2 zenon_H5d. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H128. zenon_intro zenon_H1c3. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H1c3). zenon_intro zenon_H166. zenon_intro zenon_H171. % 10.16/10.33 apply (zenon_L208_); trivial. % 10.16/10.33 (* end of lemma zenon_L704_ *) % 10.16/10.33 assert (zenon_L705_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))) = 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= (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> False). % 10.16/10.33 do 0 intro. intros zenon_H1f9 zenon_H272 zenon_H5a zenon_H8d zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2c zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H1f9). zenon_intro zenon_H72. zenon_intro zenon_H1fa. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_He2. zenon_intro zenon_Hb6. % 10.16/10.33 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 10.16/10.33 apply (zenon_L699_); trivial. % 10.16/10.33 (* end of lemma zenon_L705_ *) % 10.16/10.33 assert (zenon_L706_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.16/10.33 do 0 intro. intros zenon_H205 zenon_H5d zenon_H82. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H7f. zenon_intro zenon_H206. % 10.16/10.33 apply (zenon_L584_); trivial. % 10.16/10.33 (* end of lemma zenon_L706_ *) % 10.16/10.33 assert (zenon_L707_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.16/10.33 do 0 intro. intros zenon_H1ea zenon_H141 zenon_H16c zenon_H127 zenon_H2c zenon_He8 zenon_H1f zenon_H7a zenon_Heb zenon_H105 zenon_H1e zenon_H8d zenon_Hbe zenon_H272 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_H1ec zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_H22f zenon_H2a zenon_H14b zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H2b1 zenon_H2ae zenon_H2b4 zenon_H82 zenon_H30. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.16/10.33 apply (zenon_L32_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.16/10.33 apply (zenon_L33_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_Hd8. zenon_intro zenon_H15b. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_H15c. zenon_intro zenon_He1. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.16/10.33 apply (zenon_L39_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.16/10.33 apply (zenon_L243_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.16/10.33 apply (zenon_L46_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.16/10.33 apply (zenon_L244_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.16/10.33 apply (zenon_L246_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.16/10.33 apply (zenon_L247_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.16/10.33 apply (zenon_L248_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.16/10.33 apply (zenon_L249_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.16/10.33 apply (zenon_L55_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.16/10.33 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_H97. zenon_intro zenon_Hd5. % 10.16/10.33 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_H9e. zenon_intro zenon_Hd6. % 10.16/10.33 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.33 apply (zenon_L49_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.33 apply (zenon_L231_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.33 apply (zenon_L250_); trivial. % 10.16/10.33 apply (zenon_L253_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.16/10.33 apply (zenon_L254_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.16/10.33 apply (zenon_L256_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.16/10.33 apply (zenon_L258_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.16/10.33 apply (zenon_L261_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.16/10.33 apply (zenon_L262_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.16/10.33 apply (zenon_L263_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.16/10.33 apply (zenon_L113_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.16/10.33 apply (zenon_L264_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.16/10.33 apply (zenon_L266_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.16/10.33 apply (zenon_L267_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.16/10.33 apply (zenon_L117_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.16/10.33 apply (zenon_L268_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.16/10.33 apply (zenon_L121_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.16/10.33 apply (zenon_L271_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.16/10.33 apply (zenon_L273_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.16/10.33 apply (zenon_L274_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.16/10.33 apply (zenon_L129_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.16/10.33 apply (zenon_L275_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.16/10.33 apply (zenon_L131_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.16/10.33 apply (zenon_L133_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.16/10.33 apply (zenon_L134_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.16/10.33 apply (zenon_L276_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.16/10.33 apply (zenon_L277_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.16/10.33 apply (zenon_L278_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.16/10.33 apply (zenon_L138_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.16/10.33 apply (zenon_L279_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.16/10.33 apply (zenon_L280_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.16/10.33 apply (zenon_L281_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.16/10.33 apply (zenon_L282_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_Hd2. zenon_intro zenon_H1b6. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_Hd7. zenon_intro zenon_Hcb. % 10.16/10.33 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.16/10.33 apply (zenon_L2_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.16/10.33 apply (zenon_L58_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.16/10.33 apply (zenon_L253_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.33 apply (zenon_L283_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.33 apply (zenon_L252_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.33 apply (zenon_L259_); trivial. % 10.16/10.33 apply (zenon_L61_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.16/10.33 apply (zenon_L284_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.16/10.33 apply (zenon_L146_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.16/10.33 apply (zenon_L147_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.16/10.33 apply (zenon_L149_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.16/10.33 apply (zenon_L150_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.16/10.33 apply (zenon_L285_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.16/10.33 apply (zenon_L167_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.16/10.33 apply (zenon_L286_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.16/10.33 apply (zenon_L169_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.16/10.33 apply (zenon_L287_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.16/10.33 apply (zenon_L288_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.16/10.33 apply (zenon_L289_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.16/10.33 apply (zenon_L290_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.16/10.33 apply (zenon_L291_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.16/10.33 apply (zenon_L292_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.16/10.33 apply (zenon_L183_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.16/10.33 apply (zenon_L294_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.16/10.33 apply (zenon_L196_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.16/10.33 apply (zenon_L186_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.16/10.33 apply (zenon_L187_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.16/10.33 apply (zenon_L296_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.16/10.33 apply (zenon_L298_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.16/10.33 apply (zenon_L300_); trivial. % 10.16/10.33 apply (zenon_L301_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H3c. zenon_intro zenon_H44. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H160. zenon_intro zenon_Hf6. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.16/10.33 apply (zenon_L39_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.16/10.33 apply (zenon_L243_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.16/10.33 apply (zenon_L46_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.16/10.33 apply (zenon_L244_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.16/10.33 apply (zenon_L302_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.16/10.33 apply (zenon_L247_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.16/10.33 apply (zenon_L303_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.16/10.33 apply (zenon_L304_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.16/10.33 apply (zenon_L55_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.16/10.33 apply (zenon_L306_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.16/10.33 apply (zenon_L254_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.16/10.33 apply (zenon_L256_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.16/10.33 apply (zenon_L258_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.16/10.33 apply (zenon_L308_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.16/10.33 apply (zenon_L262_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.16/10.33 apply (zenon_L263_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.16/10.33 apply (zenon_L113_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.16/10.33 apply (zenon_L309_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.16/10.33 apply (zenon_L311_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.16/10.33 apply (zenon_L312_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.16/10.33 apply (zenon_L117_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.16/10.33 apply (zenon_L268_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.16/10.33 apply (zenon_L121_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.16/10.33 apply (zenon_L271_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H188. zenon_intro zenon_H196. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H196). zenon_intro zenon_H18c. zenon_intro zenon_Hcf. % 10.16/10.33 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd0. zenon_intro zenon_H86. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.16/10.33 apply (zenon_L2_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.16/10.33 apply (zenon_L34_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H20 | zenon_intro zenon_H1dd ]. % 10.16/10.33 apply (zenon_L2_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 10.16/10.33 apply (zenon_L314_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H9e | zenon_intro zenon_H90 ]. % 10.16/10.33 apply (zenon_L54_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.33 apply (zenon_L32_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.33 apply (zenon_L22_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.33 apply (zenon_L27_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.33 apply (zenon_L161_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.16/10.33 apply (zenon_L23_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.16/10.33 apply (zenon_L33_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.16/10.33 apply (zenon_L315_); trivial. % 10.16/10.33 apply (zenon_L307_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.33 apply (zenon_L60_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.33 apply (zenon_L317_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.16/10.33 apply (zenon_L23_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.16/10.33 apply (zenon_L319_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.16/10.33 apply (zenon_L25_); trivial. % 10.16/10.33 apply (zenon_L229_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.33 apply (zenon_L161_); trivial. % 10.16/10.33 apply (zenon_L257_); trivial. % 10.16/10.33 apply (zenon_L588_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.16/10.33 apply (zenon_L274_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.16/10.33 apply (zenon_L129_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.16/10.33 apply (zenon_L275_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.16/10.33 apply (zenon_L589_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.16/10.33 apply (zenon_L133_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.16/10.33 apply (zenon_L134_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.16/10.33 apply (zenon_L276_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.16/10.33 apply (zenon_L277_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.16/10.33 apply (zenon_L361_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.16/10.33 apply (zenon_L138_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H86. zenon_intro zenon_H1ae. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_Hd0. zenon_intro zenon_Hbd. % 10.16/10.33 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.16/10.33 apply (zenon_L588_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.16/10.33 apply (zenon_L590_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.16/10.33 apply (zenon_L281_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.16/10.33 apply (zenon_L282_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.16/10.33 apply (zenon_L591_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.16/10.33 apply (zenon_L284_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.16/10.33 apply (zenon_L146_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.16/10.33 apply (zenon_L147_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.16/10.33 apply (zenon_L149_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.16/10.33 apply (zenon_L592_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.16/10.33 apply (zenon_L593_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.16/10.33 apply (zenon_L167_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.16/10.33 apply (zenon_L286_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.16/10.33 apply (zenon_L169_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.16/10.33 apply (zenon_L195_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.16/10.33 apply (zenon_L288_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.16/10.33 apply (zenon_L289_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.16/10.33 apply (zenon_L594_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.16/10.33 apply (zenon_L291_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.16/10.33 apply (zenon_L595_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.16/10.33 apply (zenon_L183_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.16/10.33 apply (zenon_L294_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.16/10.33 apply (zenon_L196_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.16/10.33 apply (zenon_L186_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.16/10.33 apply (zenon_L187_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.16/10.33 apply (zenon_L296_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.16/10.33 apply (zenon_L298_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.16/10.33 apply (zenon_L300_); trivial. % 10.16/10.33 apply (zenon_L301_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.16/10.33 apply (zenon_L39_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.16/10.33 apply (zenon_L243_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.16/10.33 apply (zenon_L46_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.16/10.33 apply (zenon_L244_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.16/10.33 apply (zenon_L246_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.16/10.33 apply (zenon_L247_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.16/10.33 apply (zenon_L364_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.16/10.33 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H89. zenon_intro zenon_Hca. % 10.16/10.33 apply (zenon_L34_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.16/10.33 apply (zenon_L55_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.16/10.33 apply (zenon_L372_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.16/10.33 apply (zenon_L254_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.16/10.33 apply (zenon_L198_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.16/10.33 apply (zenon_L258_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.16/10.33 apply (zenon_L261_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.16/10.33 apply (zenon_L596_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.16/10.33 apply (zenon_L263_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.16/10.33 apply (zenon_L113_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.16/10.33 apply (zenon_L264_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.16/10.33 apply (zenon_L597_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.16/10.33 apply (zenon_L693_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.16/10.33 apply (zenon_L117_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.16/10.33 apply (zenon_L268_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.16/10.33 apply (zenon_L121_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.16/10.33 apply (zenon_L271_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.16/10.33 apply (zenon_L694_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.16/10.33 apply (zenon_L374_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.16/10.33 apply (zenon_L129_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.16/10.33 apply (zenon_L375_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.16/10.33 apply (zenon_L589_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.16/10.33 apply (zenon_L133_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.16/10.33 apply (zenon_L134_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.16/10.33 apply (zenon_L276_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.16/10.33 apply (zenon_L277_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.16/10.33 apply (zenon_L695_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.16/10.33 apply (zenon_L138_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.16/10.33 apply (zenon_L697_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.16/10.33 apply (zenon_L339_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.16/10.33 apply (zenon_L281_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.16/10.33 apply (zenon_L377_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_Hd2. zenon_intro zenon_H1b6. % 10.16/10.33 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_Hd7. zenon_intro zenon_Hcb. % 10.16/10.33 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b5 ]. % 10.16/10.33 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 10.16/10.33 intro zenon_D_pnotp. % 10.16/10.33 apply zenon_H2dd. % 10.16/10.33 rewrite <- zenon_D_pnotp. % 10.16/10.33 exact zenon_H1f. % 10.16/10.33 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H322]. % 10.16/10.33 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 10.16/10.33 congruence. % 10.16/10.33 apply zenon_H67. apply refl_equal. % 10.16/10.33 apply zenon_H322. apply sym_equal. exact zenon_H2b2. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H18c | zenon_intro zenon_H2b6 ]. % 10.16/10.33 apply (zenon_L205_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H102 ]. % 10.16/10.33 apply (zenon_L378_); trivial. % 10.16/10.33 apply (zenon_L69_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.16/10.33 apply (zenon_L284_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.16/10.33 apply (zenon_L146_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.16/10.33 apply (zenon_L147_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.16/10.33 apply (zenon_L201_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.16/10.33 apply (zenon_L202_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.16/10.33 apply (zenon_L203_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.16/10.33 apply (zenon_L167_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.16/10.33 apply (zenon_L286_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.16/10.33 apply (zenon_L169_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.16/10.33 apply (zenon_L287_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.16/10.33 apply (zenon_L204_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.16/10.33 apply (zenon_L289_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.16/10.33 apply (zenon_L181_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.16/10.33 apply (zenon_L291_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.16/10.33 apply (zenon_L206_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.16/10.33 apply (zenon_L183_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.16/10.33 apply (zenon_L294_); trivial. % 10.16/10.33 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.16/10.34 apply (zenon_L196_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.16/10.34 apply (zenon_L186_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.16/10.34 apply (zenon_L187_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.16/10.34 apply (zenon_L296_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.16/10.34 apply (zenon_L298_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.16/10.34 apply (zenon_L300_); trivial. % 10.16/10.34 apply (zenon_L301_); trivial. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H51. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.16/10.34 apply (zenon_L39_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.16/10.34 apply (zenon_L243_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.16/10.34 apply (zenon_L46_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.16/10.34 apply (zenon_L502_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.16/10.34 apply (zenon_L50_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.16/10.34 apply (zenon_L247_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.16/10.34 apply (zenon_L698_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.16/10.34 apply (zenon_L207_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.16/10.34 apply (zenon_L55_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.16/10.34 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_H97. zenon_intro zenon_Hd5. % 10.16/10.34 apply (zenon_L699_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.16/10.34 apply (zenon_L254_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.16/10.34 apply (zenon_L209_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.16/10.34 apply (zenon_L700_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.16/10.34 apply (zenon_L261_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.16/10.34 apply (zenon_L701_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.16/10.34 apply (zenon_L263_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.16/10.34 apply (zenon_L113_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.16/10.34 apply (zenon_L264_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.16/10.34 apply (zenon_L702_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.16/10.34 apply (zenon_L553_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.16/10.34 apply (zenon_L117_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.16/10.34 apply (zenon_L268_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.16/10.34 apply (zenon_L121_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.16/10.34 apply (zenon_L583_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H188. zenon_intro zenon_H196. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H196). zenon_intro zenon_H18c. zenon_intro zenon_Hcf. % 10.16/10.34 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd0. zenon_intro zenon_H86. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H20 | zenon_intro zenon_H1dd ]. % 10.16/10.34 apply (zenon_L2_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 10.16/10.34 apply (zenon_L314_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H9e | zenon_intro zenon_H90 ]. % 10.16/10.34 apply (zenon_L54_); trivial. % 10.16/10.34 apply (zenon_L381_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.16/10.34 apply (zenon_L274_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.16/10.34 apply (zenon_L129_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.16/10.34 apply (zenon_L211_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.16/10.34 apply (zenon_L703_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.16/10.34 apply (zenon_L133_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.16/10.34 apply (zenon_L585_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.16/10.34 apply (zenon_L276_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.16/10.34 apply (zenon_L277_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.16/10.34 apply (zenon_L695_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.16/10.34 apply (zenon_L138_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.16/10.34 apply (zenon_L578_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.16/10.34 apply (zenon_L339_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.16/10.34 apply (zenon_L281_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.16/10.34 apply (zenon_L282_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.16/10.34 apply (zenon_L586_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.16/10.34 apply (zenon_L284_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.16/10.34 apply (zenon_L146_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.16/10.34 apply (zenon_L147_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.16/10.34 apply (zenon_L213_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.16/10.34 apply (zenon_L704_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.16/10.34 apply (zenon_L285_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.16/10.34 apply (zenon_L167_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.16/10.34 apply (zenon_L286_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.16/10.34 apply (zenon_L169_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.16/10.34 apply (zenon_L287_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.16/10.34 apply (zenon_L705_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.16/10.34 apply (zenon_L579_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.16/10.34 apply (zenon_L181_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.16/10.34 apply (zenon_L291_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.16/10.34 apply (zenon_L292_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.16/10.34 apply (zenon_L183_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.16/10.34 apply (zenon_L294_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.16/10.34 apply (zenon_L706_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.16/10.34 apply (zenon_L186_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.16/10.34 apply (zenon_L187_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.16/10.34 apply (zenon_L296_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.16/10.34 apply (zenon_L298_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.16/10.34 apply (zenon_L300_); trivial. % 10.16/10.34 apply (zenon_L301_); trivial. % 10.16/10.34 apply (zenon_L26_); trivial. % 10.16/10.34 (* end of lemma zenon_L707_ *) % 10.16/10.34 assert (zenon_L708_ : ((op (e1) (e0)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> False). % 10.16/10.34 do 0 intro. intros zenon_H73 zenon_H52 zenon_H102 zenon_Hb7 zenon_H1ea zenon_H141 zenon_H16c zenon_H127 zenon_H2c zenon_He8 zenon_H1f zenon_H7a zenon_Heb zenon_H105 zenon_H1e zenon_H8d zenon_Hbe zenon_H272 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_H1ec zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_H22f zenon_H2a zenon_H14b zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H2b1 zenon_H2ae zenon_H2b4 zenon_H30. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2f1); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H2f2 ]. % 10.16/10.34 apply (zenon_L237_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2f2); [ zenon_intro zenon_H106 | zenon_intro zenon_H2f3 ]. % 10.16/10.34 apply (zenon_L240_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H128 | zenon_intro zenon_H82 ]. % 10.16/10.34 apply (zenon_L242_); trivial. % 10.16/10.34 apply (zenon_L707_); trivial. % 10.16/10.34 (* end of lemma zenon_L708_ *) % 10.16/10.34 assert (zenon_L709_ : ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((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 (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) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.16/10.34 do 0 intro. intros zenon_H2e zenon_H30 zenon_H2b4 zenon_H2ae zenon_H2b1 zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H14b zenon_H2a zenon_H22f zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H1ec zenon_H22e zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H7e zenon_H74 zenon_H2fa zenon_H1b9 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H25 zenon_H23 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_Hef zenon_H1ce zenon_H12c zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H101 zenon_H1f6 zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H272 zenon_Hbe zenon_H8d zenon_H1e zenon_H105 zenon_Heb zenon_H7a zenon_H1f zenon_He8 zenon_H2c zenon_H127 zenon_H16c zenon_H1ea zenon_Hb7 zenon_H52 zenon_H73 zenon_H143 zenon_H141. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.16/10.34 apply (zenon_L154_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.16/10.34 apply (zenon_L234_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.16/10.34 apply (zenon_L708_); trivial. % 10.16/10.34 apply (zenon_L507_); trivial. % 10.16/10.34 (* end of lemma zenon_L709_ *) % 10.16/10.34 assert (zenon_L710_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.34 do 0 intro. intros zenon_H2a8 zenon_H24 zenon_Hbe zenon_H8d zenon_H23 zenon_H166 zenon_H1ec zenon_H128 zenon_H101. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.34 apply (zenon_L385_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.34 apply (zenon_L31_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.34 apply (zenon_L219_); trivial. % 10.16/10.34 apply (zenon_L241_); trivial. % 10.16/10.34 (* end of lemma zenon_L710_ *) % 10.16/10.34 assert (zenon_L711_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.16/10.34 do 0 intro. intros zenon_H97 zenon_H2d4 zenon_H1e. % 10.16/10.34 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H11c | zenon_intro zenon_H1d ]. % 10.16/10.34 cut (((e1) = (e1)) = ((e0) = (e1))). % 10.16/10.34 intro zenon_D_pnotp. % 10.16/10.34 apply zenon_H1e. % 10.16/10.34 rewrite <- zenon_D_pnotp. % 10.16/10.34 exact zenon_H11c. % 10.16/10.34 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.16/10.34 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 10.16/10.34 congruence. % 10.16/10.34 cut (((op (e0) (e2)) = (e0)) = ((e1) = (e0))). % 10.16/10.34 intro zenon_D_pnotp. % 10.16/10.34 apply zenon_H11d. % 10.16/10.34 rewrite <- zenon_D_pnotp. % 10.16/10.34 exact zenon_H97. % 10.16/10.34 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.16/10.34 cut (((op (e0) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H323]. % 10.16/10.34 congruence. % 10.16/10.34 exact (zenon_H323 zenon_H2d4). % 10.16/10.34 apply zenon_H34. apply refl_equal. % 10.16/10.34 apply zenon_H1d. apply refl_equal. % 10.16/10.34 apply zenon_H1d. apply refl_equal. % 10.16/10.34 (* end of lemma zenon_L711_ *) % 10.16/10.34 assert (zenon_L712_ : ((op (e3) (e3)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.34 do 0 intro. intros zenon_H11b zenon_Hf3 zenon_Hb8. % 10.16/10.34 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.16/10.34 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 10.16/10.34 intro zenon_D_pnotp. % 10.16/10.34 apply zenon_Hb8. % 10.16/10.34 rewrite <- zenon_D_pnotp. % 10.16/10.34 exact zenon_Haa. % 10.16/10.34 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.16/10.34 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 10.16/10.34 congruence. % 10.16/10.34 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 10.16/10.34 intro zenon_D_pnotp. % 10.16/10.34 apply zenon_Hb9. % 10.16/10.34 rewrite <- zenon_D_pnotp. % 10.16/10.34 exact zenon_H11b. % 10.16/10.34 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 10.16/10.34 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.16/10.34 congruence. % 10.16/10.34 apply zenon_Hab. apply refl_equal. % 10.16/10.34 apply zenon_H1ca. apply sym_equal. exact zenon_Hf3. % 10.16/10.34 apply zenon_Hab. apply refl_equal. % 10.16/10.34 apply zenon_Hab. apply refl_equal. % 10.16/10.34 (* end of lemma zenon_L712_ *) % 10.16/10.34 assert (zenon_L713_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (op (e0) (e1))) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (op (e0) (e3))) = (e3))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.16/10.34 do 0 intro. intros zenon_H156 zenon_H2a zenon_H5f zenon_H8d zenon_Hb8 zenon_H11b zenon_H1e zenon_Hd8 zenon_H2c zenon_H2fe zenon_He1 zenon_H2b. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.16/10.34 apply (zenon_L7_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.16/10.34 apply (zenon_L34_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.34 apply (zenon_L32_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.34 apply (zenon_L265_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.34 apply (zenon_L711_); trivial. % 10.16/10.34 apply (zenon_L712_); trivial. % 10.16/10.34 apply (zenon_L283_); trivial. % 10.16/10.34 (* end of lemma zenon_L713_ *) % 10.16/10.34 assert (zenon_L714_ : (((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) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.34 do 0 intro. intros zenon_H1ce zenon_Ha8 zenon_H12a zenon_Hb8 zenon_H11b zenon_H106 zenon_H109 zenon_H105. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H1cf ]. % 10.16/10.34 apply (zenon_L232_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1d0 ]. % 10.16/10.34 apply (zenon_L712_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hf4 | zenon_intro zenon_He2 ]. % 10.16/10.34 apply (zenon_L70_); trivial. % 10.16/10.34 apply (zenon_L71_); trivial. % 10.16/10.34 (* end of lemma zenon_L714_ *) % 10.16/10.34 assert (zenon_L715_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (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 (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.34 do 0 intro. intros zenon_H12c zenon_H105 zenon_Hb8 zenon_H12a zenon_H1ce zenon_Ha9 zenon_H11b zenon_H106 zenon_H109 zenon_H101. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.16/10.34 apply (zenon_L714_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.16/10.34 apply (zenon_L545_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.16/10.34 apply (zenon_L241_); trivial. % 10.16/10.34 apply (zenon_L80_); trivial. % 10.16/10.34 (* end of lemma zenon_L715_ *) % 10.16/10.34 assert (zenon_L716_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (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 (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.34 do 0 intro. intros zenon_H2a8 zenon_H24 zenon_Hbe zenon_H8d zenon_H23 zenon_H25 zenon_H188 zenon_H12c zenon_H105 zenon_Hb8 zenon_H12a zenon_H1ce zenon_Ha9 zenon_H11b zenon_H109 zenon_H101. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.34 apply (zenon_L385_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.34 apply (zenon_L31_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.34 apply (zenon_L250_); trivial. % 10.16/10.34 apply (zenon_L715_); trivial. % 10.16/10.34 (* end of lemma zenon_L716_ *) % 10.16/10.34 assert (zenon_L717_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.34 do 0 intro. intros zenon_H2a8 zenon_H24 zenon_Hbe zenon_H188 zenon_H160 zenon_H166 zenon_H1ec zenon_H128 zenon_H101. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.34 apply (zenon_L385_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.34 apply (zenon_L681_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.34 apply (zenon_L219_); trivial. % 10.16/10.34 apply (zenon_L241_); trivial. % 10.16/10.34 (* end of lemma zenon_L717_ *) % 10.16/10.34 assert (zenon_L718_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.16/10.34 do 0 intro. intros zenon_H19d zenon_H11b zenon_H141. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_Hf7. zenon_intro zenon_H19e. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H171. % 10.16/10.34 apply (zenon_L507_); trivial. % 10.16/10.34 (* end of lemma zenon_L718_ *) % 10.16/10.34 assert (zenon_L719_ : (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.16/10.34 do 0 intro. intros zenon_H4d zenon_H8d zenon_H25 zenon_H11b zenon_H23 zenon_H1d4 zenon_Hd1 zenon_H22e zenon_Hbe zenon_H1ec zenon_H101 zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_Heb zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H105 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H110 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2a zenon_H2c zenon_H2ae zenon_H12a zenon_Hb7. % 10.16/10.34 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.16/10.34 apply (zenon_L197_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.16/10.34 apply (zenon_L320_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.16/10.34 apply (zenon_L581_); trivial. % 10.16/10.34 apply (zenon_L232_); trivial. % 10.16/10.34 (* end of lemma zenon_L719_ *) % 10.16/10.34 assert (zenon_L720_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((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 (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.34 do 0 intro. intros zenon_H2a8 zenon_Hbe zenon_H23 zenon_H50 zenon_H1b9 zenon_H2c4 zenon_H2dd zenon_H24 zenon_H1cb zenon_H192 zenon_H1d4 zenon_H1ec zenon_H25 zenon_H187 zenon_H64 zenon_H2ca zenon_Hae zenon_H4d zenon_H8d zenon_Hd1 zenon_H2f zenon_H2a zenon_H1ce zenon_H12a zenon_Hb8 zenon_H11b zenon_H109 zenon_H105. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.34 apply (zenon_L385_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.34 apply (zenon_L31_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.16/10.34 apply (zenon_L19_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.16/10.34 apply (zenon_L173_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.16/10.34 apply (zenon_L557_); trivial. % 10.16/10.34 apply (zenon_L400_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.16/10.34 apply (zenon_L197_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.16/10.34 apply (zenon_L320_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.16/10.34 apply (zenon_L42_); trivial. % 10.16/10.34 apply (zenon_L714_); trivial. % 10.16/10.34 (* end of lemma zenon_L720_ *) % 10.16/10.34 assert (zenon_L721_ : (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> False). % 10.16/10.34 do 0 intro. intros zenon_H5c zenon_H11b zenon_H79. % 10.16/10.34 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (op (e3) (e1))) = (e1))). % 10.16/10.34 intro zenon_D_pnotp. % 10.16/10.34 apply zenon_H5c. % 10.16/10.34 rewrite <- zenon_D_pnotp. % 10.16/10.34 exact zenon_H11b. % 10.16/10.34 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.16/10.34 cut (((op (e3) (e3)) = (op (e3) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H324]. % 10.16/10.34 congruence. % 10.16/10.34 elim (classic ((op (e3) (op (e3) (e1))) = (op (e3) (op (e3) (e1))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 10.16/10.34 cut (((op (e3) (op (e3) (e1))) = (op (e3) (op (e3) (e1)))) = ((op (e3) (e3)) = (op (e3) (op (e3) (e1))))). % 10.16/10.34 intro zenon_D_pnotp. % 10.16/10.34 apply zenon_H324. % 10.16/10.34 rewrite <- zenon_D_pnotp. % 10.16/10.34 exact zenon_H145. % 10.16/10.34 cut (((op (e3) (op (e3) (e1))) = (op (e3) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 10.16/10.34 cut (((op (e3) (op (e3) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H325]. % 10.16/10.34 congruence. % 10.16/10.34 cut (((op (e3) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H326]. % 10.16/10.34 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.16/10.34 congruence. % 10.16/10.34 apply zenon_H29. apply refl_equal. % 10.16/10.34 exact (zenon_H326 zenon_H79). % 10.16/10.34 apply zenon_H146. apply refl_equal. % 10.16/10.34 apply zenon_H146. apply refl_equal. % 10.16/10.34 apply zenon_H1d. apply refl_equal. % 10.16/10.34 (* end of lemma zenon_L721_ *) % 10.16/10.34 assert (zenon_L722_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e3) (e3)) = (e1)) -> False). % 10.16/10.34 do 0 intro. intros zenon_H172 zenon_H5c zenon_H11b. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H172). zenon_intro zenon_Hb7. zenon_intro zenon_H173. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H173). zenon_intro zenon_H90. zenon_intro zenon_H174. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.16/10.34 apply (zenon_L721_); trivial. % 10.16/10.34 (* end of lemma zenon_L722_ *) % 10.16/10.34 assert (zenon_L723_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e3) (e3)) = (e1)) -> False). % 10.16/10.34 do 0 intro. intros zenon_H21c zenon_H5c zenon_H11b. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H21c). zenon_intro zenon_H128. zenon_intro zenon_H21d. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H166. zenon_intro zenon_H174. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.16/10.34 apply (zenon_L721_); trivial. % 10.16/10.34 (* end of lemma zenon_L723_ *) % 10.16/10.34 assert (zenon_L724_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e3) (e3)) = (e1)) -> False). % 10.16/10.34 do 0 intro. intros zenon_H1fd zenon_H5c zenon_H11b. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H79. zenon_intro zenon_H1fe. % 10.16/10.34 apply (zenon_L721_); trivial. % 10.16/10.34 (* end of lemma zenon_L724_ *) % 10.16/10.34 assert (zenon_L725_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e3) (e3)) = (e1)) -> False). % 10.16/10.34 do 0 intro. intros zenon_H223 zenon_H5c zenon_H11b. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H79. zenon_intro zenon_H224. % 10.16/10.34 apply (zenon_L721_); trivial. % 10.16/10.34 (* end of lemma zenon_L725_ *) % 10.16/10.34 assert (zenon_L726_ : (((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) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.34 do 0 intro. intros zenon_H12c zenon_Hb7 zenon_H12a zenon_Ha9 zenon_H11b zenon_H2e zenon_H127 zenon_H109 zenon_H101. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.16/10.34 apply (zenon_L232_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.16/10.34 apply (zenon_L545_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.16/10.34 apply (zenon_L83_); trivial. % 10.16/10.34 apply (zenon_L80_); trivial. % 10.16/10.34 (* end of lemma zenon_L726_ *) % 10.16/10.34 assert (zenon_L727_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((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) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.34 do 0 intro. intros zenon_H22e zenon_H2b zenon_Hbe zenon_H8d zenon_H2a zenon_H2c zenon_H188 zenon_H12c zenon_Hb7 zenon_H12a zenon_Ha9 zenon_H11b zenon_H2e zenon_H127 zenon_H101. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.16/10.34 apply (zenon_L316_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.16/10.34 apply (zenon_L33_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.16/10.34 apply (zenon_L315_); trivial. % 10.16/10.34 apply (zenon_L726_); trivial. % 10.16/10.34 (* end of lemma zenon_L727_ *) % 10.16/10.34 assert (zenon_L728_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e3) (e3)) = (e1)) -> False). % 10.16/10.34 do 0 intro. intros zenon_H2ee zenon_H64 zenon_H187 zenon_H2c zenon_H1f0 zenon_H1ec zenon_H2c4 zenon_H1d4 zenon_H2b zenon_H83 zenon_H5c zenon_H11b. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.16/10.34 apply (zenon_L22_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.16/10.34 apply (zenon_L401_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.16/10.34 apply (zenon_L506_); trivial. % 10.16/10.34 apply (zenon_L721_); trivial. % 10.16/10.34 (* end of lemma zenon_L728_ *) % 10.16/10.34 assert (zenon_L729_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (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) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.16/10.34 do 0 intro. intros zenon_H101 zenon_H127 zenon_Ha9 zenon_H12a zenon_H12c zenon_H2ee zenon_H64 zenon_H187 zenon_H1ec zenon_H2c4 zenon_H1d4 zenon_H83 zenon_Hbe zenon_H22e zenon_H272 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H1ce zenon_Hef zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H12f zenon_H2dd zenon_H16c zenon_H155 zenon_H5f zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e zenon_H8d zenon_H2a zenon_H30 zenon_H2e zenon_H11b zenon_H2c. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_Hd8. zenon_intro zenon_H15b. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_H15c. zenon_intro zenon_He1. % 10.16/10.34 apply (zenon_L713_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H3c. zenon_intro zenon_H44. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H160. zenon_intro zenon_Hf6. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.16/10.34 apply (zenon_L7_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.16/10.34 apply (zenon_L34_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.34 apply (zenon_L32_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.34 apply (zenon_L310_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.34 apply (zenon_L18_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.34 apply (zenon_L317_); trivial. % 10.16/10.34 apply (zenon_L510_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.34 apply (zenon_L711_); trivial. % 10.16/10.34 apply (zenon_L712_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.34 apply (zenon_L310_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.34 apply (zenon_L12_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.34 apply (zenon_L727_); trivial. % 10.16/10.34 apply (zenon_L510_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.16/10.34 apply (zenon_L15_); trivial. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.16/10.34 apply (zenon_L7_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.16/10.34 apply (zenon_L34_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.16/10.34 apply (zenon_L699_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.16/10.34 apply (zenon_L316_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.16/10.34 apply (zenon_L33_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.16/10.34 apply (zenon_L728_); trivial. % 10.16/10.34 apply (zenon_L726_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.16/10.34 apply (zenon_L33_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.16/10.34 apply (zenon_L9_); trivial. % 10.16/10.34 apply (zenon_L505_); trivial. % 10.16/10.34 (* end of lemma zenon_L729_ *) % 10.16/10.34 assert (zenon_L730_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (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) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.16/10.34 do 0 intro. intros zenon_H2ae zenon_H2c zenon_H30 zenon_H2a zenon_H8d zenon_H1e zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H22f zenon_H105 zenon_Heb zenon_H2fe zenon_H5f zenon_H155 zenon_H16c zenon_H2dd zenon_H12f zenon_Hb8 zenon_H7e zenon_H7a zenon_H74 zenon_H2fa zenon_H1b9 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H23 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_Hef zenon_H1ce zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1f6 zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H272 zenon_H22e zenon_Hbe zenon_H83 zenon_H1d4 zenon_H2c4 zenon_H1ec zenon_H187 zenon_H64 zenon_H2ee zenon_H12c zenon_H12a zenon_Ha9 zenon_H127 zenon_H101 zenon_H11b zenon_H25. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H24 | zenon_intro zenon_H230 ]. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.16/10.34 apply (zenon_L384_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.16/10.34 apply (zenon_L33_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_Hd8. zenon_intro zenon_H15b. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_H15c. zenon_intro zenon_He1. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.16/10.34 apply (zenon_L424_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.16/10.34 apply (zenon_L425_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.16/10.34 apply (zenon_L426_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.16/10.34 apply (zenon_L503_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.16/10.34 apply (zenon_L246_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.16/10.34 apply (zenon_L247_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.16/10.34 apply (zenon_L698_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.16/10.34 apply (zenon_L511_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.16/10.34 apply (zenon_L55_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.16/10.34 apply (zenon_L563_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.16/10.34 apply (zenon_L254_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H169). zenon_intro zenon_H97. zenon_intro zenon_H16a. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H16a). zenon_intro zenon_H9e. zenon_intro zenon_H16b. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.16/10.34 apply (zenon_L710_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.16/10.34 apply (zenon_L258_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H172). zenon_intro zenon_Hb7. zenon_intro zenon_H173. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H173). zenon_intro zenon_H90. zenon_intro zenon_H174. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.34 apply (zenon_L30_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.34 apply (zenon_L265_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.34 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.34 apply (zenon_L713_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.34 apply (zenon_L24_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.34 apply (zenon_L599_); trivial. % 10.16/10.34 apply (zenon_L71_); trivial. % 10.16/10.34 apply (zenon_L712_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.16/10.34 apply (zenon_L262_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.16/10.34 apply (zenon_L515_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.16/10.34 apply (zenon_L568_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.16/10.34 apply (zenon_L264_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H68. zenon_intro zenon_H180. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H5e. zenon_intro zenon_Hb6. % 10.16/10.34 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 10.16/10.34 apply (zenon_L151_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.16/10.34 apply (zenon_L267_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.16/10.34 apply (zenon_L117_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.16/10.34 apply (zenon_L268_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.16/10.34 apply (zenon_L121_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.16/10.34 apply (zenon_L271_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.16/10.34 apply (zenon_L273_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.16/10.34 apply (zenon_L274_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.16/10.34 apply (zenon_L129_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H19b). zenon_intro zenon_H188. zenon_intro zenon_H19c. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H19c). zenon_intro zenon_H18c. zenon_intro zenon_H16b. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.16/10.34 apply (zenon_L710_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.16/10.34 apply (zenon_L131_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.16/10.34 apply (zenon_L133_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.16/10.34 apply (zenon_L134_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.16/10.34 apply (zenon_L525_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.16/10.34 apply (zenon_L461_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.16/10.34 apply (zenon_L462_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.16/10.34 apply (zenon_L138_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.16/10.34 apply (zenon_L279_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.16/10.34 apply (zenon_L574_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.16/10.34 apply (zenon_L281_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.16/10.34 apply (zenon_L282_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.16/10.34 apply (zenon_L576_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.16/10.34 apply (zenon_L284_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.16/10.34 apply (zenon_L146_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.16/10.34 apply (zenon_L147_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.16/10.34 apply (zenon_L149_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.16/10.34 apply (zenon_L150_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H21c). zenon_intro zenon_H128. zenon_intro zenon_H21d. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H166. zenon_intro zenon_H174. % 10.16/10.34 apply (zenon_L710_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.16/10.34 apply (zenon_L167_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.16/10.34 apply (zenon_L530_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.16/10.34 apply (zenon_L472_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.16/10.34 apply (zenon_L287_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.16/10.34 apply (zenon_L288_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.16/10.34 apply (zenon_L289_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.16/10.34 apply (zenon_L290_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.16/10.34 apply (zenon_L291_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H79. zenon_intro zenon_H224. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H109. zenon_intro zenon_Hc8. % 10.16/10.34 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.16/10.34 apply (zenon_L716_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.16/10.34 apply (zenon_L183_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.16/10.34 apply (zenon_L496_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.16/10.34 apply (zenon_L196_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.16/10.34 apply (zenon_L186_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.16/10.34 apply (zenon_L187_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.16/10.34 apply (zenon_L296_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.16/10.34 apply (zenon_L536_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.16/10.34 apply (zenon_L537_); trivial. % 10.16/10.34 apply (zenon_L538_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H3c. zenon_intro zenon_H44. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H160. zenon_intro zenon_Hf6. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.16/10.34 apply (zenon_L424_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.16/10.34 apply (zenon_L425_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.16/10.34 apply (zenon_L426_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.16/10.34 apply (zenon_L503_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.16/10.34 apply (zenon_L302_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.16/10.34 apply (zenon_L247_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.16/10.34 apply (zenon_L303_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.16/10.34 apply (zenon_L304_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.16/10.34 apply (zenon_L55_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.16/10.34 apply (zenon_L563_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.16/10.34 apply (zenon_L254_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H169). zenon_intro zenon_H97. zenon_intro zenon_H16a. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H16a). zenon_intro zenon_H9e. zenon_intro zenon_H16b. % 10.16/10.34 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.34 apply (zenon_L310_); trivial. % 10.16/10.34 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.35 apply (zenon_L12_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.35 apply (zenon_L717_); trivial. % 10.16/10.35 apply (zenon_L510_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.16/10.35 apply (zenon_L258_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.16/10.35 apply (zenon_L308_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.16/10.35 apply (zenon_L262_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.16/10.35 apply (zenon_L515_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.16/10.35 apply (zenon_L568_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.16/10.35 apply (zenon_L309_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.16/10.35 apply (zenon_L311_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.16/10.35 apply (zenon_L312_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.16/10.35 apply (zenon_L117_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.16/10.35 apply (zenon_L268_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.16/10.35 apply (zenon_L121_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.16/10.35 apply (zenon_L569_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.16/10.35 apply (zenon_L454_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.16/10.35 apply (zenon_L570_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.16/10.35 apply (zenon_L129_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H19b). zenon_intro zenon_H188. zenon_intro zenon_H19c. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H19c). zenon_intro zenon_H18c. zenon_intro zenon_H16b. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H166. zenon_intro zenon_H128. % 10.16/10.35 apply (zenon_L717_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.16/10.35 apply (zenon_L718_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.16/10.35 apply (zenon_L133_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.16/10.35 apply (zenon_L134_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.16/10.35 apply (zenon_L525_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.16/10.35 apply (zenon_L461_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.16/10.35 apply (zenon_L361_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.16/10.35 apply (zenon_L138_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.16/10.35 apply (zenon_L573_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.16/10.35 apply (zenon_L574_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.16/10.35 apply (zenon_L281_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.16/10.35 apply (zenon_L575_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.16/10.35 apply (zenon_L576_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.16/10.35 apply (zenon_L466_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.16/10.35 apply (zenon_L146_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.16/10.35 apply (zenon_L147_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.16/10.35 apply (zenon_L149_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.16/10.35 apply (zenon_L592_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.16/10.35 apply (zenon_L593_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.16/10.35 apply (zenon_L167_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.16/10.35 apply (zenon_L530_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.16/10.35 apply (zenon_L472_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.16/10.35 apply (zenon_L195_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.16/10.35 apply (zenon_L288_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.16/10.35 apply (zenon_L289_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.16/10.35 apply (zenon_L594_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.16/10.35 apply (zenon_L291_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.16/10.35 apply (zenon_L595_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.16/10.35 apply (zenon_L183_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.16/10.35 apply (zenon_L496_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.16/10.35 apply (zenon_L196_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.16/10.35 apply (zenon_L186_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.16/10.35 apply (zenon_L187_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.16/10.35 apply (zenon_L296_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.16/10.35 apply (zenon_L536_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.16/10.35 apply (zenon_L300_); trivial. % 10.16/10.35 apply (zenon_L538_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.16/10.35 apply (zenon_L424_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.16/10.35 apply (zenon_L425_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.16/10.35 apply (zenon_L426_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.16/10.35 apply (zenon_L503_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.16/10.35 apply (zenon_L246_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.16/10.35 apply (zenon_L247_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.16/10.35 apply (zenon_L364_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.16/10.35 apply (zenon_L511_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.16/10.35 apply (zenon_L55_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.16/10.35 apply (zenon_L372_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.16/10.35 apply (zenon_L254_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.16/10.35 apply (zenon_L198_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hb7. zenon_intro zenon_H170. % 10.16/10.35 apply (zenon_L719_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H172). zenon_intro zenon_Hb7. zenon_intro zenon_H173. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H173). zenon_intro zenon_H90. zenon_intro zenon_H174. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.16/10.35 apply (zenon_L720_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.16/10.35 apply (zenon_L262_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.16/10.35 apply (zenon_L515_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.16/10.35 apply (zenon_L568_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.16/10.35 apply (zenon_L264_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.16/10.35 apply (zenon_L597_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_H5e. zenon_intro zenon_Hbd. % 10.16/10.35 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.16/10.35 apply (zenon_L719_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.16/10.35 apply (zenon_L117_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.16/10.35 apply (zenon_L268_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.16/10.35 apply (zenon_L121_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.16/10.35 apply (zenon_L271_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.16/10.35 apply (zenon_L454_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.16/10.35 apply (zenon_L374_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.16/10.35 apply (zenon_L129_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.16/10.35 apply (zenon_L375_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.16/10.35 apply (zenon_L718_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.16/10.35 apply (zenon_L133_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.16/10.35 apply (zenon_L134_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.16/10.35 apply (zenon_L525_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.16/10.35 apply (zenon_L461_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.16/10.35 apply (zenon_L462_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.16/10.35 apply (zenon_L138_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.16/10.35 apply (zenon_L573_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.16/10.35 apply (zenon_L574_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.16/10.35 apply (zenon_L281_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.16/10.35 apply (zenon_L377_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.16/10.35 apply (zenon_L576_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.16/10.35 apply (zenon_L284_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.16/10.35 apply (zenon_L146_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.16/10.35 apply (zenon_L147_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.16/10.35 apply (zenon_L201_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.16/10.35 apply (zenon_L202_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.16/10.35 apply (zenon_L203_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.16/10.35 apply (zenon_L167_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.16/10.35 apply (zenon_L530_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.16/10.35 apply (zenon_L472_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.16/10.35 apply (zenon_L287_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.16/10.35 apply (zenon_L204_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H72. zenon_intro zenon_H1fc. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_He2. zenon_intro zenon_Hbd. % 10.16/10.35 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.16/10.35 apply (zenon_L719_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H79. zenon_intro zenon_H1fe. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H109. zenon_intro zenon_Hc2. % 10.16/10.35 apply (zenon_L720_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.16/10.35 apply (zenon_L291_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.16/10.35 apply (zenon_L206_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.16/10.35 apply (zenon_L183_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.16/10.35 apply (zenon_L496_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.16/10.35 apply (zenon_L196_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.16/10.35 apply (zenon_L186_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.16/10.35 apply (zenon_L187_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.16/10.35 apply (zenon_L296_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.16/10.35 apply (zenon_L536_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.16/10.35 apply (zenon_L537_); trivial. % 10.16/10.35 apply (zenon_L538_); trivial. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H51. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.16/10.35 apply (zenon_L424_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.16/10.35 apply (zenon_L425_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.16/10.35 apply (zenon_L426_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.16/10.35 apply (zenon_L503_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.16/10.35 apply (zenon_L246_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.16/10.35 apply (zenon_L247_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.16/10.35 apply (zenon_L698_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.16/10.35 apply (zenon_L511_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.16/10.35 apply (zenon_L55_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.16/10.35 apply (zenon_L563_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.16/10.35 apply (zenon_L254_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.16/10.35 apply (zenon_L209_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.16/10.35 apply (zenon_L700_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.16/10.35 apply (zenon_L722_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.16/10.35 apply (zenon_L262_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.16/10.35 apply (zenon_L515_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.16/10.35 apply (zenon_L568_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.16/10.35 apply (zenon_L264_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.16/10.35 apply (zenon_L702_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.16/10.35 apply (zenon_L553_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.16/10.35 apply (zenon_L117_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.16/10.35 apply (zenon_L268_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.16/10.35 apply (zenon_L121_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.16/10.35 apply (zenon_L569_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.16/10.35 apply (zenon_L454_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.16/10.35 apply (zenon_L570_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.16/10.35 apply (zenon_L129_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.16/10.35 apply (zenon_L211_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.16/10.35 apply (zenon_L703_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.16/10.35 apply (zenon_L133_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.16/10.35 apply (zenon_L134_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.16/10.35 apply (zenon_L525_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.16/10.35 apply (zenon_L461_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.16/10.35 apply (zenon_L462_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.16/10.35 apply (zenon_L138_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.16/10.35 apply (zenon_L573_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.16/10.35 apply (zenon_L574_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.16/10.35 apply (zenon_L281_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.16/10.35 apply (zenon_L575_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.16/10.35 apply (zenon_L576_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.16/10.35 apply (zenon_L466_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.16/10.35 apply (zenon_L146_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.16/10.35 apply (zenon_L147_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.16/10.35 apply (zenon_L213_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.16/10.35 apply (zenon_L704_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.16/10.35 apply (zenon_L723_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.16/10.35 apply (zenon_L167_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.16/10.35 apply (zenon_L530_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.16/10.35 apply (zenon_L472_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.16/10.35 apply (zenon_L287_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.16/10.35 apply (zenon_L705_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.16/10.35 apply (zenon_L579_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.16/10.35 apply (zenon_L724_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.16/10.35 apply (zenon_L291_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.16/10.35 apply (zenon_L725_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.16/10.35 apply (zenon_L183_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.16/10.35 apply (zenon_L496_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.16/10.35 apply (zenon_L196_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.16/10.35 apply (zenon_L186_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.16/10.35 apply (zenon_L187_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.16/10.35 apply (zenon_L296_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.16/10.35 apply (zenon_L536_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.16/10.35 apply (zenon_L300_); trivial. % 10.16/10.35 apply (zenon_L538_); trivial. % 10.16/10.35 apply (zenon_L505_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H26 | zenon_intro zenon_H231 ]. % 10.16/10.35 apply (zenon_L31_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H2e | zenon_intro zenon_H82 ]. % 10.16/10.35 apply (zenon_L729_); trivial. % 10.16/10.35 apply (zenon_L521_); trivial. % 10.16/10.35 (* end of lemma zenon_L730_ *) % 10.16/10.35 assert (zenon_L731_ : (~((e1) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (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 (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H25 zenon_H2ee zenon_H64 zenon_H187 zenon_H1ec zenon_H2c4 zenon_H1d4 zenon_H83 zenon_Hbe zenon_H22e zenon_H272 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H1ce zenon_Hef zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H12f zenon_H2dd zenon_H16c zenon_H155 zenon_H5f zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e zenon_H8d zenon_H2a zenon_H30 zenon_H2c zenon_H2ae zenon_H2b4 zenon_H2b1 zenon_H1f zenon_H73 zenon_H12c zenon_Hb7 zenon_H12a zenon_H101 zenon_H2e zenon_H127 zenon_H52 zenon_Ha9. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.35 apply (zenon_L49_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.35 apply (zenon_L231_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.16/10.35 apply (zenon_L160_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.16/10.35 apply (zenon_L709_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.16/10.35 apply (zenon_L172_); trivial. % 10.16/10.35 apply (zenon_L730_); trivial. % 10.16/10.35 apply (zenon_L234_); trivial. % 10.16/10.35 (* end of lemma zenon_L731_ *) % 10.16/10.35 assert (zenon_L732_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H9e zenon_H87 zenon_H2a. % 10.16/10.35 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 10.16/10.35 cut (((e3) = (e3)) = ((e0) = (e3))). % 10.16/10.35 intro zenon_D_pnotp. % 10.16/10.35 apply zenon_H2a. % 10.16/10.35 rewrite <- zenon_D_pnotp. % 10.16/10.35 exact zenon_H31. % 10.16/10.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.16/10.35 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 10.16/10.35 congruence. % 10.16/10.35 cut (((op (e2) (e0)) = (e0)) = ((e3) = (e0))). % 10.16/10.35 intro zenon_D_pnotp. % 10.16/10.35 apply zenon_Hdf. % 10.16/10.35 rewrite <- zenon_D_pnotp. % 10.16/10.35 exact zenon_H9e. % 10.16/10.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.16/10.35 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 10.16/10.35 congruence. % 10.16/10.35 exact (zenon_H88 zenon_H87). % 10.16/10.35 apply zenon_H34. apply refl_equal. % 10.16/10.35 apply zenon_H29. apply refl_equal. % 10.16/10.35 apply zenon_H29. apply refl_equal. % 10.16/10.35 (* end of lemma zenon_L732_ *) % 10.16/10.35 assert (zenon_L733_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.16/10.35 do 0 intro. intros zenon_Hae zenon_H2a zenon_H87 zenon_H8d zenon_Hd1 zenon_H23 zenon_H2e zenon_H12a zenon_Hb7. % 10.16/10.35 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.16/10.35 apply (zenon_L732_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.16/10.35 apply (zenon_L320_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.16/10.35 apply (zenon_L324_); trivial. % 10.16/10.35 apply (zenon_L232_); trivial. % 10.16/10.35 (* end of lemma zenon_L733_ *) % 10.16/10.35 assert (zenon_L734_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (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)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_Ha9 zenon_H127 zenon_H101 zenon_H12c zenon_H1f zenon_H2b1 zenon_H2b4 zenon_H2ae zenon_H2c zenon_H30 zenon_H1e zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha1 zenon_H9c zenon_H1cb zenon_H2f7 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H22f zenon_H105 zenon_Heb zenon_H2fe zenon_H5f zenon_H155 zenon_H2dd zenon_H12f zenon_Hb8 zenon_H7e zenon_H7a zenon_H74 zenon_H2fa zenon_H1b9 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_Hef zenon_H1ce zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1f6 zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H272 zenon_H22e zenon_Hbe zenon_H83 zenon_H1d4 zenon_H2c4 zenon_H1ec zenon_H187 zenon_H64 zenon_H2ee zenon_H25 zenon_Hb7 zenon_H12a zenon_H2e zenon_H23 zenon_Hd1 zenon_H8d zenon_H2a zenon_Hae zenon_H52 zenon_H16c. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.35 apply (zenon_L32_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.35 apply (zenon_L731_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.35 apply (zenon_L733_); trivial. % 10.16/10.35 apply (zenon_L295_); trivial. % 10.16/10.35 (* end of lemma zenon_L734_ *) % 10.16/10.35 assert (zenon_L735_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 10.16/10.35 do 0 intro. intros zenon_H127 zenon_H2b3 zenon_H102. % 10.16/10.35 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e2) (e3)))). % 10.16/10.35 intro zenon_D_pnotp. % 10.16/10.35 apply zenon_H127. % 10.16/10.35 rewrite <- zenon_D_pnotp. % 10.16/10.35 exact zenon_H2b3. % 10.16/10.35 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 10.16/10.35 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.16/10.35 congruence. % 10.16/10.35 apply zenon_H81. apply refl_equal. % 10.16/10.35 apply zenon_H103. apply sym_equal. exact zenon_H102. % 10.16/10.35 (* end of lemma zenon_L735_ *) % 10.16/10.35 assert (zenon_L736_ : (((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) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H12c zenon_Hb7 zenon_H12a zenon_H2b3 zenon_H127 zenon_H101 zenon_H1ec zenon_H166 zenon_H23 zenon_H8d zenon_Hbe zenon_H24 zenon_H2a8 zenon_H52 zenon_Ha9. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.16/10.35 apply (zenon_L232_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.16/10.35 apply (zenon_L735_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.16/10.35 apply (zenon_L710_); trivial. % 10.16/10.35 apply (zenon_L233_); trivial. % 10.16/10.35 (* end of lemma zenon_L736_ *) % 10.16/10.35 assert (zenon_L737_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((e1) = (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) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H22a zenon_Hef zenon_H30 zenon_H1f0 zenon_H25 zenon_H12c zenon_Hb7 zenon_H12a zenon_H2b3 zenon_H127 zenon_H101 zenon_H1ec zenon_H23 zenon_H8d zenon_Hbe zenon_H24 zenon_H2a8 zenon_H52 zenon_Ha9. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.16/10.35 apply (zenon_L152_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.16/10.35 apply (zenon_L251_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.16/10.35 apply (zenon_L445_); trivial. % 10.16/10.35 apply (zenon_L736_); trivial. % 10.16/10.35 (* end of lemma zenon_L737_ *) % 10.16/10.35 assert (zenon_L738_ : ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.16/10.35 do 0 intro. intros zenon_Hd2 zenon_H121 zenon_H30. % 10.16/10.35 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 10.16/10.35 cut (((e3) = (e3)) = ((e2) = (e3))). % 10.16/10.35 intro zenon_D_pnotp. % 10.16/10.35 apply zenon_H30. % 10.16/10.35 rewrite <- zenon_D_pnotp. % 10.16/10.35 exact zenon_H31. % 10.16/10.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.16/10.35 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 10.16/10.35 congruence. % 10.16/10.35 cut (((op (e2) (e1)) = (e2)) = ((e3) = (e2))). % 10.16/10.35 intro zenon_D_pnotp. % 10.16/10.35 apply zenon_H32. % 10.16/10.35 rewrite <- zenon_D_pnotp. % 10.16/10.35 exact zenon_Hd2. % 10.16/10.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.16/10.35 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H327]. % 10.16/10.35 congruence. % 10.16/10.35 exact (zenon_H327 zenon_H121). % 10.16/10.35 apply zenon_H22. apply refl_equal. % 10.16/10.35 apply zenon_H29. apply refl_equal. % 10.16/10.35 apply zenon_H29. apply refl_equal. % 10.16/10.35 (* end of lemma zenon_L738_ *) % 10.16/10.35 assert (zenon_L739_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H12f zenon_H2a zenon_H9e zenon_H30 zenon_Hd2 zenon_H2c zenon_H2b3 zenon_H52 zenon_Ha9. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.16/10.35 apply (zenon_L732_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.16/10.35 apply (zenon_L738_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.16/10.35 apply (zenon_L438_); trivial. % 10.16/10.35 apply (zenon_L233_); trivial. % 10.16/10.35 (* end of lemma zenon_L739_ *) % 10.16/10.35 assert (zenon_L740_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H1cb zenon_H24 zenon_H2dd zenon_H149 zenon_H2c4 zenon_H25 zenon_H2b3 zenon_H106 zenon_H101. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.16/10.35 apply (zenon_L399_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.16/10.35 apply (zenon_L386_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.16/10.35 apply (zenon_L445_); trivial. % 10.16/10.35 apply (zenon_L241_); trivial. % 10.16/10.35 (* end of lemma zenon_L740_ *) % 10.16/10.35 assert (zenon_L741_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H22e zenon_H2b zenon_Hbe zenon_H8d zenon_H2a zenon_H1ec zenon_H7f zenon_H112 zenon_H101. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.16/10.35 apply (zenon_L316_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.16/10.35 apply (zenon_L33_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.16/10.35 apply (zenon_L404_); trivial. % 10.16/10.35 apply (zenon_L80_); trivial. % 10.16/10.35 (* end of lemma zenon_L741_ *) % 10.16/10.35 assert (zenon_L742_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H175 zenon_H22e zenon_H2b zenon_Hbe zenon_H8d zenon_H2a zenon_H1ec zenon_H101. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H175). zenon_intro zenon_Hb7. zenon_intro zenon_H176. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H176). zenon_intro zenon_H90. zenon_intro zenon_H177. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.16/10.35 apply (zenon_L741_); trivial. % 10.16/10.35 (* end of lemma zenon_L742_ *) % 10.16/10.35 assert (zenon_L743_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H1a3 zenon_H22e zenon_H2b zenon_Hbe zenon_H8d zenon_H2a zenon_H1ec zenon_H101. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_Hf7. zenon_intro zenon_H1a4. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H1a4). zenon_intro zenon_H143. zenon_intro zenon_H177. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.16/10.35 apply (zenon_L741_); trivial. % 10.16/10.35 (* end of lemma zenon_L743_ *) % 10.16/10.35 assert (zenon_L744_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H1b5 zenon_H2fe zenon_H2b zenon_H2c zenon_H7a zenon_Heb zenon_H2b3 zenon_H105. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_Hd2. zenon_intro zenon_H1b6. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_Hd7. zenon_intro zenon_Hcb. % 10.16/10.35 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H143. zenon_intro zenon_Hf7. % 10.16/10.35 apply (zenon_L475_); trivial. % 10.16/10.35 (* end of lemma zenon_L744_ *) % 10.16/10.35 assert (zenon_L745_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H203 zenon_H22e zenon_H2b zenon_Hbe zenon_H8d zenon_H2a zenon_H1ec zenon_H101. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H203). zenon_intro zenon_H7f. zenon_intro zenon_H204. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H204). zenon_intro zenon_H112. zenon_intro zenon_Hcf. % 10.16/10.35 apply (zenon_L741_); trivial. % 10.16/10.35 (* end of lemma zenon_L745_ *) % 10.16/10.35 assert (zenon_L746_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H205 zenon_H22e zenon_H2b zenon_Hbe zenon_H8d zenon_H2a zenon_H1ec zenon_H101. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H7f. zenon_intro zenon_H206. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H112. zenon_intro zenon_Hd6. % 10.16/10.35 apply (zenon_L741_); trivial. % 10.16/10.35 (* end of lemma zenon_L746_ *) % 10.16/10.35 assert (zenon_L747_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H207 zenon_H22e zenon_H2b zenon_Hbe zenon_H8d zenon_H2a zenon_H1ec zenon_H101. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H7f. zenon_intro zenon_H208. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H208). zenon_intro zenon_H112. zenon_intro zenon_H165. % 10.16/10.35 apply (zenon_L741_); trivial. % 10.16/10.35 (* end of lemma zenon_L747_ *) % 10.16/10.35 assert (zenon_L748_ : ((op (e2) (e2)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H2b3 zenon_H2b2 zenon_H1d7. % 10.16/10.35 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hec | zenon_intro zenon_H81 ]. % 10.16/10.35 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))). % 10.16/10.35 intro zenon_D_pnotp. % 10.16/10.35 apply zenon_H1d7. % 10.16/10.35 rewrite <- zenon_D_pnotp. % 10.16/10.35 exact zenon_Hec. % 10.16/10.35 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.16/10.35 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d8]. % 10.16/10.35 congruence. % 10.16/10.35 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e2) (e0)))). % 10.16/10.35 intro zenon_D_pnotp. % 10.16/10.35 apply zenon_H1d8. % 10.16/10.35 rewrite <- zenon_D_pnotp. % 10.16/10.35 exact zenon_H2b3. % 10.16/10.35 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H322]. % 10.16/10.35 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.16/10.35 congruence. % 10.16/10.35 apply zenon_H81. apply refl_equal. % 10.16/10.35 apply zenon_H322. apply sym_equal. exact zenon_H2b2. % 10.16/10.35 apply zenon_H81. apply refl_equal. % 10.16/10.35 apply zenon_H81. apply refl_equal. % 10.16/10.35 (* end of lemma zenon_L748_ *) % 10.16/10.35 assert (zenon_L749_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H22e zenon_H2b zenon_Hbe zenon_Hf6 zenon_H30 zenon_Hd7 zenon_Hf7 zenon_H2c. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.16/10.35 apply (zenon_L316_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.16/10.35 apply (zenon_L67_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.16/10.35 apply (zenon_L251_); trivial. % 10.16/10.35 apply (zenon_L132_); trivial. % 10.16/10.35 (* end of lemma zenon_L749_ *) % 10.16/10.35 assert (zenon_L750_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H195 zenon_H2b3 zenon_H2ac. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H188. zenon_intro zenon_H196. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H196). zenon_intro zenon_H18c. zenon_intro zenon_Hcf. % 10.16/10.35 apply (zenon_L455_); trivial. % 10.16/10.35 (* end of lemma zenon_L750_ *) % 10.16/10.35 assert (zenon_L751_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H12f zenon_H2b zenon_H2dd zenon_H2c4 zenon_H79 zenon_H2c zenon_H2b3 zenon_H50. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.16/10.35 apply (zenon_L406_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.16/10.35 apply (zenon_L403_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.16/10.35 apply (zenon_L438_); trivial. % 10.16/10.35 apply (zenon_L368_); trivial. % 10.16/10.35 (* end of lemma zenon_L751_ *) % 10.16/10.35 assert (zenon_L752_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> ((op (e2) (e2)) = (e1)) -> False). % 10.16/10.35 do 0 intro. intros zenon_H1af zenon_H4f zenon_H2b3. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_Hd2. zenon_intro zenon_H1b0. % 10.16/10.35 apply (zenon_L378_); trivial. % 10.16/10.35 (* end of lemma zenon_L752_ *) % 10.16/10.35 assert (zenon_L753_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> ((op (e2) (e2)) = (e1)) -> False). % 10.16/10.35 do 0 intro. intros zenon_H205 zenon_H4f zenon_H2b3. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H7f. zenon_intro zenon_H206. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H112. zenon_intro zenon_Hd6. % 10.16/10.35 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.16/10.35 apply (zenon_L378_); trivial. % 10.16/10.35 (* end of lemma zenon_L753_ *) % 10.16/10.35 assert (zenon_L754_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H12f zenon_H2dd zenon_H82 zenon_H5d zenon_H2ac zenon_H83 zenon_H2b zenon_H1d4 zenon_H2c4 zenon_H1ec zenon_H30 zenon_Hef zenon_H2f7 zenon_H2c zenon_H2b3 zenon_H109 zenon_H101. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.16/10.35 apply (zenon_L406_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.16/10.35 apply (zenon_L643_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.16/10.35 apply (zenon_L438_); trivial. % 10.16/10.35 apply (zenon_L80_); trivial. % 10.16/10.35 (* end of lemma zenon_L754_ *) % 10.16/10.35 assert (zenon_L755_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H22e zenon_Hbe zenon_H8d zenon_H2a zenon_Hd7 zenon_H12f zenon_H2dd zenon_H82 zenon_H5d zenon_H2ac zenon_H83 zenon_H2b zenon_H1d4 zenon_H2c4 zenon_H1ec zenon_H30 zenon_Hef zenon_H2f7 zenon_H2c zenon_H2b3 zenon_H101. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.16/10.35 apply (zenon_L316_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.16/10.35 apply (zenon_L33_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.16/10.35 apply (zenon_L251_); trivial. % 10.16/10.35 apply (zenon_L754_); trivial. % 10.16/10.35 (* end of lemma zenon_L755_ *) % 10.16/10.35 assert (zenon_L756_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (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)) = (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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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 (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.16/10.35 do 0 intro. intros zenon_H1ea zenon_H141 zenon_H1d4 zenon_H25 zenon_H22e zenon_Hbe zenon_H1ec zenon_H101 zenon_H1b9 zenon_H1e zenon_H12f zenon_H2dd zenon_H2ac zenon_H83 zenon_H2c4 zenon_Hef zenon_H2f7 zenon_H272 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H14b zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H2b1 zenon_H2b4 zenon_H2ae zenon_H328 zenon_H8d zenon_H2a zenon_H2c zenon_H2b3 zenon_H82 zenon_H30. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_Hd8. zenon_intro zenon_H15b. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_H15c. zenon_intro zenon_He1. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.16/10.35 apply (zenon_L21_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.16/10.35 apply (zenon_L473_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.16/10.35 apply (zenon_L474_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.16/10.35 apply (zenon_L504_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.16/10.35 apply (zenon_L246_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.16/10.35 apply (zenon_L247_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.16/10.35 apply (zenon_L433_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.16/10.35 apply (zenon_L476_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.16/10.35 apply (zenon_L55_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_H97. zenon_intro zenon_Hd5. % 10.16/10.35 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_H9e. zenon_intro zenon_Hd6. % 10.16/10.35 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.16/10.35 apply (zenon_L316_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.16/10.35 apply (zenon_L33_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.16/10.35 apply (zenon_L251_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.16/10.35 apply (zenon_L22_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.16/10.35 apply (zenon_L73_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.16/10.35 apply (zenon_L738_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.16/10.35 apply (zenon_L406_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.16/10.35 apply (zenon_L403_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.16/10.35 apply (zenon_L438_); trivial. % 10.16/10.35 apply (zenon_L80_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.16/10.35 apply (zenon_L446_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.16/10.35 apply (zenon_L256_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.16/10.35 apply (zenon_L479_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H172). zenon_intro zenon_Hb7. zenon_intro zenon_H173. % 10.16/10.35 apply (zenon_L283_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.16/10.35 apply (zenon_L742_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.16/10.35 apply (zenon_L263_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.16/10.35 apply (zenon_L516_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.16/10.35 apply (zenon_L264_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.16/10.35 apply (zenon_L266_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.16/10.35 apply (zenon_L267_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.16/10.35 apply (zenon_L117_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.16/10.35 apply (zenon_L268_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.16/10.35 apply (zenon_L121_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.16/10.35 apply (zenon_L271_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.16/10.35 apply (zenon_L273_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.16/10.35 apply (zenon_L274_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.16/10.35 apply (zenon_L457_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.16/10.35 apply (zenon_L458_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.16/10.35 apply (zenon_L131_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.16/10.35 apply (zenon_L133_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.16/10.35 apply (zenon_L743_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.16/10.35 apply (zenon_L276_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.16/10.35 apply (zenon_L526_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.16/10.35 apply (zenon_L695_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.16/10.35 apply (zenon_L138_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.16/10.35 apply (zenon_L279_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.16/10.35 apply (zenon_L280_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.16/10.35 apply (zenon_L281_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.16/10.35 apply (zenon_L282_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.16/10.35 apply (zenon_L744_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.16/10.35 apply (zenon_L284_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.16/10.35 apply (zenon_L146_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.16/10.35 apply (zenon_L468_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.16/10.35 apply (zenon_L149_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.16/10.35 apply (zenon_L150_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.16/10.35 apply (zenon_L485_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.16/10.35 apply (zenon_L167_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.16/10.35 apply (zenon_L286_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.16/10.35 apply (zenon_L486_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.16/10.35 apply (zenon_L287_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.16/10.35 apply (zenon_L488_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.16/10.35 apply (zenon_L531_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.16/10.35 apply (zenon_L290_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.16/10.35 apply (zenon_L291_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.16/10.35 apply (zenon_L490_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.16/10.35 apply (zenon_L183_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.16/10.35 apply (zenon_L745_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.16/10.35 apply (zenon_L746_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.16/10.35 apply (zenon_L747_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.16/10.35 apply (zenon_L187_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.16/10.35 apply (zenon_L296_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.16/10.35 apply (zenon_L298_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.16/10.35 apply (zenon_L300_); trivial. % 10.16/10.35 apply (zenon_L301_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H3c. zenon_intro zenon_H44. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H160. zenon_intro zenon_Hf6. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.16/10.35 apply (zenon_L21_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.16/10.35 apply (zenon_L473_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.16/10.35 apply (zenon_L474_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.16/10.35 apply (zenon_L504_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.16/10.35 apply (zenon_L302_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.16/10.35 apply (zenon_L247_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.16/10.35 apply (zenon_L303_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.16/10.35 apply (zenon_L304_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.16/10.35 apply (zenon_L55_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_H97. zenon_intro zenon_Hd5. % 10.16/10.35 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_H9e. zenon_intro zenon_Hd6. % 10.16/10.35 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.16/10.35 apply (zenon_L32_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.16/10.35 apply (zenon_L310_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.16/10.35 apply (zenon_L748_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.35 apply (zenon_L427_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.35 apply (zenon_L231_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.35 apply (zenon_L250_); trivial. % 10.16/10.35 apply (zenon_L749_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.16/10.35 apply (zenon_L446_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.16/10.35 apply (zenon_L256_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.16/10.35 apply (zenon_L479_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.16/10.35 apply (zenon_L308_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.16/10.35 apply (zenon_L742_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.16/10.35 apply (zenon_L263_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.16/10.35 apply (zenon_L516_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.16/10.35 apply (zenon_L309_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.16/10.35 apply (zenon_L311_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.16/10.35 apply (zenon_L312_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.16/10.35 apply (zenon_L117_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.16/10.35 apply (zenon_L268_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.16/10.35 apply (zenon_L452_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.16/10.35 apply (zenon_L271_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.16/10.35 apply (zenon_L750_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.16/10.35 apply (zenon_L456_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.16/10.35 apply (zenon_L457_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.16/10.35 apply (zenon_L275_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.16/10.35 apply (zenon_L480_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.16/10.35 apply (zenon_L133_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.16/10.35 apply (zenon_L743_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.16/10.35 apply (zenon_L276_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.16/10.35 apply (zenon_L526_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.16/10.35 apply (zenon_L361_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.16/10.35 apply (zenon_L138_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H86. zenon_intro zenon_H1ae. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_Hd0. zenon_intro zenon_Hbd. % 10.16/10.35 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.16/10.35 apply (zenon_L32_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.16/10.35 apply (zenon_L310_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.16/10.35 apply (zenon_L748_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.16/10.35 apply (zenon_L316_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.16/10.35 apply (zenon_L33_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.16/10.35 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.16/10.35 apply (zenon_L54_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.16/10.35 apply (zenon_L320_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.16/10.35 apply (zenon_L652_); trivial. % 10.16/10.35 apply (zenon_L232_); trivial. % 10.16/10.35 apply (zenon_L307_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.16/10.35 apply (zenon_L590_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.16/10.35 apply (zenon_L281_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.16/10.35 apply (zenon_L464_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.16/10.35 apply (zenon_L744_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.16/10.35 apply (zenon_L284_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.16/10.35 apply (zenon_L467_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.16/10.35 apply (zenon_L468_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.16/10.35 apply (zenon_L469_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.16/10.35 apply (zenon_L483_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.16/10.35 apply (zenon_L593_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.16/10.35 apply (zenon_L167_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.16/10.35 apply (zenon_L286_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.16/10.35 apply (zenon_L486_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.16/10.35 apply (zenon_L195_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.16/10.35 apply (zenon_L488_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.16/10.35 apply (zenon_L531_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.16/10.35 apply (zenon_L594_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.16/10.35 apply (zenon_L291_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.16/10.35 apply (zenon_L595_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.16/10.35 apply (zenon_L183_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.16/10.35 apply (zenon_L745_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.16/10.35 apply (zenon_L746_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.16/10.35 apply (zenon_L491_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.16/10.35 apply (zenon_L187_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.16/10.35 apply (zenon_L535_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.16/10.35 apply (zenon_L298_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.16/10.35 apply (zenon_L300_); trivial. % 10.16/10.35 apply (zenon_L301_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.16/10.35 apply (zenon_L21_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.16/10.35 apply (zenon_L473_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.16/10.35 apply (zenon_L474_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.16/10.35 apply (zenon_L504_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.16/10.35 apply (zenon_L246_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.16/10.35 apply (zenon_L247_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.16/10.35 apply (zenon_L364_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.16/10.35 apply (zenon_L476_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.16/10.35 apply (zenon_L55_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.16/10.35 apply (zenon_L372_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.16/10.35 apply (zenon_L446_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.16/10.35 apply (zenon_L198_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.16/10.35 apply (zenon_L479_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H172). zenon_intro zenon_Hb7. zenon_intro zenon_H173. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H173). zenon_intro zenon_H90. zenon_intro zenon_H174. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.16/10.35 apply (zenon_L751_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.16/10.35 apply (zenon_L596_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.16/10.35 apply (zenon_L263_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.16/10.35 apply (zenon_L516_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.16/10.35 apply (zenon_L264_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.16/10.35 apply (zenon_L597_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.16/10.35 apply (zenon_L693_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.16/10.35 apply (zenon_L117_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.16/10.35 apply (zenon_L268_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.16/10.35 apply (zenon_L121_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.16/10.35 apply (zenon_L271_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.16/10.35 apply (zenon_L750_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.16/10.35 apply (zenon_L374_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.16/10.35 apply (zenon_L457_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.16/10.35 apply (zenon_L375_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.16/10.35 apply (zenon_L480_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.16/10.35 apply (zenon_L133_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.16/10.35 apply (zenon_L743_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.16/10.35 apply (zenon_L276_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.16/10.35 apply (zenon_L526_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.16/10.35 apply (zenon_L695_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.16/10.35 apply (zenon_L138_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.16/10.35 apply (zenon_L697_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.16/10.35 apply (zenon_L752_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.16/10.35 apply (zenon_L281_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.16/10.35 apply (zenon_L377_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.16/10.35 apply (zenon_L744_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.16/10.35 apply (zenon_L284_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.16/10.35 apply (zenon_L146_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.16/10.35 apply (zenon_L468_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.16/10.35 apply (zenon_L149_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.16/10.35 apply (zenon_L483_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.16/10.35 apply (zenon_L485_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.16/10.35 apply (zenon_L167_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.16/10.35 apply (zenon_L286_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.16/10.35 apply (zenon_L486_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.16/10.35 apply (zenon_L287_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.16/10.35 apply (zenon_L204_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.16/10.35 apply (zenon_L531_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H79. zenon_intro zenon_H1fe. % 10.16/10.35 apply (zenon_L751_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.16/10.35 apply (zenon_L291_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.16/10.35 apply (zenon_L206_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.16/10.35 apply (zenon_L183_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.16/10.35 apply (zenon_L745_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.16/10.35 apply (zenon_L753_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.16/10.35 apply (zenon_L747_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.16/10.35 apply (zenon_L187_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.16/10.35 apply (zenon_L296_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.16/10.35 apply (zenon_L298_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.16/10.35 apply (zenon_L300_); trivial. % 10.16/10.35 apply (zenon_L301_); trivial. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H51. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.16/10.35 apply (zenon_L21_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.16/10.35 apply (zenon_L473_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.16/10.35 apply (zenon_L474_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.16/10.35 apply (zenon_L502_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.16/10.35 apply (zenon_L246_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.16/10.35 apply (zenon_L247_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.16/10.35 apply (zenon_L698_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.16/10.35 apply (zenon_L207_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.16/10.35 apply (zenon_L55_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_H97. zenon_intro zenon_Hd5. % 10.16/10.35 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_H9e. zenon_intro zenon_Hd6. % 10.16/10.35 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.16/10.35 apply (zenon_L755_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.16/10.35 apply (zenon_L446_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.16/10.35 apply (zenon_L209_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.16/10.35 apply (zenon_L700_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H172). zenon_intro zenon_Hb7. zenon_intro zenon_H173. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H173). zenon_intro zenon_H90. zenon_intro zenon_H174. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.16/10.35 apply (zenon_L754_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.16/10.35 apply (zenon_L701_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.16/10.35 apply (zenon_L263_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.16/10.35 apply (zenon_L516_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.16/10.35 apply (zenon_L264_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.16/10.35 apply (zenon_L702_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.16/10.35 apply (zenon_L553_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.16/10.35 apply (zenon_L117_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.16/10.35 apply (zenon_L268_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.16/10.35 apply (zenon_L452_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.16/10.35 apply (zenon_L583_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.16/10.35 apply (zenon_L750_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.16/10.35 apply (zenon_L456_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.16/10.35 apply (zenon_L457_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.16/10.35 apply (zenon_L211_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.16/10.35 apply (zenon_L703_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.16/10.35 apply (zenon_L133_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.16/10.35 apply (zenon_L585_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.16/10.35 apply (zenon_L276_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.16/10.35 apply (zenon_L526_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.16/10.35 apply (zenon_L695_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.16/10.35 apply (zenon_L138_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.16/10.35 apply (zenon_L578_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_Hd2. zenon_intro zenon_H1b0. % 10.16/10.35 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hd7. zenon_intro zenon_Hc2. % 10.16/10.35 apply (zenon_L755_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.16/10.35 apply (zenon_L281_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.16/10.35 apply (zenon_L464_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.16/10.35 apply (zenon_L586_); trivial. % 10.16/10.35 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.16/10.36 apply (zenon_L284_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.16/10.36 apply (zenon_L467_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.16/10.36 apply (zenon_L468_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.16/10.36 apply (zenon_L213_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.16/10.36 apply (zenon_L704_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.16/10.36 apply (zenon_L485_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.16/10.36 apply (zenon_L167_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.16/10.36 apply (zenon_L286_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.16/10.36 apply (zenon_L486_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.16/10.36 apply (zenon_L487_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.16/10.36 apply (zenon_L705_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.16/10.36 apply (zenon_L579_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.16/10.36 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H79. zenon_intro zenon_H1fe. % 10.16/10.36 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H109. zenon_intro zenon_Hc2. % 10.16/10.36 apply (zenon_L754_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.16/10.36 apply (zenon_L291_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.16/10.36 apply (zenon_L490_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.16/10.36 apply (zenon_L183_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.16/10.36 apply (zenon_L745_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.16/10.36 apply (zenon_L706_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.16/10.36 apply (zenon_L491_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.16/10.36 apply (zenon_L187_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.16/10.36 apply (zenon_L535_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.16/10.36 apply (zenon_L298_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.16/10.36 apply (zenon_L300_); trivial. % 10.16/10.36 apply (zenon_L301_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.16/10.36 apply (zenon_L33_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.16/10.36 apply (zenon_L438_); trivial. % 10.16/10.36 apply (zenon_L26_); trivial. % 10.16/10.36 (* end of lemma zenon_L756_ *) % 10.16/10.36 assert (zenon_L757_ : ((op (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (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)) = (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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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 (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 10.16/10.36 do 0 intro. intros zenon_H90 zenon_Hd2 zenon_Hd7 zenon_H1ea zenon_H141 zenon_H1d4 zenon_H25 zenon_H22e zenon_Hbe zenon_H1ec zenon_H101 zenon_H1b9 zenon_H1e zenon_H12f zenon_H2dd zenon_H2ac zenon_H83 zenon_H2c4 zenon_Hef zenon_H2f7 zenon_H272 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H14b zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H2b1 zenon_H2b4 zenon_H2ae zenon_H328 zenon_H8d zenon_H2a zenon_H2c zenon_H2b3 zenon_H30. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.16/10.36 apply (zenon_L35_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.16/10.36 apply (zenon_L386_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.16/10.36 apply (zenon_L219_); trivial. % 10.16/10.36 apply (zenon_L756_); trivial. % 10.16/10.36 (* end of lemma zenon_L757_ *) % 10.16/10.36 assert (zenon_L758_ : (((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 (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.16/10.36 do 0 intro. intros zenon_H1f6 zenon_H90 zenon_H1f5 zenon_H2b3 zenon_H7e zenon_H101 zenon_H128 zenon_H1ec zenon_H23 zenon_H8d zenon_Hbe zenon_H24 zenon_H2a8 zenon_H52 zenon_H1ea. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.16/10.36 apply (zenon_L318_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.16/10.36 apply (zenon_L429_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.16/10.36 apply (zenon_L710_); trivial. % 10.16/10.36 apply (zenon_L299_); trivial. % 10.16/10.36 (* end of lemma zenon_L758_ *) % 10.16/10.36 assert (zenon_L759_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.16/10.36 do 0 intro. intros zenon_Hae zenon_H1ea zenon_H52 zenon_H2a8 zenon_H24 zenon_Hbe zenon_H23 zenon_H1ec zenon_H101 zenon_H7e zenon_H1f5 zenon_H90 zenon_H1f6 zenon_H25 zenon_H2c4 zenon_H149 zenon_H1cb zenon_H8d zenon_Hd1 zenon_H2b3 zenon_H1e zenon_H12a zenon_Hb7. % 10.16/10.36 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.16/10.36 apply (zenon_L54_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.16/10.36 apply (zenon_L386_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.16/10.36 apply (zenon_L445_); trivial. % 10.16/10.36 apply (zenon_L758_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.16/10.36 apply (zenon_L320_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.16/10.36 apply (zenon_L366_); trivial. % 10.16/10.36 apply (zenon_L232_); trivial. % 10.16/10.36 (* end of lemma zenon_L759_ *) % 10.16/10.36 assert (zenon_L760_ : (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.16/10.36 do 0 intro. intros zenon_H30 zenon_H2c zenon_H2a zenon_H328 zenon_H2ae zenon_H2b4 zenon_H2b1 zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_H187 zenon_H64 zenon_H2ca zenon_H301 zenon_H1db zenon_H14c zenon_H14b zenon_H22f zenon_H105 zenon_Heb zenon_H2fe zenon_H5f zenon_H155 zenon_H16c zenon_Hb8 zenon_H7a zenon_H74 zenon_H2fa zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H1ce zenon_H127 zenon_H12c zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H272 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H2dd zenon_H12f zenon_H1b9 zenon_H22e zenon_H1d4 zenon_H141 zenon_Hd7 zenon_Hae zenon_H1ea zenon_H52 zenon_H2a8 zenon_H24 zenon_Hbe zenon_H23 zenon_H1ec zenon_H101 zenon_H7e zenon_H1f5 zenon_H90 zenon_H1f6 zenon_H25 zenon_H2c4 zenon_H1cb zenon_H8d zenon_Hd1 zenon_H2b3 zenon_H1e zenon_H12a zenon_Hb7. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.16/10.36 apply (zenon_L19_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.16/10.36 apply (zenon_L31_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.16/10.36 apply (zenon_L757_); trivial. % 10.16/10.36 apply (zenon_L759_); trivial. % 10.16/10.36 (* end of lemma zenon_L760_ *) % 10.16/10.36 assert (zenon_L761_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.36 do 0 intro. intros zenon_H1cb zenon_H9e zenon_H23 zenon_H149 zenon_H2c4 zenon_H25 zenon_H2b3 zenon_H106 zenon_H101. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.16/10.36 apply (zenon_L54_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.16/10.36 apply (zenon_L386_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.16/10.36 apply (zenon_L445_); trivial. % 10.16/10.36 apply (zenon_L241_); trivial. % 10.16/10.36 (* end of lemma zenon_L761_ *) % 10.16/10.36 assert (zenon_L762_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.36 do 0 intro. intros zenon_H192 zenon_H1d5 zenon_H101 zenon_H2b3 zenon_H25 zenon_H2c4 zenon_H23 zenon_H9e zenon_H1cb zenon_Hd7 zenon_H1ec zenon_H106 zenon_Hfe. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.16/10.36 apply (zenon_L613_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.16/10.36 apply (zenon_L761_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.16/10.36 apply (zenon_L219_); trivial. % 10.16/10.36 apply (zenon_L313_); trivial. % 10.16/10.36 (* end of lemma zenon_L762_ *) % 10.16/10.36 assert (zenon_L763_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.36 do 0 intro. intros zenon_H1ce zenon_Ha9 zenon_H2a8 zenon_H24 zenon_Hbe zenon_H8d zenon_H23 zenon_H166 zenon_H1ec zenon_H101 zenon_H127 zenon_H2b3 zenon_H12a zenon_H12c zenon_Hf7 zenon_H106 zenon_H105 zenon_H52 zenon_Hb8. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H1cf ]. % 10.16/10.36 apply (zenon_L736_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1d0 ]. % 10.16/10.36 apply (zenon_L435_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hf4 | zenon_intro zenon_He2 ]. % 10.16/10.36 apply (zenon_L70_); trivial. % 10.16/10.36 apply (zenon_L229_); trivial. % 10.16/10.36 (* end of lemma zenon_L763_ *) % 10.16/10.36 assert (zenon_L764_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.36 do 0 intro. intros zenon_H301 zenon_H1d5 zenon_H74 zenon_H8d zenon_H1e zenon_H1b9 zenon_H2b3 zenon_Hf3 zenon_H105. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.36 apply (zenon_L427_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.36 apply (zenon_L231_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.36 apply (zenon_L432_); trivial. % 10.16/10.36 apply (zenon_L435_); trivial. % 10.16/10.36 (* end of lemma zenon_L764_ *) % 10.16/10.36 assert (zenon_L765_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.36 do 0 intro. intros zenon_H328 zenon_H24 zenon_H25 zenon_H43 zenon_H1d7 zenon_H301 zenon_H74 zenon_H8d zenon_H1e zenon_H1b9 zenon_H2b3 zenon_Hf3 zenon_H105. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.16/10.36 apply (zenon_L30_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.16/10.36 apply (zenon_L310_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.16/10.36 apply (zenon_L748_); trivial. % 10.16/10.36 apply (zenon_L764_); trivial. % 10.16/10.36 (* end of lemma zenon_L765_ *) % 10.16/10.36 assert (zenon_L766_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.16/10.36 do 0 intro. intros zenon_Hae zenon_H2b3 zenon_H25 zenon_H8d zenon_Hd1 zenon_H101 zenon_H106 zenon_H23 zenon_H2c4 zenon_H149 zenon_H2dd zenon_H24 zenon_H1cb zenon_H12a zenon_Hb7. % 10.16/10.36 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.16/10.36 apply (zenon_L761_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.16/10.36 apply (zenon_L320_); trivial. % 10.16/10.36 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.16/10.36 apply (zenon_L561_); trivial. % 10.16/10.36 apply (zenon_L232_); trivial. % 10.16/10.36 (* end of lemma zenon_L766_ *) % 10.16/10.36 assert (zenon_L767_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (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)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.16/10.37 do 0 intro. intros zenon_H2b1 zenon_H2b4 zenon_H2ae zenon_H2c zenon_H2a zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H1d9 zenon_H14c zenon_H2c7 zenon_H2ee zenon_H64 zenon_H110 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H105 zenon_H141 zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H1e zenon_H7a zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Heb zenon_H1c9 zenon_H12f zenon_H14b zenon_H7e zenon_H1f6 zenon_H1ec zenon_Hbe zenon_H22e zenon_H1d4 zenon_H1d5 zenon_H52 zenon_Hae zenon_H2b3 zenon_H25 zenon_H8d zenon_Hd1 zenon_H101 zenon_H106 zenon_H23 zenon_H2c4 zenon_H2dd zenon_H24 zenon_H1cb zenon_H12a zenon_Hb7. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.16/10.37 apply (zenon_L19_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.16/10.37 apply (zenon_L517_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.16/10.37 apply (zenon_L152_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.16/10.37 apply (zenon_L762_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.16/10.37 apply (zenon_L668_); trivial. % 10.16/10.37 apply (zenon_L736_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.16/10.37 apply (zenon_L320_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.16/10.37 apply (zenon_L691_); trivial. % 10.16/10.37 apply (zenon_L232_); trivial. % 10.16/10.37 apply (zenon_L766_); trivial. % 10.16/10.37 (* end of lemma zenon_L767_ *) % 10.16/10.37 assert (zenon_L768_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H1cb zenon_H24 zenon_H2dd zenon_H4f zenon_H25 zenon_H2b3 zenon_H106 zenon_H101. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.16/10.37 apply (zenon_L399_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.16/10.37 apply (zenon_L378_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.16/10.37 apply (zenon_L445_); trivial. % 10.16/10.37 apply (zenon_L241_); trivial. % 10.16/10.37 (* end of lemma zenon_L768_ *) % 10.16/10.37 assert (zenon_L769_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (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)) = (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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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 (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H1ea zenon_H141 zenon_H1d4 zenon_H25 zenon_H22e zenon_Hbe zenon_H1ec zenon_H101 zenon_H1b9 zenon_H1e zenon_H12f zenon_H2dd zenon_H2ac zenon_H83 zenon_H2c4 zenon_Hef zenon_H2f7 zenon_H272 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H14b zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H2b1 zenon_H2b4 zenon_H2ae zenon_H328 zenon_H8d zenon_H2a zenon_H2c zenon_H2b3 zenon_H30. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H24 | zenon_intro zenon_H230 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.16/10.37 apply (zenon_L384_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.16/10.37 apply (zenon_L33_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.16/10.37 apply (zenon_L438_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_Hd8. zenon_intro zenon_H15b. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_H15c. zenon_intro zenon_He1. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.16/10.37 apply (zenon_L4_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.16/10.37 apply (zenon_L34_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.16/10.37 apply (zenon_L151_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H20 | zenon_intro zenon_H1dd ]. % 10.16/10.37 apply (zenon_L4_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.16/10.37 apply (zenon_L371_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.16/10.37 apply (zenon_L33_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.16/10.37 apply (zenon_L737_); trivial. % 10.16/10.37 apply (zenon_L236_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H9e | zenon_intro zenon_H90 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.37 apply (zenon_L30_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.37 apply (zenon_L265_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.37 apply (zenon_L434_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.37 apply (zenon_L385_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.37 apply (zenon_L31_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.16/10.37 apply (zenon_L19_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.16/10.37 apply (zenon_L31_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.16/10.37 apply (zenon_L739_); trivial. % 10.16/10.37 apply (zenon_L612_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.16/10.37 apply (zenon_L19_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.16/10.37 apply (zenon_L517_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.16/10.37 apply (zenon_L739_); trivial. % 10.16/10.37 apply (zenon_L740_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.37 apply (zenon_L385_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.37 apply (zenon_L31_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.37 apply (zenon_L760_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.16/10.37 apply (zenon_L19_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.16/10.37 apply (zenon_L517_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.16/10.37 apply (zenon_L272_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.16/10.37 apply (zenon_L757_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.16/10.37 apply (zenon_L668_); trivial. % 10.16/10.37 apply (zenon_L736_); trivial. % 10.16/10.37 apply (zenon_L740_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H3c. zenon_intro zenon_H44. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H160. zenon_intro zenon_Hf6. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.16/10.37 apply (zenon_L4_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.16/10.37 apply (zenon_L34_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H20 | zenon_intro zenon_H1dd ]. % 10.16/10.37 apply (zenon_L4_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 10.16/10.37 apply (zenon_L88_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H9e | zenon_intro zenon_H90 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.37 apply (zenon_L30_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.16/10.37 apply (zenon_L30_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.16/10.37 apply (zenon_L310_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.16/10.37 apply (zenon_L748_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.37 apply (zenon_L427_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.37 apply (zenon_L18_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.37 apply (zenon_L432_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.37 apply (zenon_L385_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.37 apply (zenon_L31_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.37 apply (zenon_L305_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.16/10.37 apply (zenon_L19_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.16/10.37 apply (zenon_L517_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.16/10.37 apply (zenon_L152_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.16/10.37 apply (zenon_L762_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.16/10.37 apply (zenon_L668_); trivial. % 10.16/10.37 apply (zenon_L763_); trivial. % 10.16/10.37 apply (zenon_L761_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.37 apply (zenon_L434_); trivial. % 10.16/10.37 apply (zenon_L765_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.37 apply (zenon_L30_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.16/10.37 apply (zenon_L30_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.16/10.37 apply (zenon_L310_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.16/10.37 apply (zenon_L748_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.37 apply (zenon_L427_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.37 apply (zenon_L18_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.37 apply (zenon_L432_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.37 apply (zenon_L385_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.37 apply (zenon_L31_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.37 apply (zenon_L305_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.16/10.37 apply (zenon_L19_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.16/10.37 apply (zenon_L517_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.16/10.37 apply (zenon_L152_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.16/10.37 apply (zenon_L757_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.16/10.37 apply (zenon_L668_); trivial. % 10.16/10.37 apply (zenon_L763_); trivial. % 10.16/10.37 apply (zenon_L740_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.37 apply (zenon_L711_); trivial. % 10.16/10.37 apply (zenon_L765_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.16/10.37 apply (zenon_L30_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.16/10.37 apply (zenon_L310_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.16/10.37 apply (zenon_L748_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.37 apply (zenon_L385_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.37 apply (zenon_L31_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.37 apply (zenon_L305_); trivial. % 10.16/10.37 apply (zenon_L767_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.16/10.37 apply (zenon_L4_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.16/10.37 apply (zenon_L34_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.37 apply (zenon_L385_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.37 apply (zenon_L31_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.16/10.37 apply (zenon_L19_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.16/10.37 apply (zenon_L173_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.16/10.37 apply (zenon_L378_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.16/10.37 apply (zenon_L399_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.16/10.37 apply (zenon_L386_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.16/10.37 apply (zenon_L145_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.16/10.37 apply (zenon_L60_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.16/10.37 apply (zenon_L251_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.16/10.37 apply (zenon_L199_); trivial. % 10.16/10.37 apply (zenon_L299_); trivial. % 10.16/10.37 apply (zenon_L768_); trivial. % 10.16/10.37 apply (zenon_L692_); trivial. % 10.16/10.37 apply (zenon_L17_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H26 | zenon_intro zenon_H231 ]. % 10.16/10.37 apply (zenon_L31_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H2e | zenon_intro zenon_H82 ]. % 10.16/10.37 apply (zenon_L445_); trivial. % 10.16/10.37 apply (zenon_L756_); trivial. % 10.16/10.37 (* end of lemma zenon_L769_ *) % 10.16/10.37 assert (zenon_L770_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (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) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H328 zenon_H2b4 zenon_H2b1 zenon_H2ae zenon_H2c zenon_H30 zenon_H2a zenon_H8d zenon_H1e zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H22f zenon_H105 zenon_Heb zenon_H2fe zenon_H5f zenon_H155 zenon_H16c zenon_H2dd zenon_H12f zenon_Hb8 zenon_H7e zenon_H7a zenon_H74 zenon_H2fa zenon_H1b9 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H23 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_Hef zenon_H1ce zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1f6 zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H272 zenon_H22e zenon_Hbe zenon_H83 zenon_H1d4 zenon_H2c4 zenon_H1ec zenon_H187 zenon_H64 zenon_H2ee zenon_H12c zenon_H12a zenon_Ha9 zenon_H127 zenon_H101 zenon_H25. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H1f | zenon_intro zenon_H305 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H24 | zenon_intro zenon_H230 ]. % 10.16/10.37 apply (zenon_L30_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H26 | zenon_intro zenon_H231 ]. % 10.16/10.37 apply (zenon_L31_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H2e | zenon_intro zenon_H82 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.16/10.37 apply (zenon_L32_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.16/10.37 apply (zenon_L33_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.16/10.37 apply (zenon_L9_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H20 | zenon_intro zenon_H15d ]. % 10.16/10.37 apply (zenon_L2_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H89 | zenon_intro zenon_H15e ]. % 10.16/10.37 apply (zenon_L34_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H97 | zenon_intro zenon_Hb7 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.16/10.37 apply (zenon_L30_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.16/10.37 apply (zenon_L225_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.16/10.37 apply (zenon_L94_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.16/10.37 apply (zenon_L226_); trivial. % 10.16/10.37 apply (zenon_L26_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.16/10.37 apply (zenon_L63_); trivial. % 10.16/10.37 apply (zenon_L230_); trivial. % 10.16/10.37 apply (zenon_L734_); trivial. % 10.16/10.37 apply (zenon_L707_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H27 | zenon_intro zenon_H306 ]. % 10.16/10.37 apply (zenon_L231_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H306); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H11b ]. % 10.16/10.37 apply (zenon_L769_); trivial. % 10.16/10.37 apply (zenon_L730_); trivial. % 10.16/10.37 (* end of lemma zenon_L770_ *) % 10.16/10.37 assert (zenon_L771_ : ((op (e3) (e0)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H1d5 zenon_H72 zenon_H2c. % 10.16/10.37 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 10.16/10.37 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H2c. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H31. % 10.16/10.37 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.16/10.37 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 10.16/10.37 congruence. % 10.16/10.37 cut (((op (e3) (e0)) = (e1)) = ((e3) = (e1))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H19f. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H1d5. % 10.16/10.37 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.16/10.37 cut (((op (e3) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 10.16/10.37 congruence. % 10.16/10.37 exact (zenon_H153 zenon_H72). % 10.16/10.37 apply zenon_H1d. apply refl_equal. % 10.16/10.37 apply zenon_H29. apply refl_equal. % 10.16/10.37 apply zenon_H29. apply refl_equal. % 10.16/10.37 (* end of lemma zenon_L771_ *) % 10.16/10.37 assert (zenon_L772_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H130 zenon_H64 zenon_H30 zenon_H82 zenon_H7e zenon_H70 zenon_H7a zenon_H74 zenon_H83 zenon_H1d7 zenon_H2f zenon_H1d5 zenon_H2c. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.37 apply (zenon_L22_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.37 apply (zenon_L27_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.37 apply (zenon_L161_); trivial. % 10.16/10.37 apply (zenon_L771_); trivial. % 10.16/10.37 (* end of lemma zenon_L772_ *) % 10.16/10.37 assert (zenon_L773_ : (~((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 10.16/10.37 do 0 intro. intros zenon_H32b zenon_H2f. % 10.16/10.37 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.16/10.37 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 10.16/10.37 congruence. % 10.16/10.37 exact (zenon_H33 zenon_H2f). % 10.16/10.37 apply zenon_H22. apply refl_equal. % 10.16/10.37 (* end of lemma zenon_L773_ *) % 10.16/10.37 assert (zenon_L774_ : ((op (e3) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (op (op (e2) (e2)) (e2)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H1ed zenon_H2f zenon_H32c. % 10.16/10.37 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H30d | zenon_intro zenon_H30e ]. % 10.16/10.37 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e1) = (op (op (e2) (e2)) (e2)))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H32c. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H30d. % 10.16/10.37 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H30e]. % 10.16/10.37 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H32d]. % 10.16/10.37 congruence. % 10.16/10.37 cut (((op (e3) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H32d. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H1ed. % 10.16/10.37 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.16/10.37 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H32e]. % 10.16/10.37 congruence. % 10.16/10.37 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H30d | zenon_intro zenon_H30e ]. % 10.16/10.37 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H32e. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H30d. % 10.16/10.37 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H30e]. % 10.16/10.37 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H32b]. % 10.16/10.37 congruence. % 10.16/10.37 apply (zenon_L773_); trivial. % 10.16/10.37 apply zenon_H30e. apply refl_equal. % 10.16/10.37 apply zenon_H30e. apply refl_equal. % 10.16/10.37 apply zenon_H1d. apply refl_equal. % 10.16/10.37 apply zenon_H30e. apply refl_equal. % 10.16/10.37 apply zenon_H30e. apply refl_equal. % 10.16/10.37 (* end of lemma zenon_L774_ *) % 10.16/10.37 assert (zenon_L775_ : ((op (e3) (e1)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> False). % 10.16/10.37 do 0 intro. intros zenon_H94 zenon_H1ed zenon_H2f. % 10.16/10.37 apply (zenon_notand_s _ _ ax10); [ zenon_intro zenon_H330 | zenon_intro zenon_H32f ]. % 10.16/10.37 elim (classic ((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))); [ zenon_intro zenon_H313 | zenon_intro zenon_H314 ]. % 10.16/10.37 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2)))) = ((e0) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H330. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H313. % 10.16/10.37 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H314]. % 10.16/10.37 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H331]. % 10.16/10.37 congruence. % 10.16/10.37 cut (((op (e3) (e1)) = (e0)) = ((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (e0))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H331. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H94. % 10.16/10.37 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.16/10.37 cut (((op (e3) (e1)) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H332]. % 10.16/10.37 congruence. % 10.16/10.37 elim (classic ((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))); [ zenon_intro zenon_H313 | zenon_intro zenon_H314 ]. % 10.16/10.37 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2)))) = ((op (e3) (e1)) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H332. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H313. % 10.16/10.37 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H314]. % 10.16/10.37 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H333]. % 10.16/10.37 congruence. % 10.16/10.37 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H32d]. % 10.16/10.37 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 10.16/10.37 congruence. % 10.16/10.37 exact (zenon_H33 zenon_H2f). % 10.16/10.37 cut (((op (e3) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H32d. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H1ed. % 10.16/10.37 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.16/10.37 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H32e]. % 10.16/10.37 congruence. % 10.16/10.37 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H30d | zenon_intro zenon_H30e ]. % 10.16/10.37 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H32e. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H30d. % 10.16/10.37 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H30e]. % 10.16/10.37 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H32b]. % 10.16/10.37 congruence. % 10.16/10.37 apply (zenon_L773_); trivial. % 10.16/10.37 apply zenon_H30e. apply refl_equal. % 10.16/10.37 apply zenon_H30e. apply refl_equal. % 10.16/10.37 apply zenon_H1d. apply refl_equal. % 10.16/10.37 apply zenon_H314. apply refl_equal. % 10.16/10.37 apply zenon_H314. apply refl_equal. % 10.16/10.37 apply zenon_H34. apply refl_equal. % 10.16/10.37 apply zenon_H314. apply refl_equal. % 10.16/10.37 apply zenon_H314. apply refl_equal. % 10.16/10.37 apply (zenon_notand_s _ _ zenon_H32f); [ zenon_intro zenon_H334 | zenon_intro zenon_H32c ]. % 10.16/10.37 apply zenon_H334. apply sym_equal. exact zenon_H2f. % 10.16/10.37 apply (zenon_L774_); trivial. % 10.16/10.37 (* end of lemma zenon_L775_ *) % 10.16/10.37 assert (zenon_L776_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H2d4 zenon_H5e zenon_H335. % 10.16/10.37 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H336 | zenon_intro zenon_H9a ]. % 10.16/10.37 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e1)) = (op (e0) (e2)))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H335. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H336. % 10.16/10.37 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 10.16/10.37 cut (((op (e0) (e2)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H337]. % 10.16/10.37 congruence. % 10.16/10.37 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e0) (e1)))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H337. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H2d4. % 10.16/10.37 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 10.16/10.37 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 10.16/10.37 congruence. % 10.16/10.37 apply zenon_H9a. apply refl_equal. % 10.16/10.37 apply zenon_H63. apply sym_equal. exact zenon_H5e. % 10.16/10.37 apply zenon_H9a. apply refl_equal. % 10.16/10.37 apply zenon_H9a. apply refl_equal. % 10.16/10.37 (* end of lemma zenon_L776_ *) % 10.16/10.37 assert (zenon_L777_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H11b zenon_H1ed zenon_H1ea. % 10.16/10.37 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.16/10.37 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H1ea. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_Haa. % 10.16/10.37 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.16/10.37 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1eb]. % 10.16/10.37 congruence. % 10.16/10.37 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H1eb. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H11b. % 10.16/10.37 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 10.16/10.37 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.16/10.37 congruence. % 10.16/10.37 apply zenon_Hab. apply refl_equal. % 10.16/10.37 apply zenon_H1ee. apply sym_equal. exact zenon_H1ed. % 10.16/10.37 apply zenon_Hab. apply refl_equal. % 10.16/10.37 apply zenon_Hab. apply refl_equal. % 10.16/10.37 (* end of lemma zenon_L777_ *) % 10.16/10.37 assert (zenon_L778_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H338 zenon_H335 zenon_H5e zenon_H26 zenon_H160 zenon_H2c zenon_H2f zenon_H11b zenon_H1ea. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H2d4 | zenon_intro zenon_H339 ]. % 10.16/10.37 apply (zenon_L776_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H188 | zenon_intro zenon_H33a ]. % 10.16/10.37 apply (zenon_L681_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H1ed ]. % 10.16/10.37 apply (zenon_L438_); trivial. % 10.16/10.37 apply (zenon_L777_); trivial. % 10.16/10.37 (* end of lemma zenon_L778_ *) % 10.16/10.37 assert (zenon_L779_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H22e zenon_H74 zenon_H72 zenon_H5f zenon_H70 zenon_H1b9 zenon_H2f zenon_Hf6. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.16/10.37 apply (zenon_L23_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.16/10.37 apply (zenon_L59_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.16/10.37 apply (zenon_L174_); trivial. % 10.16/10.37 apply (zenon_L307_); trivial. % 10.16/10.37 (* end of lemma zenon_L779_ *) % 10.16/10.37 assert (zenon_L780_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H83 zenon_Hf6 zenon_H1b9 zenon_H5f zenon_H74 zenon_H22e zenon_H7a zenon_H70 zenon_H2f zenon_H7e zenon_H11b zenon_H2c. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.16/10.37 apply (zenon_L779_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.16/10.37 apply (zenon_L24_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.16/10.37 apply (zenon_L25_); trivial. % 10.16/10.37 apply (zenon_L505_); trivial. % 10.16/10.37 (* end of lemma zenon_L780_ *) % 10.16/10.37 assert (zenon_L781_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H22e zenon_H74 zenon_H72 zenon_H30 zenon_H26 zenon_H1b9 zenon_H2f zenon_He2 zenon_H105. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.16/10.37 apply (zenon_L23_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.16/10.37 apply (zenon_L38_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.16/10.37 apply (zenon_L174_); trivial. % 10.16/10.37 apply (zenon_L71_); trivial. % 10.16/10.37 (* end of lemma zenon_L781_ *) % 10.16/10.37 assert (zenon_L782_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H83 zenon_H105 zenon_H1b9 zenon_H26 zenon_H30 zenon_H74 zenon_H22e zenon_H7a zenon_H70 zenon_H2f zenon_H7e zenon_He2 zenon_Hb8. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.16/10.37 apply (zenon_L781_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.16/10.37 apply (zenon_L24_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.16/10.37 apply (zenon_L25_); trivial. % 10.16/10.37 apply (zenon_L229_); trivial. % 10.16/10.37 (* end of lemma zenon_L782_ *) % 10.16/10.37 assert (zenon_L783_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> False). % 10.16/10.37 do 0 intro. intros zenon_H2dd zenon_H20 zenon_H9e. % 10.16/10.37 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H2dd. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H20. % 10.16/10.37 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 10.16/10.37 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 10.16/10.37 congruence. % 10.16/10.37 apply zenon_H67. apply refl_equal. % 10.16/10.37 apply zenon_H9f. apply sym_equal. exact zenon_H9e. % 10.16/10.37 (* end of lemma zenon_L783_ *) % 10.16/10.37 assert (zenon_L784_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H33b zenon_Ha2 zenon_Ha1 zenon_H335 zenon_H2d4 zenon_H5f zenon_H26 zenon_H79 zenon_H7a. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H89 | zenon_intro zenon_H33c ]. % 10.16/10.37 apply (zenon_L41_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H33c); [ zenon_intro zenon_H5e | zenon_intro zenon_H33d ]. % 10.16/10.37 apply (zenon_L776_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H33d); [ zenon_intro zenon_H65 | zenon_intro zenon_H70 ]. % 10.16/10.37 apply (zenon_L103_); trivial. % 10.16/10.37 apply (zenon_L24_); trivial. % 10.16/10.37 (* end of lemma zenon_L784_ *) % 10.16/10.37 assert (zenon_L785_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 10.16/10.37 do 0 intro. intros zenon_H101 zenon_Hfd zenon_Ha8. % 10.16/10.37 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H101. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_Hfd. % 10.16/10.37 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 10.16/10.37 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 10.16/10.37 congruence. % 10.16/10.37 apply zenon_H104. apply refl_equal. % 10.16/10.37 apply zenon_Had. apply sym_equal. exact zenon_Ha8. % 10.16/10.37 (* end of lemma zenon_L785_ *) % 10.16/10.37 assert (zenon_L786_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H1ce zenon_Ha8 zenon_Hb8 zenon_H11b zenon_H12a zenon_H128 zenon_H109 zenon_H105. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H1cf ]. % 10.16/10.37 apply (zenon_L232_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1d0 ]. % 10.16/10.37 apply (zenon_L712_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hf4 | zenon_intro zenon_He2 ]. % 10.16/10.37 apply (zenon_L105_); trivial. % 10.16/10.37 apply (zenon_L71_); trivial. % 10.16/10.37 (* end of lemma zenon_L786_ *) % 10.16/10.37 assert (zenon_L787_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (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 (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H10d zenon_H101 zenon_Hfe zenon_H26 zenon_H110 zenon_H1ce zenon_Ha8 zenon_Hb8 zenon_H11b zenon_H12a zenon_H128 zenon_H105. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hfd | zenon_intro zenon_H10e ]. % 10.16/10.37 apply (zenon_L785_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H10f ]. % 10.16/10.37 apply (zenon_L510_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H106 | zenon_intro zenon_H109 ]. % 10.16/10.37 apply (zenon_L517_); trivial. % 10.16/10.37 apply (zenon_L786_); trivial. % 10.16/10.37 (* end of lemma zenon_L787_ *) % 10.16/10.37 assert (zenon_L788_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (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 (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_Hae zenon_H20 zenon_H2dd zenon_H7a zenon_H79 zenon_H5f zenon_H2d4 zenon_H335 zenon_Ha1 zenon_H33b zenon_H1b9 zenon_H13b zenon_H1cb zenon_H91 zenon_H11f zenon_Hd1 zenon_Heb zenon_Hd0 zenon_H10d zenon_H101 zenon_Hfe zenon_H26 zenon_H110 zenon_H1ce zenon_Hb8 zenon_H11b zenon_H12a zenon_H105. % 10.16/10.37 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.16/10.37 apply (zenon_L783_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.16/10.37 apply (zenon_L784_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.16/10.37 apply (zenon_L341_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.16/10.37 apply (zenon_L123_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.16/10.37 apply (zenon_L56_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.16/10.37 apply (zenon_L63_); trivial. % 10.16/10.37 apply (zenon_L787_); trivial. % 10.16/10.37 (* end of lemma zenon_L788_ *) % 10.16/10.37 assert (zenon_L789_ : ((op (e0) (e3)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (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)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 10.16/10.37 do 0 intro. intros zenon_He2 zenon_H2f zenon_H20 zenon_H2d4 zenon_H335 zenon_H33b zenon_H2c zenon_H11b zenon_H2a zenon_H26 zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H12a zenon_H1d9 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H64 zenon_H110 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H105 zenon_H141 zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H1e zenon_H7a zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Heb zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H25 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1ec zenon_Hbe zenon_H22e zenon_Hd1 zenon_H23 zenon_H1d4 zenon_H101 zenon_Hfd. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.16/10.37 apply (zenon_L782_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.16/10.37 apply (zenon_L38_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.16/10.37 apply (zenon_L389_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.16/10.37 apply (zenon_L783_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.16/10.37 apply (zenon_L784_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.16/10.37 apply (zenon_L556_); trivial. % 10.16/10.37 apply (zenon_L785_); trivial. % 10.16/10.37 (* end of lemma zenon_L789_ *) % 10.16/10.37 assert (zenon_L790_ : (~((op (e1) (op (e1) (e0))) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (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)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H43 zenon_H2ae zenon_Hd0 zenon_H91 zenon_H73 zenon_He2 zenon_H2f zenon_H20 zenon_H2d4 zenon_H335 zenon_H33b zenon_H2c zenon_H11b zenon_H2a zenon_H26 zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H12a zenon_H1d9 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H64 zenon_H110 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H105 zenon_H141 zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H22f zenon_H1e zenon_H7a zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Heb zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H25 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1ec zenon_Hbe zenon_H22e zenon_Hd1 zenon_H23 zenon_H1d4 zenon_H101. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.16/10.37 apply (zenon_L88_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.16/10.37 apply (zenon_L730_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.16/10.37 apply (zenon_L782_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.16/10.37 apply (zenon_L65_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.16/10.37 apply (zenon_L389_); trivial. % 10.16/10.37 apply (zenon_L788_); trivial. % 10.16/10.37 apply (zenon_L789_); trivial. % 10.16/10.37 (* end of lemma zenon_L790_ *) % 10.16/10.37 assert (zenon_L791_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H1d1 zenon_H20 zenon_H25 zenon_H68 zenon_H9e zenon_H23 zenon_H1cb zenon_H11f zenon_H26 zenon_Hd1 zenon_H30 zenon_H2f zenon_Hf4 zenon_H12a. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.37 apply (zenon_L4_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.37 apply (zenon_L20_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.37 apply (zenon_L54_); trivial. % 10.16/10.37 apply (zenon_L156_); trivial. % 10.16/10.37 (* end of lemma zenon_L791_ *) % 10.16/10.37 assert (zenon_L792_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H1d1 zenon_H20 zenon_H23 zenon_Hf1 zenon_H25 zenon_H2b2 zenon_H1cb zenon_H11f zenon_H26 zenon_Hd1 zenon_H30 zenon_H2f zenon_Hf4 zenon_H12a. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.37 apply (zenon_L4_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.37 apply (zenon_L163_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.37 apply (zenon_L684_); trivial. % 10.16/10.37 apply (zenon_L156_); trivial. % 10.16/10.37 (* end of lemma zenon_L792_ *) % 10.16/10.37 assert (zenon_L793_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H11b zenon_H1d5 zenon_H16c. % 10.16/10.37 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 10.16/10.37 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H16c. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_Haa. % 10.16/10.37 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.16/10.37 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 10.16/10.37 congruence. % 10.16/10.37 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H16d. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H11b. % 10.16/10.37 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 10.16/10.37 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.16/10.37 congruence. % 10.16/10.37 apply zenon_Hab. apply refl_equal. % 10.16/10.37 apply zenon_H1d6. apply sym_equal. exact zenon_H1d5. % 10.16/10.37 apply zenon_Hab. apply refl_equal. % 10.16/10.37 apply zenon_Hab. apply refl_equal. % 10.16/10.37 (* end of lemma zenon_L793_ *) % 10.16/10.37 assert (zenon_L794_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> False). % 10.16/10.37 do 0 intro. intros zenon_Hbe zenon_H20 zenon_H9d. % 10.16/10.37 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_Hbe. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H20. % 10.16/10.37 cut (((e0) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H33e]. % 10.16/10.37 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 10.16/10.37 congruence. % 10.16/10.37 apply zenon_H67. apply refl_equal. % 10.16/10.37 apply zenon_H33e. apply sym_equal. exact zenon_H9d. % 10.16/10.37 (* end of lemma zenon_L794_ *) % 10.16/10.37 assert (zenon_L795_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_Hb1 zenon_Hbe. % 10.16/10.37 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_H20. zenon_intro zenon_Hb2. % 10.16/10.37 apply (zenon_and_s _ _ zenon_Hb2). zenon_intro zenon_H20. zenon_intro zenon_Hb3. % 10.16/10.37 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.16/10.37 apply (zenon_L794_); trivial. % 10.16/10.37 (* end of lemma zenon_L795_ *) % 10.16/10.37 assert (zenon_L796_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H1d1 zenon_Hef zenon_H68 zenon_H25 zenon_H11b zenon_H96 zenon_Hd0 zenon_H93 zenon_H26 zenon_H11f zenon_H192 zenon_H90 zenon_H23. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.37 apply (zenon_L152_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.37 apply (zenon_L20_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.37 apply (zenon_L522_); trivial. % 10.16/10.37 apply (zenon_L35_); trivial. % 10.16/10.37 (* end of lemma zenon_L796_ *) % 10.16/10.37 assert (zenon_L797_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.16/10.37 do 0 intro. intros zenon_Hae zenon_H86 zenon_H7a zenon_H79 zenon_H5f zenon_H2d4 zenon_H335 zenon_Ha1 zenon_H33b zenon_H105 zenon_H1b9 zenon_H23 zenon_H26 zenon_H73 zenon_H2a zenon_H13d zenon_H12a zenon_Hb7. % 10.16/10.37 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.16/10.37 apply (zenon_L54_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.16/10.37 apply (zenon_L784_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.16/10.37 apply (zenon_L598_); trivial. % 10.16/10.37 apply (zenon_L232_); trivial. % 10.16/10.37 (* end of lemma zenon_L797_ *) % 10.16/10.37 assert (zenon_L798_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (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) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H83 zenon_H74 zenon_Hb7 zenon_H12a zenon_H13d zenon_H2a zenon_H73 zenon_H23 zenon_H1b9 zenon_H105 zenon_H33b zenon_Ha1 zenon_H335 zenon_H2d4 zenon_H5f zenon_H7a zenon_H86 zenon_Hae zenon_H14b zenon_H93 zenon_H26 zenon_H141 zenon_H1d9 zenon_H90 zenon_H14c zenon_H11b zenon_H2c. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.16/10.37 apply (zenon_L23_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.16/10.37 apply (zenon_L797_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.16/10.37 apply (zenon_L508_); trivial. % 10.16/10.37 apply (zenon_L505_); trivial. % 10.16/10.37 (* end of lemma zenon_L798_ *) % 10.16/10.37 assert (zenon_L799_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H130 zenon_Hbb zenon_Hb7 zenon_H12a zenon_H13d zenon_H2a zenon_H23 zenon_H33b zenon_Ha1 zenon_H335 zenon_H2d4 zenon_H5f zenon_H7a zenon_H86 zenon_Hae zenon_H2ac zenon_Hf1 zenon_H83 zenon_H7e zenon_Hb8 zenon_H2ee zenon_H1d7 zenon_H22e zenon_H74 zenon_H30 zenon_H26 zenon_H1b9 zenon_H2f zenon_He2 zenon_H105. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.37 apply (zenon_L504_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.16/10.37 apply (zenon_L782_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.16/10.37 apply (zenon_L65_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.16/10.37 apply (zenon_L389_); trivial. % 10.16/10.37 apply (zenon_L797_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.37 apply (zenon_L161_); trivial. % 10.16/10.37 apply (zenon_L781_); trivial. % 10.16/10.37 (* end of lemma zenon_L799_ *) % 10.16/10.37 assert (zenon_L800_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H155 zenon_H5f zenon_H90 zenon_H192 zenon_H93 zenon_H96 zenon_H11b zenon_Hbb zenon_H1d1 zenon_H20 zenon_H23 zenon_Hf1 zenon_H25 zenon_H2b2 zenon_H1cb zenon_H11f zenon_H26 zenon_Hd1 zenon_H30 zenon_H2f zenon_H12a. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.16/10.37 apply (zenon_L503_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.16/10.37 apply (zenon_L103_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.37 apply (zenon_L503_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.37 apply (zenon_L163_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.37 apply (zenon_L522_); trivial. % 10.16/10.37 apply (zenon_L35_); trivial. % 10.16/10.37 apply (zenon_L792_); trivial. % 10.16/10.37 (* end of lemma zenon_L800_ *) % 10.16/10.37 assert (zenon_L801_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H16f zenon_H22e zenon_H74 zenon_H30 zenon_H26 zenon_H1b9 zenon_H2f zenon_H105. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hb7. zenon_intro zenon_H170. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_H90. zenon_intro zenon_H171. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.16/10.37 apply (zenon_L781_); trivial. % 10.16/10.37 (* end of lemma zenon_L801_ *) % 10.16/10.37 assert (zenon_L802_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> ((op (e1) (e1)) = (e2)) -> False). % 10.16/10.37 do 0 intro. intros zenon_H19b zenon_H160 zenon_H26. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H19b). zenon_intro zenon_H188. zenon_intro zenon_H19c. % 10.16/10.37 apply (zenon_L681_); trivial. % 10.16/10.37 (* end of lemma zenon_L802_ *) % 10.16/10.37 assert (zenon_L803_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H1a7 zenon_H192 zenon_H11f zenon_H26 zenon_H93 zenon_H96 zenon_H11b zenon_H25. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H86. zenon_intro zenon_H1a8. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hd0. zenon_intro zenon_H6f. % 10.16/10.37 apply (zenon_L522_); trivial. % 10.16/10.37 (* end of lemma zenon_L803_ *) % 10.16/10.37 assert (zenon_L804_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H1e6 zenon_H22e zenon_H74 zenon_H30 zenon_H26 zenon_H1b9 zenon_H2f zenon_H105. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H72. zenon_intro zenon_H1e7. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_He2. zenon_intro zenon_H6f. % 10.16/10.37 apply (zenon_L781_); trivial. % 10.16/10.37 (* end of lemma zenon_L804_ *) % 10.16/10.37 assert (zenon_L805_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H1f9 zenon_H22e zenon_H74 zenon_H30 zenon_H26 zenon_H1b9 zenon_H2f zenon_H105. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H1f9). zenon_intro zenon_H72. zenon_intro zenon_H1fa. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_He2. zenon_intro zenon_Hb6. % 10.16/10.37 apply (zenon_L781_); trivial. % 10.16/10.37 (* end of lemma zenon_L805_ *) % 10.16/10.37 assert (zenon_L806_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H1fb zenon_H22e zenon_H74 zenon_H30 zenon_H26 zenon_H1b9 zenon_H2f zenon_H105. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H72. zenon_intro zenon_H1fc. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_He2. zenon_intro zenon_Hbd. % 10.16/10.37 apply (zenon_L781_); trivial. % 10.16/10.37 (* end of lemma zenon_L806_ *) % 10.16/10.37 assert (zenon_L807_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_H79 zenon_Heb zenon_H2f zenon_H109 zenon_H105. % 10.16/10.37 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.37 apply (zenon_L7_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.37 apply (zenon_L24_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.37 apply (zenon_L259_); trivial. % 10.16/10.37 apply (zenon_L71_); trivial. % 10.16/10.37 (* end of lemma zenon_L807_ *) % 10.16/10.37 assert (zenon_L808_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H1fd zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H2f zenon_H105. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H79. zenon_intro zenon_H1fe. % 10.16/10.37 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H109. zenon_intro zenon_Hc2. % 10.16/10.37 apply (zenon_L807_); trivial. % 10.16/10.37 (* end of lemma zenon_L808_ *) % 10.16/10.37 assert (zenon_L809_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e2)) = (e3)) -> False). % 10.16/10.37 do 0 intro. intros zenon_H1cb zenon_H25 zenon_H2b2 zenon_H26 zenon_Hd1 zenon_H45 zenon_H50 zenon_H2f. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.16/10.37 apply (zenon_L684_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.16/10.37 apply (zenon_L56_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.16/10.37 apply (zenon_L14_); trivial. % 10.16/10.37 apply (zenon_L199_); trivial. % 10.16/10.37 (* end of lemma zenon_L809_ *) % 10.16/10.37 assert (zenon_L810_ : (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e2)) = (e0)) -> False). % 10.16/10.37 do 0 intro. intros zenon_H5d zenon_H91 zenon_H98. % 10.16/10.37 cut (((op (e3) (e0)) = (e2)) = ((op (e3) (op (e3) (e2))) = (e2))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H5d. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H91. % 10.16/10.37 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.16/10.37 cut (((op (e3) (e0)) = (op (e3) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H33f]. % 10.16/10.37 congruence. % 10.16/10.37 elim (classic ((op (e3) (op (e3) (e2))) = (op (e3) (op (e3) (e2))))); [ zenon_intro zenon_H226 | zenon_intro zenon_H227 ]. % 10.16/10.37 cut (((op (e3) (op (e3) (e2))) = (op (e3) (op (e3) (e2)))) = ((op (e3) (e0)) = (op (e3) (op (e3) (e2))))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H33f. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H226. % 10.16/10.37 cut (((op (e3) (op (e3) (e2))) = (op (e3) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H227]. % 10.16/10.37 cut (((op (e3) (op (e3) (e2))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H340]. % 10.16/10.37 congruence. % 10.16/10.37 cut (((op (e3) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H341]. % 10.16/10.37 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.16/10.37 congruence. % 10.16/10.37 apply zenon_H29. apply refl_equal. % 10.16/10.37 exact (zenon_H341 zenon_H98). % 10.16/10.37 apply zenon_H227. apply refl_equal. % 10.16/10.37 apply zenon_H227. apply refl_equal. % 10.16/10.37 apply zenon_H22. apply refl_equal. % 10.16/10.37 (* end of lemma zenon_L810_ *) % 10.16/10.37 assert (zenon_L811_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.16/10.37 do 0 intro. intros zenon_H1f6 zenon_H91 zenon_H1ea zenon_H11b zenon_H5d zenon_H1f5 zenon_H72. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.16/10.37 apply (zenon_L810_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.16/10.37 apply (zenon_L777_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.16/10.37 apply (zenon_L208_); trivial. % 10.16/10.37 apply (zenon_L176_); trivial. % 10.16/10.37 (* end of lemma zenon_L811_ *) % 10.16/10.37 assert (zenon_L812_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H83 zenon_H1f5 zenon_H5d zenon_H11b zenon_H1ea zenon_H91 zenon_H1f6 zenon_H7a zenon_H70 zenon_H2f zenon_H7e zenon_H51. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.16/10.37 apply (zenon_L811_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.16/10.37 apply (zenon_L24_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.16/10.37 apply (zenon_L25_); trivial. % 10.16/10.37 apply (zenon_L16_); trivial. % 10.16/10.37 (* end of lemma zenon_L812_ *) % 10.16/10.37 assert (zenon_L813_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e3) (e3)) = (e1)) -> False). % 10.16/10.37 do 0 intro. intros zenon_H2ee zenon_Hb8 zenon_He2 zenon_H7e zenon_H7a zenon_H22e zenon_H74 zenon_H1b9 zenon_H105 zenon_H83 zenon_H30 zenon_H26 zenon_H2ac zenon_H2f zenon_H5c zenon_H11b. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.16/10.37 apply (zenon_L782_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.16/10.37 apply (zenon_L38_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.16/10.37 apply (zenon_L389_); trivial. % 10.16/10.37 apply (zenon_L721_); trivial. % 10.16/10.37 (* end of lemma zenon_L813_ *) % 10.16/10.37 assert (zenon_L814_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e3) (e3)) = (e1)) -> False). % 10.16/10.37 do 0 intro. intros zenon_He8 zenon_H20 zenon_H2a zenon_H51 zenon_H1f6 zenon_H91 zenon_H1ea zenon_H5d zenon_H1f5 zenon_Heb zenon_H2ee zenon_Hb8 zenon_H7e zenon_H7a zenon_H22e zenon_H74 zenon_H1b9 zenon_H105 zenon_H83 zenon_H30 zenon_H26 zenon_H2ac zenon_H2f zenon_H5c zenon_H11b. % 10.16/10.37 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.37 apply (zenon_L7_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.37 apply (zenon_L812_); trivial. % 10.16/10.37 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.37 apply (zenon_L259_); trivial. % 10.16/10.37 apply (zenon_L813_); trivial. % 10.16/10.37 (* end of lemma zenon_L814_ *) % 10.16/10.37 assert (zenon_L815_ : (~((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 10.16/10.37 do 0 intro. intros zenon_H342 zenon_H11b. % 10.16/10.37 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.16/10.37 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 10.16/10.37 congruence. % 10.16/10.37 exact (zenon_H11e zenon_H11b). % 10.16/10.37 apply zenon_H29. apply refl_equal. % 10.16/10.37 (* end of lemma zenon_L815_ *) % 10.16/10.37 assert (zenon_L816_ : ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((e2) = (op (op (e3) (e3)) (e3)))) -> False). % 10.16/10.37 do 0 intro. intros zenon_H106 zenon_H11b zenon_H2cf. % 10.16/10.37 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H2d0 | zenon_intro zenon_H2d1 ]. % 10.16/10.37 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e2) = (op (op (e3) (e3)) (e3)))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H2cf. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H2d0. % 10.16/10.37 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d1]. % 10.16/10.37 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2d2]. % 10.16/10.37 congruence. % 10.16/10.37 cut (((op (e1) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H2d2. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H106. % 10.16/10.37 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.16/10.37 cut (((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H343]. % 10.16/10.37 congruence. % 10.16/10.37 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H2d0 | zenon_intro zenon_H2d1 ]. % 10.16/10.37 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H343. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H2d0. % 10.16/10.37 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d1]. % 10.16/10.37 cut (((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H342]. % 10.16/10.37 congruence. % 10.16/10.37 apply (zenon_L815_); trivial. % 10.16/10.37 apply zenon_H2d1. apply refl_equal. % 10.16/10.37 apply zenon_H2d1. apply refl_equal. % 10.16/10.37 apply zenon_H22. apply refl_equal. % 10.16/10.37 apply zenon_H2d1. apply refl_equal. % 10.16/10.37 apply zenon_H2d1. apply refl_equal. % 10.16/10.37 (* end of lemma zenon_L816_ *) % 10.16/10.37 assert (zenon_L817_ : ((op (e1) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> False). % 10.16/10.37 do 0 intro. intros zenon_H13b zenon_H106 zenon_H11b. % 10.16/10.37 apply (zenon_notand_s _ _ ax6); [ zenon_intro zenon_H345 | zenon_intro zenon_H344 ]. % 10.16/10.37 elim (classic ((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))); [ zenon_intro zenon_H2d7 | zenon_intro zenon_H2d8 ]. % 10.16/10.37 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3)))) = ((e0) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H345. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H2d7. % 10.16/10.37 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2d8]. % 10.16/10.37 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H346]. % 10.16/10.37 congruence. % 10.16/10.37 cut (((op (e1) (e2)) = (e0)) = ((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (e0))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H346. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H13b. % 10.16/10.37 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.16/10.37 cut (((op (e1) (e2)) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H347]. % 10.16/10.37 congruence. % 10.16/10.37 elim (classic ((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))); [ zenon_intro zenon_H2d7 | zenon_intro zenon_H2d8 ]. % 10.16/10.37 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3)))) = ((op (e1) (e2)) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H347. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H2d7. % 10.16/10.37 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2d8]. % 10.16/10.37 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H348]. % 10.16/10.37 congruence. % 10.16/10.37 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2d2]. % 10.16/10.37 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 10.16/10.37 congruence. % 10.16/10.37 exact (zenon_H11e zenon_H11b). % 10.16/10.37 cut (((op (e1) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H2d2. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H106. % 10.16/10.37 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.16/10.37 cut (((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H343]. % 10.16/10.37 congruence. % 10.16/10.37 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H2d0 | zenon_intro zenon_H2d1 ]. % 10.16/10.37 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))). % 10.16/10.37 intro zenon_D_pnotp. % 10.16/10.37 apply zenon_H343. % 10.16/10.37 rewrite <- zenon_D_pnotp. % 10.16/10.37 exact zenon_H2d0. % 10.16/10.37 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d1]. % 10.16/10.37 cut (((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H342]. % 10.16/10.38 congruence. % 10.16/10.38 apply (zenon_L815_); trivial. % 10.16/10.38 apply zenon_H2d1. apply refl_equal. % 10.16/10.38 apply zenon_H2d1. apply refl_equal. % 10.16/10.38 apply zenon_H22. apply refl_equal. % 10.16/10.38 apply zenon_H2d8. apply refl_equal. % 10.16/10.38 apply zenon_H2d8. apply refl_equal. % 10.16/10.38 apply zenon_H34. apply refl_equal. % 10.16/10.38 apply zenon_H2d8. apply refl_equal. % 10.16/10.38 apply zenon_H2d8. apply refl_equal. % 10.16/10.38 apply (zenon_notand_s _ _ zenon_H344); [ zenon_intro zenon_H349 | zenon_intro zenon_H2cf ]. % 10.16/10.38 apply zenon_H349. apply sym_equal. exact zenon_H11b. % 10.16/10.38 apply (zenon_L816_); trivial. % 10.16/10.38 (* end of lemma zenon_L817_ *) % 10.16/10.38 assert (zenon_L818_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> False). % 10.16/10.38 do 0 intro. intros zenon_H2a8 zenon_H25 zenon_H68 zenon_H5f zenon_H65 zenon_H1b9 zenon_H2e zenon_H13b zenon_H11b. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.38 apply (zenon_L20_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.38 apply (zenon_L103_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.38 apply (zenon_L145_); trivial. % 10.16/10.38 apply (zenon_L817_); trivial. % 10.16/10.38 (* end of lemma zenon_L818_ *) % 10.16/10.38 assert (zenon_L819_ : (((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 (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_H1ce zenon_Hfd zenon_Hb8 zenon_H11b zenon_H106 zenon_H105 zenon_H112 zenon_H12a. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H1cf ]. % 10.16/10.38 apply (zenon_L235_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1d0 ]. % 10.16/10.38 apply (zenon_L712_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hf4 | zenon_intro zenon_He2 ]. % 10.16/10.38 apply (zenon_L70_); trivial. % 10.16/10.38 apply (zenon_L84_); trivial. % 10.16/10.38 (* end of lemma zenon_L819_ *) % 10.16/10.38 assert (zenon_L820_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hfd zenon_Hb8 zenon_H11b zenon_H106 zenon_H105 zenon_H12a. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.16/10.38 apply (zenon_L785_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.16/10.38 apply (zenon_L545_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.16/10.38 apply (zenon_L241_); trivial. % 10.16/10.38 apply (zenon_L819_); trivial. % 10.16/10.38 (* end of lemma zenon_L820_ *) % 10.16/10.38 assert (zenon_L821_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_H2a8 zenon_H25 zenon_H68 zenon_H30 zenon_H2d zenon_H1b9 zenon_H2e zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hfd zenon_Hb8 zenon_H11b zenon_H105 zenon_H12a. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.38 apply (zenon_L20_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.38 apply (zenon_L38_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.38 apply (zenon_L145_); trivial. % 10.16/10.38 apply (zenon_L820_); trivial. % 10.16/10.38 (* end of lemma zenon_L821_ *) % 10.16/10.38 assert (zenon_L822_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 10.16/10.38 do 0 intro. intros zenon_H2a8 zenon_H25 zenon_H68 zenon_H30 zenon_H2d zenon_H1b9 zenon_H2e zenon_H105 zenon_Hf4. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.16/10.38 apply (zenon_L20_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.16/10.38 apply (zenon_L38_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.16/10.38 apply (zenon_L145_); trivial. % 10.16/10.38 apply (zenon_L70_); trivial. % 10.16/10.38 (* end of lemma zenon_L822_ *) % 10.16/10.38 assert (zenon_L823_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (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) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_H155 zenon_H23 zenon_H12a zenon_H11b zenon_Hb8 zenon_H1ce zenon_H101 zenon_Ha9 zenon_H12c zenon_H5f zenon_H2a zenon_Hbe zenon_H20 zenon_H13d zenon_Heb zenon_H2a8 zenon_H25 zenon_H68 zenon_H30 zenon_H2d zenon_H1b9 zenon_H2e zenon_H105. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.16/10.38 apply (zenon_L4_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.16/10.38 apply (zenon_L794_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.16/10.38 apply (zenon_L33_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.16/10.38 apply (zenon_L818_); trivial. % 10.16/10.38 apply (zenon_L821_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.16/10.38 apply (zenon_L63_); trivial. % 10.16/10.38 apply (zenon_L822_); trivial. % 10.16/10.38 (* end of lemma zenon_L823_ *) % 10.16/10.38 assert (zenon_L824_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_H12f zenon_H11f zenon_H72 zenon_H2d zenon_Hd1 zenon_H30 zenon_H2e zenon_He2 zenon_H12a. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.16/10.38 apply (zenon_L78_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.16/10.38 apply (zenon_L79_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.16/10.38 apply (zenon_L9_); trivial. % 10.16/10.38 apply (zenon_L84_); trivial. % 10.16/10.38 (* end of lemma zenon_L824_ *) % 10.16/10.38 assert (zenon_L825_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H2c zenon_H2b2 zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_H30 zenon_H2e zenon_He2 zenon_H12a. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.38 apply (zenon_L370_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.38 apply (zenon_L65_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.38 apply (zenon_L365_); trivial. % 10.16/10.38 apply (zenon_L824_); trivial. % 10.16/10.38 (* end of lemma zenon_L825_ *) % 10.16/10.38 assert (zenon_L826_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H2d4 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H2c zenon_H2b2 zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_H30 zenon_H2e zenon_H12a. % 10.16/10.38 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.38 apply (zenon_L7_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.38 apply (zenon_L59_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.38 apply (zenon_L599_); trivial. % 10.16/10.38 apply (zenon_L825_); trivial. % 10.16/10.38 (* end of lemma zenon_L826_ *) % 10.16/10.38 assert (zenon_L827_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_H328 zenon_H1e zenon_H105 zenon_H1b9 zenon_H25 zenon_H2a8 zenon_Heb zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hb8 zenon_H23 zenon_H155 zenon_H12a zenon_H2e zenon_H30 zenon_Hd1 zenon_H2d zenon_H11f zenon_H12f zenon_H2c zenon_Hf1 zenon_H1c9 zenon_H130 zenon_H2d4 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H11b zenon_H16c. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.16/10.38 apply (zenon_L2_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.16/10.38 apply (zenon_L823_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.16/10.38 apply (zenon_L826_); trivial. % 10.16/10.38 apply (zenon_L793_); trivial. % 10.16/10.38 (* end of lemma zenon_L827_ *) % 10.16/10.38 assert (zenon_L828_ : (~((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.16/10.38 do 0 intro. intros zenon_H34a zenon_H2d. % 10.16/10.38 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.16/10.38 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 10.16/10.38 congruence. % 10.16/10.38 exact (zenon_H9b zenon_H2d). % 10.16/10.38 apply zenon_H1d. apply refl_equal. % 10.16/10.38 (* end of lemma zenon_L828_ *) % 10.16/10.38 assert (zenon_L829_ : ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (op (op (e1) (e1)) (e1)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_H149 zenon_H2d zenon_H34b. % 10.16/10.38 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H277 | zenon_intro zenon_H278 ]. % 10.16/10.38 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e2) = (op (op (e1) (e1)) (e1)))). % 10.16/10.38 intro zenon_D_pnotp. % 10.16/10.38 apply zenon_H34b. % 10.16/10.38 rewrite <- zenon_D_pnotp. % 10.16/10.38 exact zenon_H277. % 10.16/10.38 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 10.16/10.38 cut (((op (op (e1) (e1)) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H34c]. % 10.16/10.38 congruence. % 10.16/10.38 cut (((op (e3) (e1)) = (e2)) = ((op (op (e1) (e1)) (e1)) = (e2))). % 10.16/10.38 intro zenon_D_pnotp. % 10.16/10.38 apply zenon_H34c. % 10.16/10.38 rewrite <- zenon_D_pnotp. % 10.16/10.38 exact zenon_H149. % 10.16/10.38 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.16/10.38 cut (((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H34d]. % 10.16/10.38 congruence. % 10.16/10.38 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H277 | zenon_intro zenon_H278 ]. % 10.16/10.38 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))). % 10.16/10.38 intro zenon_D_pnotp. % 10.16/10.38 apply zenon_H34d. % 10.16/10.38 rewrite <- zenon_D_pnotp. % 10.16/10.38 exact zenon_H277. % 10.16/10.38 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 10.16/10.38 cut (((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H34a]. % 10.16/10.38 congruence. % 10.16/10.38 apply (zenon_L828_); trivial. % 10.16/10.38 apply zenon_H278. apply refl_equal. % 10.16/10.38 apply zenon_H278. apply refl_equal. % 10.16/10.38 apply zenon_H22. apply refl_equal. % 10.16/10.38 apply zenon_H278. apply refl_equal. % 10.16/10.38 apply zenon_H278. apply refl_equal. % 10.16/10.38 (* end of lemma zenon_L829_ *) % 10.16/10.38 assert (zenon_L830_ : ((op (e3) (e2)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> False). % 10.16/10.38 do 0 intro. intros zenon_H98 zenon_H149 zenon_H2d. % 10.16/10.38 apply (zenon_notand_s _ _ ax11); [ zenon_intro zenon_H34f | zenon_intro zenon_H34e ]. % 10.16/10.38 elim (classic ((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))); [ zenon_intro zenon_H27d | zenon_intro zenon_H27e ]. % 10.16/10.38 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1)))) = ((e0) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))). % 10.16/10.38 intro zenon_D_pnotp. % 10.16/10.38 apply zenon_H34f. % 10.16/10.38 rewrite <- zenon_D_pnotp. % 10.16/10.38 exact zenon_H27d. % 10.16/10.38 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H27e]. % 10.16/10.38 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H350]. % 10.16/10.38 congruence. % 10.16/10.38 cut (((op (e3) (e2)) = (e0)) = ((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (e0))). % 10.16/10.38 intro zenon_D_pnotp. % 10.16/10.38 apply zenon_H350. % 10.16/10.38 rewrite <- zenon_D_pnotp. % 10.16/10.38 exact zenon_H98. % 10.16/10.38 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.16/10.38 cut (((op (e3) (e2)) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H351]. % 10.16/10.38 congruence. % 10.16/10.38 elim (classic ((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))); [ zenon_intro zenon_H27d | zenon_intro zenon_H27e ]. % 10.16/10.38 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1)))) = ((op (e3) (e2)) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))). % 10.16/10.38 intro zenon_D_pnotp. % 10.16/10.38 apply zenon_H351. % 10.16/10.38 rewrite <- zenon_D_pnotp. % 10.16/10.38 exact zenon_H27d. % 10.16/10.38 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H27e]. % 10.16/10.38 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H352]. % 10.16/10.38 congruence. % 10.16/10.38 cut (((op (op (e1) (e1)) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H34c]. % 10.16/10.38 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 10.16/10.38 congruence. % 10.16/10.38 exact (zenon_H9b zenon_H2d). % 10.16/10.38 cut (((op (e3) (e1)) = (e2)) = ((op (op (e1) (e1)) (e1)) = (e2))). % 10.16/10.38 intro zenon_D_pnotp. % 10.16/10.38 apply zenon_H34c. % 10.16/10.38 rewrite <- zenon_D_pnotp. % 10.16/10.38 exact zenon_H149. % 10.16/10.38 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.16/10.38 cut (((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H34d]. % 10.16/10.38 congruence. % 10.16/10.38 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H277 | zenon_intro zenon_H278 ]. % 10.16/10.38 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))). % 10.16/10.38 intro zenon_D_pnotp. % 10.16/10.38 apply zenon_H34d. % 10.16/10.38 rewrite <- zenon_D_pnotp. % 10.16/10.38 exact zenon_H277. % 10.16/10.38 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 10.16/10.38 cut (((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H34a]. % 10.16/10.38 congruence. % 10.16/10.38 apply (zenon_L828_); trivial. % 10.16/10.38 apply zenon_H278. apply refl_equal. % 10.16/10.38 apply zenon_H278. apply refl_equal. % 10.16/10.38 apply zenon_H22. apply refl_equal. % 10.16/10.38 apply zenon_H27e. apply refl_equal. % 10.16/10.38 apply zenon_H27e. apply refl_equal. % 10.16/10.38 apply zenon_H34. apply refl_equal. % 10.16/10.38 apply zenon_H27e. apply refl_equal. % 10.16/10.38 apply zenon_H27e. apply refl_equal. % 10.16/10.38 apply (zenon_notand_s _ _ zenon_H34e); [ zenon_intro zenon_H353 | zenon_intro zenon_H34b ]. % 10.16/10.38 apply zenon_H353. apply sym_equal. exact zenon_H2d. % 10.16/10.38 apply (zenon_L829_); trivial. % 10.16/10.38 (* end of lemma zenon_L830_ *) % 10.16/10.38 assert (zenon_L831_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H7f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H112 zenon_H12a. % 10.16/10.38 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.38 apply (zenon_L7_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.38 apply (zenon_L59_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.38 apply (zenon_L329_); trivial. % 10.16/10.38 apply (zenon_L84_); trivial. % 10.16/10.38 (* end of lemma zenon_L831_ *) % 10.16/10.38 assert (zenon_L832_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_H1f6 zenon_H149 zenon_H1ea zenon_H11b zenon_H2e zenon_H7e zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H112 zenon_H12a. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.16/10.38 apply (zenon_L830_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.16/10.38 apply (zenon_L777_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.16/10.38 apply (zenon_L226_); trivial. % 10.16/10.38 apply (zenon_L831_); trivial. % 10.16/10.38 (* end of lemma zenon_L832_ *) % 10.16/10.38 assert (zenon_L833_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 10.16/10.38 do 0 intro. intros zenon_H14b zenon_H94 zenon_H98. % 10.16/10.38 cut (((op (e3) (e1)) = (e0)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 10.16/10.38 intro zenon_D_pnotp. % 10.16/10.38 apply zenon_H14b. % 10.16/10.38 rewrite <- zenon_D_pnotp. % 10.16/10.38 exact zenon_H94. % 10.16/10.38 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 10.16/10.38 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 10.16/10.38 congruence. % 10.16/10.38 apply zenon_H7c. apply refl_equal. % 10.16/10.38 apply zenon_H99. apply sym_equal. exact zenon_H98. % 10.16/10.38 (* end of lemma zenon_L833_ *) % 10.16/10.38 assert (zenon_L834_ : (((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 (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_H1f6 zenon_H94 zenon_H14b zenon_H188 zenon_H1ec zenon_H2e zenon_H7e zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H112 zenon_H12a. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.16/10.38 apply (zenon_L833_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.16/10.38 apply (zenon_L172_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.16/10.38 apply (zenon_L226_); trivial. % 10.16/10.38 apply (zenon_L831_); trivial. % 10.16/10.38 (* end of lemma zenon_L834_ *) % 10.16/10.38 assert (zenon_L835_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.16/10.38 do 0 intro. intros zenon_H14c zenon_H12a zenon_H112 zenon_H130 zenon_Hef zenon_Hf1 zenon_H113 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H7e zenon_H2e zenon_H1ec zenon_H188 zenon_H14b zenon_H1f6 zenon_H5e zenon_H7a zenon_H98 zenon_H93 zenon_H2d. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H94 | zenon_intro zenon_H14d ]. % 10.16/10.38 apply (zenon_L834_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 10.16/10.38 apply (zenon_L428_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H149 | zenon_intro zenon_H79 ]. % 10.16/10.38 apply (zenon_L830_); trivial. % 10.16/10.38 apply (zenon_L91_); trivial. % 10.16/10.38 (* end of lemma zenon_L835_ *) % 10.16/10.38 assert (zenon_L836_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.16/10.38 do 0 intro. intros zenon_H12f zenon_H11f zenon_H72 zenon_Hd1 zenon_H30 zenon_H14c zenon_H12a zenon_H130 zenon_Hef zenon_Hf1 zenon_H113 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H7e zenon_H2e zenon_H1ec zenon_H188 zenon_H14b zenon_H1f6 zenon_H5e zenon_H7a zenon_H98 zenon_H93 zenon_H2d. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.16/10.38 apply (zenon_L78_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.16/10.38 apply (zenon_L79_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.16/10.38 apply (zenon_L9_); trivial. % 10.16/10.38 apply (zenon_L835_); trivial. % 10.16/10.38 (* end of lemma zenon_L836_ *) % 10.16/10.38 assert (zenon_L837_ : (((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 (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.16/10.38 do 0 intro. intros zenon_H192 zenon_H86 zenon_H11f zenon_H65 zenon_H7a zenon_H2e zenon_H7e zenon_H11b zenon_H25. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.16/10.38 apply (zenon_L123_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.16/10.38 apply (zenon_L94_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.16/10.38 apply (zenon_L226_); trivial. % 10.16/10.38 apply (zenon_L521_); trivial. % 10.16/10.38 (* end of lemma zenon_L837_ *) % 10.16/10.38 assert (zenon_L838_ : ((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3)))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_H41 zenon_H1e zenon_H22d zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H2c zenon_H30 zenon_H22f zenon_H105 zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H16c zenon_H1ec zenon_Hbe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H7e zenon_H7a zenon_H74 zenon_H2fa zenon_H1b9 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H25 zenon_H23 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_Hef zenon_H1ce zenon_H127 zenon_H12c zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H101 zenon_H1ea zenon_H1f6 zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H20 zenon_H2e zenon_H5e zenon_H2d zenon_H91 zenon_H272 zenon_H2b2 zenon_H11b zenon_Hfe. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.38 apply (zenon_L823_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.38 apply (zenon_L13_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.16/10.38 apply (zenon_L365_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.16/10.38 apply (zenon_L79_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.16/10.38 apply (zenon_L9_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.16/10.38 apply (zenon_L35_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.16/10.38 apply (zenon_L834_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.16/10.38 apply (zenon_L835_); trivial. % 10.16/10.38 apply (zenon_L500_); trivial. % 10.16/10.38 apply (zenon_L510_); trivial. % 10.16/10.38 (* end of lemma zenon_L838_ *) % 10.16/10.38 assert (zenon_L839_ : ((op (e0) (e1)) = (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)))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((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 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(e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_H65 zenon_H41 zenon_H1e zenon_H22d zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H2c zenon_H30 zenon_H22f zenon_H105 zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H16c zenon_H1ec zenon_Hbe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H7e zenon_H7a zenon_H74 zenon_H2fa zenon_H1b9 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H25 zenon_H23 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_Hef zenon_H1ce zenon_H127 zenon_H12c zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H101 zenon_H1ea zenon_H1f6 zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H20 zenon_H2e zenon_H5e zenon_H2d zenon_H272 zenon_H2b2 zenon_H11b zenon_Hfe. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.38 apply (zenon_L4_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.38 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.38 apply (zenon_L7_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.38 apply (zenon_L59_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.38 apply (zenon_L64_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.38 apply (zenon_L65_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.38 apply (zenon_L365_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.38 apply (zenon_L20_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.38 apply (zenon_L13_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.16/10.38 apply (zenon_L365_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.16/10.38 apply (zenon_L79_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.16/10.38 apply (zenon_L9_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.16/10.38 apply (zenon_L35_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.16/10.38 apply (zenon_L832_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.16/10.38 apply (zenon_L226_); trivial. % 10.16/10.38 apply (zenon_L521_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.16/10.38 apply (zenon_L834_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.16/10.38 apply (zenon_L836_); trivial. % 10.16/10.38 apply (zenon_L500_); trivial. % 10.16/10.38 apply (zenon_L510_); trivial. % 10.16/10.38 apply (zenon_L825_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.38 apply (zenon_L837_); trivial. % 10.16/10.38 apply (zenon_L838_); trivial. % 10.16/10.38 (* end of lemma zenon_L839_ *) % 10.16/10.38 assert (zenon_L840_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_H192 zenon_H23 zenon_H90 zenon_H12a zenon_H112 zenon_H130 zenon_Hef zenon_Hf1 zenon_H2d zenon_H113 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H11b zenon_H1ea zenon_H1f6 zenon_H2e zenon_H7e zenon_Hf4 zenon_Hb8. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.16/10.38 apply (zenon_L35_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.16/10.38 apply (zenon_L832_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.16/10.38 apply (zenon_L226_); trivial. % 10.16/10.38 apply (zenon_L344_); trivial. % 10.16/10.38 (* end of lemma zenon_L840_ *) % 10.16/10.38 assert (zenon_L841_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((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)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((~((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) (e0)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.38 do 0 intro. intros zenon_Hfe zenon_H11b zenon_H272 zenon_Hb8 zenon_H1ea zenon_H23 zenon_H192 zenon_H93 zenon_H7a zenon_H5e zenon_H1f6 zenon_H14b zenon_H1ec zenon_H7e zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H113 zenon_Hef zenon_H14c zenon_H124 zenon_H25 zenon_Hf6 zenon_H101 zenon_H105 zenon_Hf4 zenon_H10d zenon_H1e zenon_H41 zenon_H69 zenon_H301 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H2c zenon_H2b2 zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_H30 zenon_H2e zenon_H12a. % 10.16/10.38 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.38 apply (zenon_L7_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.38 apply (zenon_L59_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.38 apply (zenon_L64_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.38 apply (zenon_L65_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.38 apply (zenon_L365_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.38 apply (zenon_L20_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.38 apply (zenon_L13_); trivial. % 10.16/10.38 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.16/10.39 apply (zenon_L78_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.16/10.39 apply (zenon_L79_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.16/10.39 apply (zenon_L9_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.16/10.39 apply (zenon_L840_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.16/10.39 apply (zenon_L834_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.16/10.39 apply (zenon_L836_); trivial. % 10.16/10.39 apply (zenon_L82_); trivial. % 10.16/10.39 apply (zenon_L510_); trivial. % 10.16/10.39 apply (zenon_L825_); trivial. % 10.16/10.39 (* end of lemma zenon_L841_ *) % 10.16/10.39 assert (zenon_L842_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((~((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) (op (e1) (e3))) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.16/10.39 do 0 intro. intros zenon_H328 zenon_Hfe zenon_H272 zenon_H2d zenon_H5e zenon_H2e zenon_H20 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2c zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_H22d zenon_H1e zenon_H41 zenon_Hf6 zenon_H11b zenon_H16c. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.16/10.39 apply (zenon_L2_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.16/10.39 apply (zenon_L823_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.16/10.39 apply (zenon_L4_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.16/10.39 apply (zenon_L839_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.16/10.39 apply (zenon_L63_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.39 apply (zenon_L4_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.39 apply (zenon_L841_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.39 apply (zenon_L684_); trivial. % 10.16/10.39 apply (zenon_L838_); trivial. % 10.16/10.39 apply (zenon_L793_); trivial. % 10.16/10.39 (* end of lemma zenon_L842_ *) % 10.16/10.39 assert (zenon_L843_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.39 do 0 intro. intros zenon_H1f6 zenon_H91 zenon_H188 zenon_H1ec zenon_H5d zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H112 zenon_H12a. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.16/10.39 apply (zenon_L810_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.16/10.39 apply (zenon_L172_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.16/10.39 apply (zenon_L208_); trivial. % 10.16/10.39 apply (zenon_L831_); trivial. % 10.16/10.39 (* end of lemma zenon_L843_ *) % 10.16/10.39 assert (zenon_L844_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.16/10.39 do 0 intro. intros zenon_H192 zenon_H12a zenon_H112 zenon_H130 zenon_Hef zenon_Hf1 zenon_H113 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H5d zenon_H1ec zenon_H188 zenon_H1f6 zenon_H2d zenon_H98 zenon_H2e zenon_H7e zenon_H11b zenon_H25. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.16/10.39 apply (zenon_L843_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.16/10.39 apply (zenon_L830_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.16/10.39 apply (zenon_L226_); trivial. % 10.16/10.39 apply (zenon_L521_); trivial. % 10.16/10.39 (* end of lemma zenon_L844_ *) % 10.16/10.39 assert (zenon_L845_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> False). % 10.16/10.39 do 0 intro. intros zenon_H272 zenon_H14b zenon_H25 zenon_H11b zenon_H7e zenon_H2e zenon_H1f6 zenon_H188 zenon_H1ec zenon_H5d zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H12a zenon_H192 zenon_H130 zenon_Hde zenon_Hef zenon_Hf1 zenon_H2d zenon_H113 zenon_H112 zenon_H5a. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.16/10.39 apply (zenon_L381_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.16/10.39 apply (zenon_L834_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.16/10.39 apply (zenon_L844_); trivial. % 10.16/10.39 apply (zenon_L99_); trivial. % 10.16/10.39 (* end of lemma zenon_L845_ *) % 10.16/10.39 assert (zenon_L846_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> False). % 10.16/10.39 do 0 intro. intros zenon_H12f zenon_H11f zenon_H72 zenon_Hd1 zenon_Heb zenon_H272 zenon_H14b zenon_H25 zenon_H11b zenon_H7e zenon_H2e zenon_H1f6 zenon_H188 zenon_H1ec zenon_H5d zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H12a zenon_H192 zenon_H130 zenon_Hde zenon_Hef zenon_Hf1 zenon_H2d zenon_H113 zenon_H5a. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.16/10.39 apply (zenon_L78_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.16/10.39 apply (zenon_L79_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.16/10.39 apply (zenon_L259_); trivial. % 10.16/10.39 apply (zenon_L845_); trivial. % 10.16/10.39 (* end of lemma zenon_L846_ *) % 10.16/10.39 assert (zenon_L847_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((((op (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.16/10.39 do 0 intro. intros zenon_H16c zenon_Hfe zenon_Heb zenon_H272 zenon_H14b zenon_H25 zenon_H7e zenon_H1f6 zenon_H1ec zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H155 zenon_H23 zenon_Hb8 zenon_H1ce zenon_H101 zenon_Ha9 zenon_H12c zenon_Hbe zenon_H13d zenon_H2a8 zenon_H1b9 zenon_H105 zenon_H301 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_H1e zenon_H328 zenon_H22d zenon_H13a zenon_H2ac zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H141 zenon_H22f zenon_H2fe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H1d4 zenon_H7a zenon_H74 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H1ea zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H10d zenon_H304 zenon_H30 zenon_H2e zenon_H11b zenon_H2c. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.16/10.39 apply (zenon_L7_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.16/10.39 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 10.16/10.39 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_Hd8. zenon_intro zenon_H15b. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.39 apply (zenon_L2_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.39 apply (zenon_L265_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.39 apply (zenon_L827_); trivial. % 10.16/10.39 apply (zenon_L712_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.16/10.39 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 10.16/10.39 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H3c. zenon_intro zenon_H44. % 10.16/10.39 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H160. zenon_intro zenon_Hf6. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.39 apply (zenon_L2_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.39 apply (zenon_L842_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.39 apply (zenon_L827_); trivial. % 10.16/10.39 apply (zenon_L712_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.16/10.39 apply (zenon_L15_); trivial. % 10.16/10.39 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.16/10.39 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 10.16/10.39 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H51. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.16/10.39 apply (zenon_L2_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.16/10.39 apply (zenon_L823_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.16/10.39 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.39 apply (zenon_L7_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.39 apply (zenon_L59_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.39 apply (zenon_L64_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.39 apply (zenon_L65_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.39 apply (zenon_L365_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.16/10.39 apply (zenon_L823_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.16/10.39 apply (zenon_L8_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.16/10.39 apply (zenon_L846_); trivial. % 10.16/10.39 apply (zenon_L510_); trivial. % 10.16/10.39 apply (zenon_L825_); trivial. % 10.16/10.39 apply (zenon_L793_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.16/10.39 apply (zenon_L9_); trivial. % 10.16/10.39 apply (zenon_L505_); trivial. % 10.16/10.39 (* end of lemma zenon_L847_ *) % 10.16/10.39 assert (zenon_L848_ : ((op (e1) (e1)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (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) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (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 (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> False). % 10.16/10.39 do 0 intro. intros zenon_H26 zenon_H86 zenon_H188 zenon_H2c zenon_H11b zenon_H30 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1ea zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H127 zenon_H2ee zenon_H156 zenon_H1dc zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H1d4 zenon_H2dd zenon_H2c4 zenon_H22e zenon_H2fe zenon_H22f zenon_H141 zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13a zenon_H22d zenon_H328 zenon_H1e zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_Hf1 zenon_H1c9 zenon_H130 zenon_H301 zenon_H105 zenon_H1b9 zenon_H2a8 zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hb8 zenon_H23 zenon_H155 zenon_H113 zenon_Hef zenon_H192 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H1ec zenon_H1f6 zenon_H7e zenon_H25 zenon_H14b zenon_H272 zenon_Heb zenon_Hfe zenon_H16c zenon_H5d. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.16/10.39 apply (zenon_L522_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.16/10.39 apply (zenon_L250_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.16/10.39 apply (zenon_L847_); trivial. % 10.16/10.39 apply (zenon_L208_); trivial. % 10.16/10.39 (* end of lemma zenon_L848_ *) % 10.16/10.39 assert (zenon_L849_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((((op (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.16/10.39 do 0 intro. intros zenon_H338 zenon_H335 zenon_H5e zenon_H5d zenon_H16c zenon_Hfe zenon_Heb zenon_H272 zenon_H14b zenon_H25 zenon_H7e zenon_H1f6 zenon_H1ec zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H155 zenon_H23 zenon_Hb8 zenon_H1ce zenon_H101 zenon_Ha9 zenon_H12c zenon_Hbe zenon_H13d zenon_H2a8 zenon_H1b9 zenon_H105 zenon_H301 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_H1e zenon_H328 zenon_H22d zenon_H13a zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H141 zenon_H22f zenon_H2fe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H1d4 zenon_H7a zenon_H74 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H10d zenon_H304 zenon_H30 zenon_H2c zenon_H86 zenon_H26 zenon_H2ac zenon_H18c zenon_H11b zenon_H1ea. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H2d4 | zenon_intro zenon_H339 ]. % 10.16/10.39 apply (zenon_L776_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H188 | zenon_intro zenon_H33a ]. % 10.16/10.39 apply (zenon_L848_); trivial. % 10.16/10.39 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H1ed ]. % 10.16/10.39 apply (zenon_L455_); trivial. % 10.16/10.39 apply (zenon_L777_); trivial. % 10.16/10.39 (* end of lemma zenon_L849_ *) % 10.16/10.39 assert (zenon_L850_ : ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((((op (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.40 do 0 intro. intros zenon_H68 zenon_Ha9 zenon_H11b zenon_H2c zenon_H338 zenon_H335 zenon_H5e zenon_H5d zenon_H16c zenon_Hfe zenon_Heb zenon_H272 zenon_H14b zenon_H25 zenon_H7e zenon_H1f6 zenon_H1ec zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H155 zenon_H23 zenon_Hb8 zenon_H1ce zenon_H101 zenon_H12c zenon_Hbe zenon_H13d zenon_H2a8 zenon_H1b9 zenon_H105 zenon_H301 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H12f zenon_H1e zenon_H328 zenon_H22d zenon_H13a zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H141 zenon_H22f zenon_H2fe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H1d4 zenon_H7a zenon_H74 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H10d zenon_H304 zenon_H2ac zenon_H1ea zenon_H2b4 zenon_H1cb zenon_H11f zenon_H26 zenon_Hd1 zenon_H30 zenon_H2f zenon_Hf4 zenon_H12a. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.40 apply (zenon_L4_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.40 apply (zenon_L20_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b5 ]. % 10.16/10.40 apply (zenon_L792_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H18c | zenon_intro zenon_H2b6 ]. % 10.16/10.40 apply (zenon_L849_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H102 ]. % 10.16/10.40 apply (zenon_L438_); trivial. % 10.16/10.40 apply (zenon_L545_); trivial. % 10.16/10.40 apply (zenon_L156_); trivial. % 10.16/10.40 (* end of lemma zenon_L850_ *) % 10.16/10.40 assert (zenon_L851_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e3) (e3)) = (e1)) -> False). % 10.16/10.40 do 0 intro. intros zenon_H1d1 zenon_Hef zenon_Hf1 zenon_H25 zenon_H96 zenon_Hd0 zenon_H93 zenon_H11f zenon_H192 zenon_He8 zenon_H2a zenon_H6d zenon_H51 zenon_H1f6 zenon_H1ea zenon_H5d zenon_H1f5 zenon_H2c zenon_H2d4 zenon_H2ee zenon_Hb8 zenon_H7e zenon_H7a zenon_H22e zenon_H74 zenon_H1b9 zenon_H105 zenon_H83 zenon_H30 zenon_H26 zenon_H2ac zenon_H2f zenon_H5c zenon_H11b. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.40 apply (zenon_L152_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.40 apply (zenon_L163_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.40 apply (zenon_L522_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.40 apply (zenon_L21_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.40 apply (zenon_L812_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.40 apply (zenon_L599_); trivial. % 10.16/10.40 apply (zenon_L813_); trivial. % 10.16/10.40 (* end of lemma zenon_L851_ *) % 10.16/10.40 assert (zenon_L852_ : (((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 (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.40 do 0 intro. intros zenon_H1ce zenon_Hfd zenon_Hb8 zenon_H11b zenon_H12a zenon_H128 zenon_H109 zenon_H105. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H1cf ]. % 10.16/10.40 apply (zenon_L235_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1d0 ]. % 10.16/10.40 apply (zenon_L712_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hf4 | zenon_intro zenon_He2 ]. % 10.16/10.40 apply (zenon_L105_); trivial. % 10.16/10.40 apply (zenon_L71_); trivial. % 10.16/10.40 (* end of lemma zenon_L852_ *) % 10.16/10.40 assert (zenon_L853_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (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)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.40 do 0 intro. intros zenon_H22e zenon_H74 zenon_H72 zenon_H30 zenon_H1b9 zenon_H2f zenon_H1cb zenon_H91 zenon_H11f zenon_H26 zenon_Hd1 zenon_Heb zenon_Hd0 zenon_H1ce zenon_Hfd zenon_Hb8 zenon_H11b zenon_H12a zenon_H105. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.16/10.40 apply (zenon_L23_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.16/10.40 apply (zenon_L38_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.16/10.40 apply (zenon_L174_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.16/10.40 apply (zenon_L123_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.16/10.40 apply (zenon_L56_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.16/10.40 apply (zenon_L63_); trivial. % 10.16/10.40 apply (zenon_L852_); trivial. % 10.16/10.40 (* end of lemma zenon_L853_ *) % 10.16/10.40 assert (zenon_L854_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (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))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.16/10.40 do 0 intro. intros zenon_H83 zenon_H105 zenon_H12a zenon_Hb8 zenon_Hfd zenon_H1ce zenon_Hd0 zenon_Heb zenon_Hd1 zenon_H26 zenon_H11f zenon_H91 zenon_H1cb zenon_H1b9 zenon_H30 zenon_H74 zenon_H22e zenon_H5c zenon_H2f zenon_H7e zenon_H11b zenon_H2c. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.16/10.40 apply (zenon_L853_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.16/10.40 apply (zenon_L721_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.16/10.40 apply (zenon_L25_); trivial. % 10.16/10.40 apply (zenon_L505_); trivial. % 10.16/10.40 (* end of lemma zenon_L854_ *) % 10.16/10.40 assert (zenon_L855_ : ((op (e0) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (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) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (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) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.16/10.40 do 0 intro. intros zenon_H20 zenon_H25 zenon_H101 zenon_H127 zenon_Ha9 zenon_H12c zenon_H2ee zenon_H64 zenon_H187 zenon_H1ec zenon_H2c4 zenon_H1d4 zenon_Hbe zenon_H272 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_Hef zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H154 zenon_H192 zenon_H93 zenon_H96 zenon_H2fa zenon_H7a zenon_H12f zenon_H2dd zenon_H16c zenon_H155 zenon_H5f zenon_H2fe zenon_H22f zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H2f7 zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13d zenon_Hfe zenon_H22d zenon_H1e zenon_H2a zenon_H2ae zenon_H97 zenon_H13a zenon_H83 zenon_H105 zenon_H12a zenon_Hb8 zenon_H1ce zenon_Hd0 zenon_Heb zenon_Hd1 zenon_H26 zenon_H11f zenon_H1cb zenon_H1b9 zenon_H30 zenon_H74 zenon_H22e zenon_H5c zenon_H2f zenon_H7e zenon_H11b zenon_H2c. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.40 apply (zenon_L152_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.40 apply (zenon_L163_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.40 apply (zenon_L522_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.16/10.40 apply (zenon_L794_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.16/10.40 apply (zenon_L730_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.16/10.40 apply (zenon_L89_); trivial. % 10.16/10.40 apply (zenon_L854_); trivial. % 10.16/10.40 (* end of lemma zenon_L855_ *) % 10.16/10.40 assert (zenon_L856_ : (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (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) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.16/10.40 do 0 intro. intros zenon_H2c zenon_H11b zenon_H7e zenon_H5c zenon_H22e zenon_H74 zenon_H1b9 zenon_Heb zenon_H1ce zenon_Hb8 zenon_H105 zenon_H83 zenon_H13a zenon_H97 zenon_H2ae zenon_H2a zenon_H1e zenon_H22d zenon_Hfe zenon_H13d zenon_H2ac zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H2f7 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H22f zenon_H2fe zenon_H5f zenon_H155 zenon_H16c zenon_H2dd zenon_H12f zenon_H7a zenon_H2fa zenon_H96 zenon_H93 zenon_H192 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_Hef zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1f6 zenon_H1d9 zenon_H1d7 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H272 zenon_Hbe zenon_H1d4 zenon_H2c4 zenon_H1ec zenon_H187 zenon_H64 zenon_H2ee zenon_H12c zenon_Ha9 zenon_H127 zenon_H101 zenon_H1d1 zenon_H20 zenon_H25 zenon_H68 zenon_H9e zenon_H23 zenon_H1cb zenon_H11f zenon_H26 zenon_Hd1 zenon_H30 zenon_H2f zenon_H12a. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.16/10.40 apply (zenon_L4_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.16/10.40 apply (zenon_L103_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.16/10.40 apply (zenon_L855_); trivial. % 10.16/10.40 apply (zenon_L791_); trivial. % 10.16/10.40 (* end of lemma zenon_L856_ *) % 10.16/10.40 assert (zenon_L857_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 10.16/10.40 do 0 intro. intros zenon_Hc6 zenon_Hbe zenon_H20. % 10.16/10.40 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_H89. zenon_intro zenon_Hc7. % 10.16/10.40 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_H9d. zenon_intro zenon_Hc8. % 10.16/10.40 apply (zenon_L794_); trivial. % 10.16/10.40 (* end of lemma zenon_L857_ *) % 10.16/10.40 assert (zenon_L858_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 10.16/10.40 do 0 intro. intros zenon_H1e8 zenon_Hbe zenon_H20. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H1e8). zenon_intro zenon_H72. zenon_intro zenon_H1e9. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H1e9). zenon_intro zenon_He2. zenon_intro zenon_Hb3. % 10.16/10.40 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.16/10.40 apply (zenon_L794_); trivial. % 10.16/10.40 (* end of lemma zenon_L858_ *) % 10.16/10.40 assert (zenon_L859_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (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) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.16/10.40 do 0 intro. intros zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H2ae zenon_H2c zenon_H30 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1ea zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H127 zenon_H2ee zenon_H156 zenon_H1dc zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H1d4 zenon_H2dd zenon_H2c4 zenon_H22e zenon_H2fe zenon_H22f zenon_H141 zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13a zenon_H22d zenon_H328 zenon_H1e zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_Hf1 zenon_H1c9 zenon_H130 zenon_H301 zenon_H105 zenon_H1b9 zenon_H2a8 zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hb8 zenon_H23 zenon_H155 zenon_H113 zenon_Hef zenon_H192 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H272 zenon_Heb zenon_Hfe zenon_H16c zenon_H11b zenon_H25. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H24 | zenon_intro zenon_H230 ]. % 10.16/10.40 apply (zenon_L4_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H26 | zenon_intro zenon_H231 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.16/10.40 apply (zenon_L7_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.16/10.40 apply (zenon_L38_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.16/10.40 apply (zenon_L11_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H3c. zenon_intro zenon_H44. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H160. zenon_intro zenon_Hf6. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.40 apply (zenon_L2_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.40 apply (zenon_L778_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.16/10.40 apply (zenon_L2_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.16/10.40 apply (zenon_L4_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.16/10.40 apply (zenon_L103_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.40 apply (zenon_L152_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.40 apply (zenon_L163_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.40 apply (zenon_L522_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.40 apply (zenon_L21_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.40 apply (zenon_L780_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.40 apply (zenon_L259_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.40 apply (zenon_L370_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.40 apply (zenon_L790_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.40 apply (zenon_L161_); trivial. % 10.16/10.40 apply (zenon_L781_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.40 apply (zenon_L7_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.40 apply (zenon_L780_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.40 apply (zenon_L599_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.40 apply (zenon_L370_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.16/10.40 apply (zenon_L782_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.16/10.40 apply (zenon_L65_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.16/10.40 apply (zenon_L389_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.16/10.40 apply (zenon_L791_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.16/10.40 apply (zenon_L784_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.16/10.40 apply (zenon_L556_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hfd | zenon_intro zenon_H10e ]. % 10.16/10.40 apply (zenon_L785_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H10f ]. % 10.16/10.40 apply (zenon_L510_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H106 | zenon_intro zenon_H109 ]. % 10.16/10.40 apply (zenon_L70_); trivial. % 10.16/10.40 apply (zenon_L71_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.40 apply (zenon_L161_); trivial. % 10.16/10.40 apply (zenon_L781_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.16/10.40 apply (zenon_L424_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.16/10.40 apply (zenon_L103_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.40 apply (zenon_L152_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.40 apply (zenon_L163_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.40 apply (zenon_L522_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.40 apply (zenon_L7_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.40 apply (zenon_L780_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.40 apply (zenon_L259_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.40 apply (zenon_L370_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.40 apply (zenon_L790_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.40 apply (zenon_L365_); trivial. % 10.16/10.40 apply (zenon_L781_); trivial. % 10.16/10.40 apply (zenon_L792_); trivial. % 10.16/10.40 apply (zenon_L793_); trivial. % 10.16/10.40 apply (zenon_L712_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.16/10.40 apply (zenon_L795_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.16/10.40 apply (zenon_and_s _ _ zenon_Hb4). zenon_intro zenon_H20. zenon_intro zenon_Hb5. % 10.16/10.40 apply (zenon_and_s _ _ zenon_Hb5). zenon_intro zenon_H20. zenon_intro zenon_Hb6. % 10.16/10.40 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.40 apply (zenon_L2_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.40 apply (zenon_L778_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.40 apply (zenon_L711_); trivial. % 10.16/10.40 apply (zenon_L712_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.16/10.40 apply (zenon_and_s _ _ zenon_Hbb). zenon_intro zenon_H20. zenon_intro zenon_Hbc. % 10.16/10.40 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_H20. zenon_intro zenon_Hbd. % 10.16/10.40 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.40 apply (zenon_L2_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.40 apply (zenon_L778_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.16/10.40 apply (zenon_L2_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.16/10.40 apply (zenon_L4_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.16/10.40 apply (zenon_L103_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.16/10.40 apply (zenon_L796_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.40 apply (zenon_L4_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.40 apply (zenon_L163_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.40 apply (zenon_L7_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.16/10.40 apply (zenon_L7_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.16/10.40 apply (zenon_L798_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.16/10.40 apply (zenon_L161_); trivial. % 10.16/10.40 apply (zenon_L779_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.40 apply (zenon_L599_); trivial. % 10.16/10.40 apply (zenon_L799_); trivial. % 10.16/10.40 apply (zenon_L156_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.16/10.40 apply (zenon_L800_); trivial. % 10.16/10.40 apply (zenon_L793_); trivial. % 10.16/10.40 apply (zenon_L712_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.16/10.40 apply (zenon_L302_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.16/10.40 apply (zenon_L51_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.16/10.40 apply (zenon_L303_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.16/10.40 apply (zenon_L304_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.16/10.40 apply (zenon_L55_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.16/10.40 apply (zenon_L306_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.16/10.40 apply (zenon_L254_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H169). zenon_intro zenon_H97. zenon_intro zenon_H16a. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.40 apply (zenon_L107_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.40 apply (zenon_L778_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.40 apply (zenon_L711_); trivial. % 10.16/10.40 apply (zenon_L712_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.16/10.40 apply (zenon_L801_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.16/10.40 apply (zenon_L308_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.16/10.40 apply (zenon_L262_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.16/10.40 apply (zenon_L515_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H68. zenon_intro zenon_H17c. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H17c). zenon_intro zenon_H5e. zenon_intro zenon_H6f. % 10.16/10.40 apply (zenon_L778_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.16/10.40 apply (zenon_L309_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H68. zenon_intro zenon_H180. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H5e. zenon_intro zenon_Hb6. % 10.16/10.40 apply (zenon_L778_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_H5e. zenon_intro zenon_Hbd. % 10.16/10.40 apply (zenon_L778_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.16/10.40 apply (zenon_L117_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.16/10.40 apply (zenon_L118_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.16/10.40 apply (zenon_L121_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.16/10.40 apply (zenon_L122_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.16/10.40 apply (zenon_L523_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.16/10.40 apply (zenon_L128_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.16/10.40 apply (zenon_L129_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.16/10.40 apply (zenon_L802_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.16/10.40 apply (zenon_L718_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.16/10.40 apply (zenon_L133_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.16/10.40 apply (zenon_L134_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.16/10.40 apply (zenon_L525_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.16/10.40 apply (zenon_L803_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.16/10.40 apply (zenon_L361_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.16/10.40 apply (zenon_L138_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.16/10.40 apply (zenon_L528_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.16/10.40 apply (zenon_L140_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.16/10.40 apply (zenon_L141_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.16/10.40 apply (zenon_L142_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.16/10.40 apply (zenon_L591_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.16/10.40 apply (zenon_L284_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.16/10.40 apply (zenon_L193_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.16/10.40 apply (zenon_L147_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.16/10.40 apply (zenon_L149_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H128. zenon_intro zenon_H1c3. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H1c3). zenon_intro zenon_H166. zenon_intro zenon_H171. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.16/10.40 apply (zenon_L781_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.16/10.40 apply (zenon_L593_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.16/10.40 apply (zenon_L167_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.16/10.40 apply (zenon_L530_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.16/10.40 apply (zenon_L804_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.16/10.40 apply (zenon_L195_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.16/10.40 apply (zenon_L805_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.16/10.40 apply (zenon_L806_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.16/10.40 apply (zenon_L808_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.16/10.40 apply (zenon_L182_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.16/10.40 apply (zenon_L595_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.16/10.40 apply (zenon_L183_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.16/10.40 apply (zenon_L294_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.16/10.40 apply (zenon_L196_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.16/10.40 apply (zenon_L186_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.16/10.40 apply (zenon_L187_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.16/10.40 apply (zenon_L296_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.16/10.40 apply (zenon_L298_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.16/10.40 apply (zenon_L300_); trivial. % 10.16/10.40 apply (zenon_L538_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b5 ]. % 10.16/10.40 apply (zenon_L809_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H18c | zenon_intro zenon_H2b6 ]. % 10.16/10.40 apply (zenon_L205_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H102 ]. % 10.16/10.40 apply (zenon_L438_); trivial. % 10.16/10.40 apply (zenon_L545_); trivial. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H51. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.16/10.40 apply (zenon_L2_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.16/10.40 apply (zenon_L2_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.16/10.40 apply (zenon_L4_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.16/10.40 apply (zenon_L103_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.40 apply (zenon_L152_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.40 apply (zenon_L163_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.40 apply (zenon_L522_); trivial. % 10.16/10.40 apply (zenon_L814_); trivial. % 10.16/10.40 apply (zenon_L850_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.16/10.40 apply (zenon_L424_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.16/10.40 apply (zenon_L103_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.40 apply (zenon_L152_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.40 apply (zenon_L163_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.40 apply (zenon_L684_); trivial. % 10.16/10.40 apply (zenon_L814_); trivial. % 10.16/10.40 apply (zenon_L792_); trivial. % 10.16/10.40 apply (zenon_L793_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.16/10.40 apply (zenon_L4_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.16/10.40 apply (zenon_L103_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.16/10.40 apply (zenon_L851_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.40 apply (zenon_L424_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.40 apply (zenon_L163_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.16/10.40 apply (zenon_L522_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.16/10.40 apply (zenon_L173_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.16/10.40 apply (zenon_L847_); trivial. % 10.16/10.40 apply (zenon_L208_); trivial. % 10.16/10.40 apply (zenon_L156_); trivial. % 10.16/10.40 apply (zenon_L712_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.16/10.40 apply (zenon_L795_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.16/10.40 apply (zenon_and_s _ _ zenon_Hb4). zenon_intro zenon_H20. zenon_intro zenon_Hb5. % 10.16/10.40 apply (zenon_and_s _ _ zenon_Hb5). zenon_intro zenon_H20. zenon_intro zenon_Hb6. % 10.16/10.40 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.16/10.40 apply (zenon_L46_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.16/10.40 apply (zenon_L856_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.16/10.40 apply (zenon_L426_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.16/10.40 apply (zenon_L103_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.16/10.40 apply (zenon_L855_); trivial. % 10.16/10.40 apply (zenon_L792_); trivial. % 10.16/10.40 apply (zenon_L793_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.16/10.40 apply (zenon_L502_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.16/10.40 apply (zenon_L246_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.16/10.40 apply (zenon_L51_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.16/10.40 apply (zenon_L857_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.16/10.40 apply (zenon_L207_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.16/10.40 apply (zenon_L55_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.16/10.40 apply (zenon_L57_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.16/10.40 apply (zenon_L254_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.16/10.40 apply (zenon_L209_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.16/10.40 apply (zenon_L700_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.16/10.40 apply (zenon_L722_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.16/10.40 apply (zenon_L262_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.16/10.40 apply (zenon_L515_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H68. zenon_intro zenon_H17c. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H17c). zenon_intro zenon_H5e. zenon_intro zenon_H6f. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H20. zenon_intro zenon_H20. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.16/10.40 apply (zenon_L568_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.16/10.40 apply (zenon_L103_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.16/10.40 apply (zenon_L152_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.16/10.40 apply (zenon_L163_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.16/10.40 apply (zenon_L522_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.16/10.40 apply (zenon_L516_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.16/10.40 apply (zenon_L812_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.16/10.40 apply (zenon_L259_); trivial. % 10.16/10.40 apply (zenon_L813_); trivial. % 10.16/10.40 apply (zenon_L850_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.16/10.40 apply (zenon_L264_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H68. zenon_intro zenon_H180. % 10.16/10.40 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H5e. zenon_intro zenon_Hb6. % 10.16/10.40 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 10.16/10.40 apply (zenon_L856_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.16/10.40 apply (zenon_L553_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.16/10.40 apply (zenon_L117_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.16/10.40 apply (zenon_L118_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.16/10.40 apply (zenon_L121_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.16/10.40 apply (zenon_L583_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.16/10.40 apply (zenon_L523_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.16/10.40 apply (zenon_L128_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.16/10.40 apply (zenon_L129_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.16/10.40 apply (zenon_L211_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.16/10.40 apply (zenon_L703_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.16/10.40 apply (zenon_L133_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.16/10.40 apply (zenon_L134_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.16/10.40 apply (zenon_L525_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.16/10.40 apply (zenon_L803_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.16/10.40 apply (zenon_L527_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.16/10.40 apply (zenon_L138_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.16/10.40 apply (zenon_L578_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.16/10.40 apply (zenon_L140_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.16/10.40 apply (zenon_L141_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.16/10.40 apply (zenon_L142_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.16/10.40 apply (zenon_L586_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.16/10.40 apply (zenon_L284_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.16/10.40 apply (zenon_L193_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.16/10.40 apply (zenon_L147_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.16/10.40 apply (zenon_L213_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.16/10.40 apply (zenon_L704_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.16/10.40 apply (zenon_L723_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.16/10.40 apply (zenon_L167_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.16/10.40 apply (zenon_L530_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.16/10.40 apply (zenon_L804_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.16/10.40 apply (zenon_L858_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.16/10.40 apply (zenon_L805_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.16/10.40 apply (zenon_L579_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.16/10.40 apply (zenon_L724_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.16/10.40 apply (zenon_L182_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.16/10.40 apply (zenon_L725_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.16/10.40 apply (zenon_L183_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.16/10.40 apply (zenon_L294_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.16/10.40 apply (zenon_L196_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.16/10.40 apply (zenon_L186_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.16/10.40 apply (zenon_L187_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.16/10.40 apply (zenon_L296_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.16/10.40 apply (zenon_L298_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.16/10.40 apply (zenon_L300_); trivial. % 10.16/10.40 apply (zenon_L538_); trivial. % 10.16/10.40 apply (zenon_L505_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H2e | zenon_intro zenon_H82 ]. % 10.16/10.40 apply (zenon_L847_); trivial. % 10.16/10.40 apply (zenon_L521_); trivial. % 10.16/10.40 (* end of lemma zenon_L859_ *) % 10.16/10.40 assert (zenon_L860_ : ((op (e0) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (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) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> False). % 10.16/10.40 do 0 intro. intros zenon_H70 zenon_H82 zenon_H27 zenon_H2f zenon_H94 zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H2ae zenon_H2c zenon_H30 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1ea zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H127 zenon_H2ee zenon_H156 zenon_H1dc zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H1d4 zenon_H2dd zenon_H2c4 zenon_H22e zenon_H2fe zenon_H22f zenon_H141 zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13a zenon_H22d zenon_H328 zenon_H1e zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_Hf1 zenon_H1c9 zenon_H130 zenon_H301 zenon_H105 zenon_H1b9 zenon_H2a8 zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hb8 zenon_H23 zenon_H155 zenon_H113 zenon_Hef zenon_H192 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H272 zenon_Heb zenon_Hfe zenon_H16c zenon_H25. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.16/10.40 apply (zenon_L772_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.16/10.40 apply (zenon_L269_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.16/10.40 apply (zenon_L775_); trivial. % 10.16/10.40 apply (zenon_L859_); trivial. % 10.16/10.40 (* end of lemma zenon_L860_ *) % 10.16/10.40 assert (zenon_L861_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 10.16/10.40 do 0 intro. intros zenon_H14b zenon_H143 zenon_H1ed. % 10.16/10.40 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 10.16/10.40 intro zenon_D_pnotp. % 10.16/10.40 apply zenon_H14b. % 10.16/10.40 rewrite <- zenon_D_pnotp. % 10.16/10.40 exact zenon_H143. % 10.16/10.40 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 10.16/10.40 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 10.16/10.40 congruence. % 10.16/10.40 apply zenon_H7c. apply refl_equal. % 10.16/10.40 apply zenon_H1ee. apply sym_equal. exact zenon_H1ed. % 10.16/10.40 (* end of lemma zenon_L861_ *) % 10.16/10.40 assert (zenon_L862_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.40 do 0 intro. intros zenon_H10d zenon_Ha8 zenon_H101 zenon_Hf3 zenon_Hfe zenon_H82 zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_H79 zenon_Heb zenon_H2f zenon_H105. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hfd | zenon_intro zenon_H10e ]. % 10.16/10.40 apply (zenon_L785_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H10f ]. % 10.16/10.40 apply (zenon_L435_); trivial. % 10.16/10.40 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H106 | zenon_intro zenon_H109 ]. % 10.16/10.40 apply (zenon_L313_); trivial. % 10.16/10.40 apply (zenon_L807_); trivial. % 10.16/10.40 (* end of lemma zenon_L862_ *) % 10.16/10.40 assert (zenon_L863_ : (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (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)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.16/10.41 do 0 intro. intros zenon_H25 zenon_H16c zenon_H272 zenon_H7e zenon_H1f6 zenon_H1ec zenon_H5f zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H155 zenon_H23 zenon_Hb8 zenon_H1ce zenon_Ha9 zenon_H12c zenon_Hbe zenon_H13d zenon_H2a8 zenon_H1b9 zenon_H301 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_H1e zenon_H328 zenon_H22d zenon_H13a zenon_H2ac zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H22f zenon_H2fe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H1d4 zenon_H74 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H1ea zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H304 zenon_H30 zenon_H2c zenon_H2ae zenon_H338 zenon_H335 zenon_H2b4 zenon_H33b zenon_H27 zenon_H70 zenon_H1ed zenon_H14b zenon_H141 zenon_H10d zenon_Ha8 zenon_H101 zenon_Hf3 zenon_Hfe zenon_H82 zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H2f zenon_H105. % 10.16/10.41 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H94 | zenon_intro zenon_H14d ]. % 10.16/10.41 apply (zenon_L860_); trivial. % 10.16/10.41 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 10.16/10.41 apply (zenon_L861_); trivial. % 10.16/10.41 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H149 | zenon_intro zenon_H79 ]. % 10.16/10.41 apply (zenon_L358_); trivial. % 10.16/10.41 apply (zenon_L862_); trivial. % 10.16/10.41 (* end of lemma zenon_L863_ *) % 10.16/10.41 assert (zenon_L864_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) 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(e1) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (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) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> False). % 10.16/10.41 do 0 intro. intros zenon_H105 zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_H82 zenon_Hfe zenon_H101 zenon_H10d zenon_H141 zenon_H14b zenon_H1ed zenon_H70 zenon_H27 zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H2ae zenon_H2c zenon_H30 zenon_H304 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1ea zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H127 zenon_H2ee zenon_H156 zenon_H1dc zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H1d4 zenon_H2dd zenon_H2c4 zenon_H22e zenon_H2fe zenon_H22f zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13a zenon_H22d zenon_H328 zenon_H1e zenon_Hd1 zenon_H11f zenon_H12f zenon_Hf1 zenon_H1c9 zenon_H130 zenon_H301 zenon_H1b9 zenon_H2a8 zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H1ce zenon_Hb8 zenon_H23 zenon_H155 zenon_H113 zenon_Hef zenon_H192 zenon_H1f5 zenon_H5f zenon_H1ec zenon_H1f6 zenon_H7e zenon_H272 zenon_H16c zenon_H25 zenon_Hf3 zenon_H12a zenon_H2f zenon_H50. % 10.16/10.41 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.16/10.41 apply (zenon_L863_); trivial. % 10.16/10.41 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.16/10.41 apply (zenon_L155_); trivial. % 10.16/10.41 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.16/10.41 apply (zenon_L199_); trivial. % 10.16/10.41 apply (zenon_L368_); trivial. % 10.16/10.41 (* end of lemma zenon_L864_ *) % 10.16/10.41 assert (zenon_L865_ : (~((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.16/10.41 do 0 intro. intros zenon_H354 zenon_H82. % 10.16/10.41 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.16/10.41 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 10.16/10.41 congruence. % 10.16/10.41 exact (zenon_H191 zenon_H82). % 10.16/10.41 apply zenon_H29. apply refl_equal. % 10.16/10.41 (* end of lemma zenon_L865_ *) % 10.16/10.41 assert (zenon_L866_ : ((op (e2) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (op (op (e3) (e3)) (e3)))) -> False). % 10.16/10.41 do 0 intro. intros zenon_H102 zenon_H82 zenon_H355. % 10.16/10.41 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H2d0 | zenon_intro zenon_H2d1 ]. % 10.16/10.41 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e1) = (op (op (e3) (e3)) (e3)))). % 10.16/10.41 intro zenon_D_pnotp. % 10.16/10.41 apply zenon_H355. % 10.16/10.41 rewrite <- zenon_D_pnotp. % 10.16/10.41 exact zenon_H2d0. % 10.16/10.41 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d1]. % 10.16/10.41 cut (((op (op (e3) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H356]. % 10.16/10.41 congruence. % 10.16/10.41 cut (((op (e2) (e3)) = (e1)) = ((op (op (e3) (e3)) (e3)) = (e1))). % 10.16/10.41 intro zenon_D_pnotp. % 10.16/10.41 apply zenon_H356. % 10.16/10.41 rewrite <- zenon_D_pnotp. % 10.16/10.41 exact zenon_H102. % 10.16/10.41 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.16/10.41 cut (((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H357]. % 10.16/10.41 congruence. % 10.16/10.41 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H2d0 | zenon_intro zenon_H2d1 ]. % 10.16/10.41 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))). % 10.16/10.41 intro zenon_D_pnotp. % 10.16/10.41 apply zenon_H357. % 10.16/10.41 rewrite <- zenon_D_pnotp. % 10.16/10.41 exact zenon_H2d0. % 10.16/10.41 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d1]. % 10.16/10.41 cut (((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H354]. % 10.16/10.41 congruence. % 10.16/10.41 apply (zenon_L865_); trivial. % 10.16/10.41 apply zenon_H2d1. apply refl_equal. % 10.16/10.41 apply zenon_H2d1. apply refl_equal. % 10.16/10.41 apply zenon_H1d. apply refl_equal. % 10.16/10.41 apply zenon_H2d1. apply refl_equal. % 10.16/10.41 apply zenon_H2d1. apply refl_equal. % 10.16/10.41 (* end of lemma zenon_L866_ *) % 10.16/10.41 assert (zenon_L867_ : ((op (e2) (e1)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> False). % 10.16/10.41 do 0 intro. intros zenon_Ha2 zenon_H102 zenon_H82. % 10.16/10.41 apply (zenon_notand_s _ _ ax8); [ zenon_intro zenon_H345 | zenon_intro zenon_H358 ]. % 10.16/10.41 elim (classic ((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))); [ zenon_intro zenon_H2d7 | zenon_intro zenon_H2d8 ]. % 10.16/10.41 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3)))) = ((e0) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))). % 10.16/10.41 intro zenon_D_pnotp. % 10.16/10.41 apply zenon_H345. % 10.16/10.41 rewrite <- zenon_D_pnotp. % 10.16/10.41 exact zenon_H2d7. % 10.16/10.41 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2d8]. % 10.16/10.41 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H346]. % 10.16/10.41 congruence. % 10.16/10.41 cut (((op (e2) (e1)) = (e0)) = ((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (e0))). % 10.16/10.41 intro zenon_D_pnotp. % 10.16/10.41 apply zenon_H346. % 10.16/10.41 rewrite <- zenon_D_pnotp. % 10.16/10.41 exact zenon_Ha2. % 10.16/10.41 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.16/10.41 cut (((op (e2) (e1)) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H359]. % 10.16/10.41 congruence. % 10.16/10.41 elim (classic ((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))); [ zenon_intro zenon_H2d7 | zenon_intro zenon_H2d8 ]. % 10.16/10.41 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3)))) = ((op (e2) (e1)) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))). % 10.16/10.41 intro zenon_D_pnotp. % 10.16/10.41 apply zenon_H359. % 10.16/10.41 rewrite <- zenon_D_pnotp. % 10.16/10.41 exact zenon_H2d7. % 10.16/10.41 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (op (e3) (e3)) (op (op (e3) (e3)) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2d8]. % 10.16/10.41 cut (((op (op (e3) (e3)) (op (op (e3) (e3)) (e3))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H35a]. % 10.16/10.41 congruence. % 10.16/10.41 cut (((op (op (e3) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H356]. % 10.16/10.41 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 10.16/10.41 congruence. % 10.16/10.41 exact (zenon_H191 zenon_H82). % 10.16/10.41 cut (((op (e2) (e3)) = (e1)) = ((op (op (e3) (e3)) (e3)) = (e1))). % 10.16/10.41 intro zenon_D_pnotp. % 10.16/10.41 apply zenon_H356. % 10.16/10.41 rewrite <- zenon_D_pnotp. % 10.16/10.41 exact zenon_H102. % 10.16/10.41 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.16/10.41 cut (((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H357]. % 10.16/10.41 congruence. % 10.16/10.41 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H2d0 | zenon_intro zenon_H2d1 ]. % 10.16/10.41 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))). % 10.16/10.41 intro zenon_D_pnotp. % 10.16/10.41 apply zenon_H357. % 10.16/10.41 rewrite <- zenon_D_pnotp. % 10.16/10.41 exact zenon_H2d0. % 10.16/10.41 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d1]. % 10.16/10.41 cut (((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H354]. % 10.16/10.41 congruence. % 10.16/10.41 apply (zenon_L865_); trivial. % 10.16/10.41 apply zenon_H2d1. apply refl_equal. % 10.16/10.41 apply zenon_H2d1. apply refl_equal. % 10.16/10.41 apply zenon_H1d. apply refl_equal. % 10.16/10.41 apply zenon_H2d8. apply refl_equal. % 10.16/10.41 apply zenon_H2d8. apply refl_equal. % 10.16/10.41 apply zenon_H34. apply refl_equal. % 10.16/10.41 apply zenon_H2d8. apply refl_equal. % 10.16/10.41 apply zenon_H2d8. apply refl_equal. % 10.16/10.41 apply (zenon_notand_s _ _ zenon_H358); [ zenon_intro zenon_H35b | zenon_intro zenon_H355 ]. % 10.16/10.41 apply zenon_H35b. apply sym_equal. exact zenon_H82. % 10.16/10.41 apply (zenon_L866_); trivial. % 10.16/10.41 (* end of lemma zenon_L867_ *) % 10.16/10.41 assert (zenon_L868_ : (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op 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(e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> False). % 10.16/10.41 do 0 intro. intros zenon_H50 zenon_H2f zenon_H27 zenon_H70 zenon_H1ed zenon_H109 zenon_H82 zenon_Ha2 zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H2ae zenon_H2c zenon_H30 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1ea zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H127 zenon_H2ee zenon_H156 zenon_H1dc zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H1d4 zenon_H2dd zenon_H2c4 zenon_H22e zenon_H2fe zenon_H22f zenon_H141 zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13a zenon_H22d zenon_H328 zenon_H1e zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_Hf1 zenon_H1c9 zenon_H130 zenon_H301 zenon_H105 zenon_H1b9 zenon_H2a8 zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hb8 zenon_H23 zenon_H155 zenon_H113 zenon_Hef zenon_H192 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H272 zenon_Heb zenon_Hfe zenon_H16c zenon_H25. % 10.16/10.41 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.16/10.41 apply (zenon_L864_); trivial. % 10.16/10.41 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.16/10.41 apply (zenon_L132_); trivial. % 10.16/10.41 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.16/10.41 apply (zenon_L867_); trivial. % 10.16/10.41 apply (zenon_L859_); trivial. % 10.16/10.41 (* end of lemma zenon_L868_ *) % 10.16/10.41 assert (zenon_L869_ : ((op (e3) (e0)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (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) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> False). % 10.16/10.41 do 0 intro. intros zenon_H72 zenon_Ha2 zenon_H82 zenon_H109 zenon_H70 zenon_H27 zenon_H2f zenon_H50 zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H2ae zenon_H2c zenon_H30 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1ea zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H127 zenon_H2ee zenon_H156 zenon_H1dc zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H1d4 zenon_H2dd zenon_H2c4 zenon_H22e zenon_H2fe zenon_H22f zenon_H141 zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13a zenon_H22d zenon_H328 zenon_H1e zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_Hf1 zenon_H1c9 zenon_H130 zenon_H301 zenon_H105 zenon_H1b9 zenon_H2a8 zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hb8 zenon_H23 zenon_H155 zenon_H113 zenon_Hef zenon_H192 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H272 zenon_Heb zenon_Hfe zenon_H16c zenon_H25. % 10.16/10.41 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.16/10.41 apply (zenon_L771_); trivial. % 10.16/10.41 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.16/10.41 apply (zenon_L269_); trivial. % 10.16/10.41 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.16/10.41 apply (zenon_L868_); trivial. % 10.16/10.41 apply (zenon_L859_); trivial. % 10.16/10.41 (* end of lemma zenon_L869_ *) % 10.16/10.41 assert (zenon_L870_ : ((op (e3) (e0)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (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) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> False). % 10.16/10.41 do 0 intro. intros zenon_H72 zenon_Ha2 zenon_H82 zenon_H70 zenon_H27 zenon_H2f zenon_H50 zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H2ae zenon_H2c zenon_H30 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1ea zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H127 zenon_H2ee zenon_H156 zenon_H1dc zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H1d4 zenon_H2dd zenon_H2c4 zenon_H22e zenon_H2fe zenon_H22f zenon_H141 zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13a zenon_H22d zenon_H328 zenon_H1e zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_Hf1 zenon_H1c9 zenon_H130 zenon_H301 zenon_H105 zenon_H1b9 zenon_H2a8 zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hb8 zenon_H23 zenon_H155 zenon_H113 zenon_Hef zenon_H192 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H272 zenon_Heb zenon_Hfe zenon_H16c zenon_H25. % 10.16/10.41 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.29/10.42 apply (zenon_L23_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.29/10.42 apply (zenon_L8_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.29/10.42 apply (zenon_L174_); trivial. % 10.29/10.42 apply (zenon_L869_); trivial. % 10.29/10.42 (* end of lemma zenon_L870_ *) % 10.29/10.42 assert (zenon_L871_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 10.29/10.42 do 0 intro. intros zenon_H2ee zenon_Hb8 zenon_He2 zenon_H7e zenon_H22e zenon_H74 zenon_H1b9 zenon_H105 zenon_H83 zenon_H30 zenon_H2ac zenon_H2f zenon_H33b zenon_Ha2 zenon_Ha1 zenon_H335 zenon_H2d4 zenon_H5f zenon_H26 zenon_H7a. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.29/10.42 apply (zenon_L782_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.29/10.42 apply (zenon_L38_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.29/10.42 apply (zenon_L389_); trivial. % 10.29/10.42 apply (zenon_L784_); trivial. % 10.29/10.42 (* end of lemma zenon_L871_ *) % 10.29/10.42 assert (zenon_L872_ : ((op (e1) (e2)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 10.29/10.42 do 0 intro. intros zenon_Hd7 zenon_H69 zenon_H35c. % 10.29/10.42 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H35d | zenon_intro zenon_H1ef ]. % 10.29/10.42 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e0)) = (op (e1) (e2)))). % 10.29/10.42 intro zenon_D_pnotp. % 10.29/10.42 apply zenon_H35c. % 10.29/10.42 rewrite <- zenon_D_pnotp. % 10.29/10.42 exact zenon_H35d. % 10.29/10.42 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 10.29/10.42 cut (((op (e1) (e2)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H35e]. % 10.29/10.42 congruence. % 10.29/10.42 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e1) (e0)))). % 10.29/10.42 intro zenon_D_pnotp. % 10.29/10.42 apply zenon_H35e. % 10.29/10.42 rewrite <- zenon_D_pnotp. % 10.29/10.42 exact zenon_Hd7. % 10.29/10.42 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 10.29/10.42 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 10.29/10.42 congruence. % 10.29/10.42 apply zenon_H1ef. apply refl_equal. % 10.29/10.42 apply zenon_H1da. apply sym_equal. exact zenon_H69. % 10.29/10.42 apply zenon_H1ef. apply refl_equal. % 10.29/10.42 apply zenon_H1ef. apply refl_equal. % 10.29/10.42 (* end of lemma zenon_L872_ *) % 10.29/10.42 assert (zenon_L873_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.29/10.42 do 0 intro. intros zenon_H1d1 zenon_H65 zenon_H64 zenon_H35c zenon_Hd7 zenon_H25 zenon_H2b2 zenon_H82 zenon_H16c. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.29/10.42 apply (zenon_L19_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.29/10.42 apply (zenon_L872_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.29/10.42 apply (zenon_L684_); trivial. % 10.29/10.42 apply (zenon_L343_); trivial. % 10.29/10.42 (* end of lemma zenon_L873_ *) % 10.29/10.42 assert (zenon_L874_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> False). % 10.29/10.42 do 0 intro. intros zenon_H2b4 zenon_H16c zenon_H25 zenon_Hd7 zenon_H35c zenon_H64 zenon_H65 zenon_H1d1 zenon_H27 zenon_Hd1 zenon_Heb zenon_H2d4 zenon_Ha2 zenon_H82. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b5 ]. % 10.29/10.42 apply (zenon_L873_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H18c | zenon_intro zenon_H2b6 ]. % 10.29/10.42 apply (zenon_L388_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H102 ]. % 10.29/10.42 apply (zenon_L434_); trivial. % 10.29/10.42 apply (zenon_L867_); trivial. % 10.29/10.42 (* end of lemma zenon_L874_ *) % 10.29/10.42 assert (zenon_L875_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.29/10.42 do 0 intro. intros zenon_H10d zenon_Ha8 zenon_H102 zenon_H101 zenon_Hfe zenon_H82 zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_H79 zenon_Heb zenon_H2f zenon_H105. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hfd | zenon_intro zenon_H10e ]. % 10.29/10.42 apply (zenon_L785_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H10f ]. % 10.29/10.42 apply (zenon_L69_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H106 | zenon_intro zenon_H109 ]. % 10.29/10.42 apply (zenon_L313_); trivial. % 10.29/10.42 apply (zenon_L807_); trivial. % 10.29/10.42 (* end of lemma zenon_L875_ *) % 10.29/10.42 assert (zenon_L876_ : ((op (e1) (e0)) = (e3)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (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) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.29/10.42 do 0 intro. intros zenon_H73 zenon_H23 zenon_H1d4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H1e zenon_H22f zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H2fe zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H22a zenon_H130 zenon_Hf1 zenon_H113 zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H110 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H12a zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2c zenon_H2ae zenon_H2b1 zenon_H2b4 zenon_H16c zenon_H25 zenon_Hd7 zenon_H35c zenon_H64 zenon_H65 zenon_H1d1 zenon_H27 zenon_Hd1 zenon_H2d4 zenon_H10d zenon_H101 zenon_Hfe zenon_H82 zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H2f zenon_H105. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.29/10.42 apply (zenon_L27_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.29/10.42 apply (zenon_L8_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.29/10.42 apply (zenon_L389_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.29/10.42 apply (zenon_L783_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.29/10.42 apply (zenon_L874_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.29/10.42 apply (zenon_L691_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b5 ]. % 10.29/10.42 apply (zenon_L873_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H18c | zenon_intro zenon_H2b6 ]. % 10.29/10.42 apply (zenon_L388_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H102 ]. % 10.29/10.42 apply (zenon_L434_); trivial. % 10.29/10.42 apply (zenon_L875_); trivial. % 10.29/10.42 (* end of lemma zenon_L876_ *) % 10.29/10.42 assert (zenon_L877_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.29/10.42 do 0 intro. intros zenon_H33b zenon_H94 zenon_H335 zenon_H2d4 zenon_H5f zenon_H83 zenon_H105 zenon_H1b9 zenon_H26 zenon_H30 zenon_H74 zenon_H22e zenon_H7a zenon_H2f zenon_H7e zenon_He2 zenon_Hb8. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H89 | zenon_intro zenon_H33c ]. % 10.29/10.42 apply (zenon_L382_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H33c); [ zenon_intro zenon_H5e | zenon_intro zenon_H33d ]. % 10.29/10.42 apply (zenon_L776_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H33d); [ zenon_intro zenon_H65 | zenon_intro zenon_H70 ]. % 10.29/10.42 apply (zenon_L103_); trivial. % 10.29/10.42 apply (zenon_L782_); trivial. % 10.29/10.42 (* end of lemma zenon_L877_ *) % 10.29/10.42 assert (zenon_L878_ : ((op (e1) (e0)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (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) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (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 (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.29/10.42 do 0 intro. intros zenon_H68 zenon_He2 zenon_H335 zenon_H94 zenon_H33b zenon_H105 zenon_H2f zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_H101 zenon_H10d zenon_H2d4 zenon_Hd1 zenon_H27 zenon_H1d1 zenon_H65 zenon_H64 zenon_H35c zenon_H25 zenon_H16c zenon_H2b4 zenon_H2b1 zenon_H2ae zenon_H2c zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H12a zenon_H1d9 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H110 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H113 zenon_Hf1 zenon_H130 zenon_H22a zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H2fe zenon_H141 zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H22f zenon_H1e zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H14b zenon_H7e zenon_H1f6 zenon_H1ec zenon_Hbe zenon_H22e zenon_H1d4 zenon_H23 zenon_H73 zenon_H82 zenon_Hfe. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.29/10.42 apply (zenon_L20_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.29/10.42 apply (zenon_L877_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.29/10.42 apply (zenon_L876_); trivial. % 10.29/10.42 apply (zenon_L313_); trivial. % 10.29/10.42 (* end of lemma zenon_L878_ *) % 10.29/10.42 assert (zenon_L879_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.29/10.42 do 0 intro. intros zenon_H22e zenon_H74 zenon_H72 zenon_H27 zenon_H2c zenon_H1b9 zenon_H2f zenon_He2 zenon_H105. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.29/10.42 apply (zenon_L23_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.29/10.42 apply (zenon_L8_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.29/10.42 apply (zenon_L174_); trivial. % 10.29/10.42 apply (zenon_L71_); trivial. % 10.29/10.42 (* end of lemma zenon_L879_ *) % 10.29/10.42 assert (zenon_L880_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((((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)) = 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(e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.29/10.42 do 0 intro. intros zenon_Hfe zenon_H82 zenon_H23 zenon_H1d4 zenon_Hbe zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H1e zenon_H22f zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H2fe zenon_Hb8 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H22a zenon_H130 zenon_Hf1 zenon_H113 zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H110 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H12a zenon_H155 zenon_H127 zenon_H2ae zenon_H2b1 zenon_H2b4 zenon_H16c zenon_H25 zenon_H35c zenon_H64 zenon_H65 zenon_H1d1 zenon_Hd1 zenon_H2d4 zenon_H10d zenon_H101 zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H33b zenon_H335 zenon_H68 zenon_H328 zenon_H30 zenon_H86 zenon_H22e zenon_H74 zenon_H27 zenon_H2c zenon_H1b9 zenon_H2f zenon_He2 zenon_H105. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.29/10.42 apply (zenon_L370_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.29/10.42 apply (zenon_L29_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.29/10.42 apply (zenon_L770_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.29/10.42 apply (zenon_L20_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.29/10.42 apply (zenon_L871_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.29/10.42 apply (zenon_L876_); trivial. % 10.29/10.42 apply (zenon_L313_); trivial. % 10.29/10.42 apply (zenon_L878_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.29/10.42 apply (zenon_L28_); trivial. % 10.29/10.42 apply (zenon_L879_); trivial. % 10.29/10.42 (* end of lemma zenon_L880_ *) % 10.29/10.42 assert (zenon_L881_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> False). % 10.29/10.42 do 0 intro. intros zenon_H13a zenon_Hd0 zenon_Hd7. % 10.29/10.42 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 10.29/10.42 intro zenon_D_pnotp. % 10.29/10.42 apply zenon_H13a. % 10.29/10.42 rewrite <- zenon_D_pnotp. % 10.29/10.42 exact zenon_Hd0. % 10.29/10.42 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 10.29/10.42 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 10.29/10.42 congruence. % 10.29/10.42 apply zenon_H9a. apply refl_equal. % 10.29/10.42 apply zenon_H1bb. apply sym_equal. exact zenon_Hd7. % 10.29/10.42 (* end of lemma zenon_L881_ *) % 10.29/10.42 assert (zenon_L882_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.29/10.42 do 0 intro. intros zenon_H2a8 zenon_H68 zenon_H27 zenon_H25 zenon_Hd0 zenon_H13a zenon_H82 zenon_Hfe. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.29/10.42 apply (zenon_L20_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.29/10.42 apply (zenon_L5_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.29/10.42 apply (zenon_L881_); trivial. % 10.29/10.42 apply (zenon_L313_); trivial. % 10.29/10.42 (* end of lemma zenon_L882_ *) % 10.29/10.42 assert (zenon_L883_ : ((op (e2) (e2)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (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) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> False). % 10.29/10.42 do 0 intro. intros zenon_H2f zenon_H1ed zenon_H70 zenon_H27 zenon_H109 zenon_H82 zenon_Ha8 zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H2ae zenon_H2c zenon_H30 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1ea zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H127 zenon_H2ee zenon_H156 zenon_H1dc zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H1d4 zenon_H2dd zenon_H2c4 zenon_H22e zenon_H2fe zenon_H22f zenon_H141 zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13a zenon_H22d zenon_H328 zenon_H1e zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_Hf1 zenon_H1c9 zenon_H130 zenon_H301 zenon_H105 zenon_H1b9 zenon_H2a8 zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hb8 zenon_H23 zenon_H155 zenon_H113 zenon_Hef zenon_H192 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H272 zenon_Heb zenon_Hfe zenon_H16c zenon_H25. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.29/10.42 apply (zenon_L863_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.29/10.42 apply (zenon_L132_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H1cf ]. % 10.29/10.42 apply (zenon_L232_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1d0 ]. % 10.29/10.42 apply (zenon_L155_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hf4 | zenon_intro zenon_He2 ]. % 10.29/10.42 apply (zenon_L344_); trivial. % 10.29/10.42 apply (zenon_L71_); trivial. % 10.29/10.42 apply (zenon_L859_); trivial. % 10.29/10.42 (* end of lemma zenon_L883_ *) % 10.29/10.42 assert (zenon_L884_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (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 (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.42 do 0 intro. intros zenon_H12c zenon_Ha9 zenon_H105 zenon_H12a zenon_H11b zenon_Hb8 zenon_Hfd zenon_H1ce zenon_H109 zenon_H101. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.29/10.42 apply (zenon_L785_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.29/10.42 apply (zenon_L545_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.29/10.42 apply (zenon_L852_); trivial. % 10.29/10.42 apply (zenon_L80_); trivial. % 10.29/10.42 (* end of lemma zenon_L884_ *) % 10.29/10.42 assert (zenon_L885_ : ((op (e3) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((((op (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (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))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.42 do 0 intro. intros zenon_H72 zenon_H25 zenon_H16c zenon_Hfe zenon_Heb zenon_H272 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1ec zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H155 zenon_H23 zenon_Hbe zenon_H13d zenon_H2a8 zenon_H1b9 zenon_H301 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H12f zenon_H11f zenon_Hd1 zenon_H1e zenon_H328 zenon_H22d zenon_H13a zenon_H2ac zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H141 zenon_H22f zenon_H2fe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H1d4 zenon_H7a zenon_H74 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H1ea zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H10d zenon_H304 zenon_H30 zenon_H2c zenon_H2ae zenon_H338 zenon_H335 zenon_H2b4 zenon_H33b zenon_Ha2 zenon_H82 zenon_H70 zenon_H27 zenon_H2f zenon_H50 zenon_H12c zenon_Ha9 zenon_H105 zenon_H12a zenon_Hb8 zenon_Hfd zenon_H1ce zenon_H109 zenon_H101. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.29/10.42 apply (zenon_L771_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.29/10.42 apply (zenon_L269_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.29/10.42 apply (zenon_L868_); trivial. % 10.29/10.42 apply (zenon_L884_); trivial. % 10.29/10.42 (* end of lemma zenon_L885_ *) % 10.29/10.42 assert (zenon_L886_ : (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (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) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 10.29/10.42 do 0 intro. intros zenon_H4d zenon_H109 zenon_H50 zenon_H2f zenon_H27 zenon_H70 zenon_H82 zenon_H33b zenon_H335 zenon_H338 zenon_H328 zenon_H20 zenon_H72 zenon_H25 zenon_H23 zenon_H1d4 zenon_Hd1 zenon_H22e zenon_Hbe zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_Heb zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H105 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H110 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H12a zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2a zenon_H2c zenon_H2ae zenon_H2b4 zenon_H2b1 zenon_H101 zenon_Hfd. % 10.29/10.42 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.29/10.42 apply (zenon_L197_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.29/10.42 apply (zenon_L885_); trivial. % 10.29/10.42 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.29/10.42 apply (zenon_L691_); trivial. % 10.29/10.42 apply (zenon_L785_); trivial. % 10.29/10.42 (* end of lemma zenon_L886_ *) % 10.29/10.42 assert (zenon_L887_ : (~((op (e2) (op (e2) (e0))) = (e0))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = 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(e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (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) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 10.29/10.43 do 0 intro. intros zenon_H4d zenon_H50 zenon_H2f zenon_H27 zenon_H70 zenon_H82 zenon_H33b zenon_H335 zenon_H338 zenon_H328 zenon_H20 zenon_H72 zenon_H25 zenon_H23 zenon_H1d4 zenon_Hd1 zenon_H22e zenon_Hbe zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_Heb zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H105 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H110 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H12a zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2a zenon_H2c zenon_H2ae zenon_H2b4 zenon_H2b1 zenon_H101 zenon_Hfd. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.29/10.43 apply (zenon_L27_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.29/10.43 apply (zenon_L59_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.29/10.43 apply (zenon_L174_); trivial. % 10.29/10.43 apply (zenon_L886_); trivial. % 10.29/10.43 (* end of lemma zenon_L887_ *) % 10.29/10.43 assert (zenon_L888_ : (~((op (e2) (op (e2) (e2))) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (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) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.43 do 0 intro. intros zenon_H45 zenon_H2b2 zenon_H4d zenon_H50 zenon_H2f zenon_H27 zenon_H70 zenon_H82 zenon_H33b zenon_H335 zenon_H338 zenon_H328 zenon_H20 zenon_H25 zenon_H23 zenon_H1d4 zenon_Hd1 zenon_H22e zenon_Hbe zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_Heb zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H105 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H110 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H12a zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2a zenon_H2c zenon_H2ae zenon_H2b4 zenon_H2b1 zenon_H101. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.29/10.43 apply (zenon_L7_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.29/10.43 apply (zenon_L27_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.29/10.43 apply (zenon_L365_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.29/10.43 apply (zenon_L794_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.29/10.43 apply (zenon_L231_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.29/10.43 apply (zenon_L29_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.29/10.43 apply (zenon_L809_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.29/10.43 apply (zenon_L23_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.29/10.43 apply (zenon_L59_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.29/10.43 apply (zenon_L174_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.29/10.43 apply (zenon_L197_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.29/10.43 apply (zenon_L869_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.29/10.43 apply (zenon_L341_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.29/10.43 apply (zenon_L772_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.29/10.43 apply (zenon_L269_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.29/10.43 apply (zenon_L883_); trivial. % 10.29/10.43 apply (zenon_L560_); trivial. % 10.29/10.43 apply (zenon_L358_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.29/10.43 apply (zenon_L770_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.29/10.43 apply (zenon_L870_); trivial. % 10.29/10.43 apply (zenon_L860_); trivial. % 10.29/10.43 apply (zenon_L887_); trivial. % 10.29/10.43 (* end of lemma zenon_L888_ *) % 10.29/10.43 assert (zenon_L889_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.29/10.43 do 0 intro. intros zenon_H10d zenon_Hb7 zenon_Hf3 zenon_Hfe zenon_H82 zenon_He2 zenon_H105. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hfd | zenon_intro zenon_H10e ]. % 10.29/10.43 apply (zenon_L235_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H10f ]. % 10.29/10.43 apply (zenon_L435_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H106 | zenon_intro zenon_H109 ]. % 10.29/10.43 apply (zenon_L313_); trivial. % 10.29/10.43 apply (zenon_L71_); trivial. % 10.29/10.43 (* end of lemma zenon_L889_ *) % 10.29/10.43 assert (zenon_L890_ : ((op (e0) (e3)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (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) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> False). % 10.29/10.43 do 0 intro. intros zenon_He2 zenon_Hb7 zenon_H27 zenon_H82 zenon_Ha2 zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H2ae zenon_H2c zenon_H30 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1ea zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H127 zenon_H2ee zenon_H156 zenon_H1dc zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H1d4 zenon_H2dd zenon_H2c4 zenon_H22e zenon_H2fe zenon_H22f zenon_H141 zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13a zenon_H22d zenon_H328 zenon_H1e zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_Hf1 zenon_H1c9 zenon_H130 zenon_H301 zenon_H105 zenon_H1b9 zenon_H2a8 zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hb8 zenon_H23 zenon_H155 zenon_H113 zenon_Hef zenon_H192 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H272 zenon_Heb zenon_Hfe zenon_H16c zenon_H25. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.29/10.43 apply (zenon_L889_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.29/10.43 apply (zenon_L616_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.29/10.43 apply (zenon_L867_); trivial. % 10.29/10.43 apply (zenon_L859_); trivial. % 10.29/10.43 (* end of lemma zenon_L890_ *) % 10.29/10.43 assert (zenon_L891_ : ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((((op (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 10.29/10.43 do 0 intro. intros zenon_H65 zenon_H2b1 zenon_H4d zenon_H25 zenon_H16c zenon_Hfe zenon_Heb zenon_H272 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1ec zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H155 zenon_H23 zenon_Hb8 zenon_H1ce zenon_H101 zenon_Ha9 zenon_H12c zenon_Hbe zenon_H13d zenon_H2a8 zenon_H1b9 zenon_H105 zenon_H301 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_H1e zenon_H328 zenon_H22d zenon_H13a zenon_H2ac zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H141 zenon_H22f zenon_H2fe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H1d4 zenon_H7a zenon_H74 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H10d zenon_H304 zenon_H30 zenon_H2c zenon_H2ae zenon_H338 zenon_H335 zenon_H2b4 zenon_H33b zenon_H82 zenon_H27 zenon_Hb7 zenon_He2 zenon_H1d9 zenon_H90. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.29/10.43 apply (zenon_L29_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.29/10.43 apply (zenon_L692_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.29/10.43 apply (zenon_L890_); trivial. % 10.29/10.43 apply (zenon_L334_); trivial. % 10.29/10.43 (* end of lemma zenon_L891_ *) % 10.29/10.43 assert (zenon_L892_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.29/10.43 do 0 intro. intros zenon_H124 zenon_H27 zenon_H110 zenon_H105 zenon_H2f zenon_Heb zenon_H79 zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_H101 zenon_Ha8 zenon_H10d zenon_H82 zenon_H25. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.29/10.43 apply (zenon_L862_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.29/10.43 apply (zenon_L616_); trivial. % 10.29/10.43 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.29/10.43 apply (zenon_L875_); trivial. % 10.29/10.43 apply (zenon_L521_); trivial. % 10.29/10.43 (* end of lemma zenon_L892_ *) % 10.29/10.43 assert (zenon_L893_ : ((op (e1) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((((op (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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 (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.29/10.43 do 0 intro. intros zenon_H73 zenon_Hd2 zenon_H4d zenon_H16c zenon_H272 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1ec zenon_H5f zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H155 zenon_Hb8 zenon_H1ce zenon_Ha9 zenon_H12c zenon_Hbe zenon_H2a8 zenon_H301 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_H328 zenon_H22d zenon_H13a zenon_H2ac zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H141 zenon_H22f zenon_H2fe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H1d4 zenon_H74 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H1ea zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H304 zenon_H30 zenon_H2c zenon_H2ae zenon_H338 zenon_H335 zenon_H2b4 zenon_H33b zenon_He2 zenon_Hb7 zenon_H1b9 zenon_H1e zenon_H69 zenon_H23 zenon_H13d zenon_H124 zenon_H27 zenon_H110 zenon_H105 zenon_H2f zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_H101 zenon_H10d zenon_H82 zenon_H25. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.29/10.44 apply (zenon_L27_); trivial. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.29/10.44 apply (zenon_L65_); trivial. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.29/10.44 apply (zenon_L738_); trivial. % 10.29/10.44 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.29/10.44 apply (zenon_L197_); trivial. % 10.29/10.44 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.29/10.44 apply (zenon_L890_); trivial. % 10.29/10.44 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.29/10.44 apply (zenon_L610_); trivial. % 10.29/10.44 apply (zenon_L892_); trivial. % 10.29/10.44 (* end of lemma zenon_L893_ *) % 10.29/10.44 assert (zenon_L894_ : ((op (e2) (e2)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((((op (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 10.29/10.44 do 0 intro. intros zenon_H2f zenon_H73 zenon_H4d zenon_H69 zenon_H2b2 zenon_H45 zenon_H50 zenon_H2b1 zenon_H25 zenon_H16c zenon_Hfe zenon_Heb zenon_H272 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1ec zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H155 zenon_H23 zenon_Hb8 zenon_H1ce zenon_H101 zenon_Ha9 zenon_H12c zenon_Hbe zenon_H13d zenon_H2a8 zenon_H1b9 zenon_H105 zenon_H301 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_H1e zenon_H328 zenon_H22d zenon_H13a zenon_H2ac zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H141 zenon_H22f zenon_H2fe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H1d4 zenon_H7a zenon_H74 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H10d zenon_H304 zenon_H30 zenon_H2c zenon_H2ae zenon_H338 zenon_H335 zenon_H2b4 zenon_H33b zenon_H82 zenon_H27 zenon_Hb7 zenon_He2 zenon_H1d9 zenon_H90. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.29/10.44 apply (zenon_L891_); trivial. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.29/10.44 apply (zenon_L809_); trivial. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.29/10.44 apply (zenon_L893_); trivial. % 10.29/10.44 apply (zenon_L390_); trivial. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.29/10.44 apply (zenon_L770_); trivial. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.29/10.44 apply (zenon_L890_); trivial. % 10.29/10.44 apply (zenon_L334_); trivial. % 10.29/10.44 (* end of lemma zenon_L894_ *) % 10.29/10.44 assert (zenon_L895_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.44 do 0 intro. intros zenon_H12c zenon_Hfd zenon_H101 zenon_Hf3 zenon_Ha9 zenon_H82 zenon_He2 zenon_H12a. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.29/10.44 apply (zenon_L785_); trivial. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.29/10.44 apply (zenon_L155_); trivial. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.29/10.44 apply (zenon_L255_); trivial. % 10.29/10.44 apply (zenon_L84_); trivial. % 10.29/10.44 (* end of lemma zenon_L895_ *) % 10.29/10.44 assert (zenon_L896_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> False). % 10.29/10.44 do 0 intro. intros zenon_H35f zenon_He2 zenon_H2f zenon_H79 zenon_H20 zenon_H82 zenon_Hf3 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2c zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.29/10.44 apply (zenon_L889_); trivial. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.29/10.44 apply (zenon_L895_); trivial. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.29/10.44 apply (zenon_L862_); trivial. % 10.29/10.44 apply (zenon_L500_); trivial. % 10.29/10.44 (* end of lemma zenon_L896_ *) % 10.29/10.44 assert (zenon_L897_ : (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.29/10.44 do 0 intro. intros zenon_H1e zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H2c zenon_H30 zenon_H22f zenon_H105 zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H1ec zenon_Hbe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H7e zenon_H7a zenon_H74 zenon_H2fa zenon_H1b9 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H25 zenon_H23 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_Hef zenon_H1ce zenon_H127 zenon_H12c zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H101 zenon_H1ea zenon_H1f6 zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H20 zenon_H79 zenon_H2f zenon_He2 zenon_H35f zenon_H27 zenon_H110 zenon_H82 zenon_Ha2 zenon_H1d5 zenon_H16c. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.29/10.44 apply (zenon_L896_); trivial. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.29/10.44 apply (zenon_L616_); trivial. % 10.29/10.44 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.29/10.44 apply (zenon_L867_); trivial. % 10.29/10.44 apply (zenon_L793_); trivial. % 10.29/10.44 (* end of lemma zenon_L897_ *) % 10.29/10.44 assert (zenon_L898_ : ((op (e3) (e0)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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) 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-> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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 (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.29/10.45 do 0 intro. intros zenon_H1d5 zenon_H35f zenon_He2 zenon_H30 zenon_H2c zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H64 zenon_H2ee zenon_H1d9 zenon_H2ae zenon_H127 zenon_H155 zenon_H12a zenon_H14c zenon_H1cb zenon_H2c7 zenon_Ha9 zenon_H12c zenon_H304 zenon_H113 zenon_Hf1 zenon_H130 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H2fe zenon_H141 zenon_H301 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H22f zenon_H1e zenon_H272 zenon_H5f zenon_H96 zenon_H11f zenon_H192 zenon_H1c9 zenon_Hd1 zenon_H1db zenon_H16c zenon_H1f5 zenon_H1ea zenon_H187 zenon_H93 zenon_H1b9 zenon_H23 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1d4 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1ec zenon_Hbe zenon_H22e zenon_H124 zenon_H27 zenon_H110 zenon_H105 zenon_H2f zenon_Heb zenon_H79 zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_H101 zenon_H10d zenon_H82 zenon_H25. % 10.29/10.45 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.29/10.45 apply (zenon_L783_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.29/10.45 apply (zenon_L897_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.29/10.45 apply (zenon_L657_); trivial. % 10.29/10.45 apply (zenon_L892_); trivial. % 10.29/10.45 (* end of lemma zenon_L898_ *) % 10.29/10.45 assert (zenon_L899_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((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) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.29/10.45 do 0 intro. intros zenon_H10d zenon_Hfe zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_H79 zenon_Heb zenon_H2f zenon_H105 zenon_H22e zenon_Hbe zenon_H1ec zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1d4 zenon_H1f6 zenon_H7e zenon_H14b zenon_H23 zenon_H1b9 zenon_H187 zenon_H1f5 zenon_H16c zenon_H1db zenon_Hd1 zenon_H1c9 zenon_H192 zenon_H11f zenon_H96 zenon_H5f zenon_H272 zenon_H1e zenon_H22f zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H301 zenon_H141 zenon_H2fe zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H130 zenon_Hf1 zenon_H113 zenon_H304 zenon_H2c7 zenon_H1cb zenon_H14c zenon_H155 zenon_H127 zenon_H2ae zenon_H1d9 zenon_H2ee zenon_H64 zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H2c zenon_H30 zenon_H35f zenon_H93 zenon_H1ea zenon_Ha2 zenon_H110 zenon_H27 zenon_H12c zenon_Hfd zenon_H101 zenon_Ha9 zenon_He2 zenon_H12a zenon_H124 zenon_H82 zenon_H25. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.29/10.45 apply (zenon_L898_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.29/10.45 apply (zenon_L269_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.29/10.45 apply (zenon_L895_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.29/10.45 apply (zenon_L616_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.29/10.45 apply (zenon_L867_); trivial. % 10.29/10.45 apply (zenon_L777_); trivial. % 10.29/10.45 apply (zenon_L521_); trivial. % 10.29/10.45 (* end of lemma zenon_L899_ *) % 10.29/10.45 assert (zenon_L900_ : ((op (e3) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> False). % 10.29/10.45 do 0 intro. intros zenon_H90 zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H328 zenon_H2b1 zenon_H50 zenon_H45 zenon_H2b2 zenon_H69 zenon_H4d zenon_H73 zenon_He2 zenon_Ha2 zenon_H35f zenon_H2ae zenon_H272 zenon_H82 zenon_H20 zenon_H79 zenon_H2f zenon_H27 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2c zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.29/10.45 apply (zenon_L894_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.29/10.45 apply (zenon_L899_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.29/10.45 apply (zenon_L892_); trivial. % 10.29/10.45 apply (zenon_L500_); trivial. % 10.29/10.45 (* end of lemma zenon_L900_ *) % 10.29/10.45 assert (zenon_L901_ : (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (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) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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 (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.29/10.45 do 0 intro. intros zenon_H4d zenon_He2 zenon_Hfd zenon_H35f zenon_H23 zenon_H1d4 zenon_Hd1 zenon_H22e zenon_Hbe zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H1e zenon_H22f zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H130 zenon_Hf1 zenon_H113 zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H12a zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2c zenon_H2ae zenon_H2b4 zenon_H2b1 zenon_H124 zenon_H27 zenon_H110 zenon_H105 zenon_H2f zenon_Heb zenon_H79 zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_H101 zenon_H10d zenon_H82 zenon_H25. % 10.29/10.45 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.29/10.45 apply (zenon_L197_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.29/10.45 apply (zenon_L899_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.29/10.45 apply (zenon_L691_); trivial. % 10.29/10.45 apply (zenon_L892_); trivial. % 10.29/10.45 (* end of lemma zenon_L901_ *) % 10.29/10.45 assert (zenon_L902_ : ((op (e1) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (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) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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 (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.29/10.45 do 0 intro. intros zenon_H73 zenon_Hd2 zenon_H4d zenon_He2 zenon_Hfd zenon_H35f zenon_H23 zenon_H1d4 zenon_Hd1 zenon_H22e zenon_Hbe zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H1e zenon_H22f zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H130 zenon_Hf1 zenon_H113 zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H12a zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2c zenon_H2ae zenon_H2b4 zenon_H2b1 zenon_H124 zenon_H27 zenon_H110 zenon_H105 zenon_H2f zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_H101 zenon_H10d zenon_H82 zenon_H25. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.29/10.45 apply (zenon_L27_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.29/10.45 apply (zenon_L65_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.29/10.45 apply (zenon_L738_); trivial. % 10.29/10.45 apply (zenon_L901_); trivial. % 10.29/10.45 (* end of lemma zenon_L902_ *) % 10.29/10.45 assert (zenon_L903_ : ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (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) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.29/10.45 do 0 intro. intros zenon_H2b2 zenon_H141 zenon_H94 zenon_H124 zenon_H27 zenon_H110 zenon_H105 zenon_H2f zenon_Heb zenon_H79 zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_H101 zenon_H10d zenon_H25 zenon_H73 zenon_H4d zenon_He2 zenon_H35f zenon_H23 zenon_H1d4 zenon_Hd1 zenon_H22e zenon_Hbe zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H1e zenon_H22f zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H130 zenon_Hf1 zenon_H113 zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H12a zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2c zenon_H2ae zenon_H2b4 zenon_H2b1 zenon_Ha2 zenon_H33b zenon_H335 zenon_H338 zenon_H328 zenon_H45 zenon_H82 zenon_Ha9. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.29/10.45 apply (zenon_L684_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.29/10.45 apply (zenon_L890_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.29/10.45 apply (zenon_L902_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.29/10.45 apply (zenon_L892_); trivial. % 10.29/10.45 apply (zenon_L92_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.29/10.45 apply (zenon_L14_); trivial. % 10.29/10.45 apply (zenon_L255_); trivial. % 10.29/10.45 (* end of lemma zenon_L903_ *) % 10.29/10.45 assert (zenon_L904_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (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)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.29/10.45 do 0 intro. intros zenon_H14c zenon_H98 zenon_H1ed zenon_H14b zenon_H141 zenon_H10d zenon_Ha8 zenon_H101 zenon_Hf3 zenon_Hfe zenon_H82 zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H2f zenon_H105. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H94 | zenon_intro zenon_H14d ]. % 10.29/10.45 apply (zenon_L833_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 10.29/10.45 apply (zenon_L861_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H149 | zenon_intro zenon_H79 ]. % 10.29/10.45 apply (zenon_L358_); trivial. % 10.29/10.45 apply (zenon_L862_); trivial. % 10.29/10.45 (* end of lemma zenon_L904_ *) % 10.29/10.45 assert (zenon_L905_ : (((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 (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.45 do 0 intro. intros zenon_H10d zenon_Hb7 zenon_H105 zenon_Hf3 zenon_Hfe zenon_H82 zenon_H112 zenon_H101. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hfd | zenon_intro zenon_H10e ]. % 10.29/10.45 apply (zenon_L235_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H10f ]. % 10.29/10.45 apply (zenon_L435_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H106 | zenon_intro zenon_H109 ]. % 10.29/10.45 apply (zenon_L313_); trivial. % 10.29/10.45 apply (zenon_L80_); trivial. % 10.29/10.45 (* end of lemma zenon_L905_ *) % 10.29/10.45 assert (zenon_L906_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((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 (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.45 do 0 intro. intros zenon_H12c zenon_H2f zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_H141 zenon_H14b zenon_H1ed zenon_H98 zenon_H14c zenon_H12a zenon_Ha9 zenon_H10d zenon_Hb7 zenon_H105 zenon_Hf3 zenon_Hfe zenon_H82 zenon_H101. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.29/10.45 apply (zenon_L904_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.29/10.45 apply (zenon_L155_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.29/10.45 apply (zenon_L255_); trivial. % 10.29/10.45 apply (zenon_L905_); trivial. % 10.29/10.45 (* end of lemma zenon_L906_ *) % 10.29/10.45 assert (zenon_L907_ : ((op (e3) (e2)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))) = 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-> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> (~((e1) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.29/10.45 do 0 intro. intros zenon_H98 zenon_Ha2 zenon_H33b zenon_H335 zenon_H338 zenon_H328 zenon_H2b1 zenon_H2b4 zenon_H2ae zenon_H2c zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H12a zenon_H1d9 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H2ee zenon_H64 zenon_Ha9 zenon_H12c zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H113 zenon_Hf1 zenon_H130 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H141 zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H22f zenon_H1e zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_H1c9 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H14b zenon_H7e zenon_H1f6 zenon_H1ec zenon_Hbe zenon_H22e zenon_Hd1 zenon_H1d4 zenon_H35f zenon_He2 zenon_H4d zenon_H25 zenon_H10d zenon_H101 zenon_Hfe zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_H79 zenon_Heb zenon_H2f zenon_H105 zenon_H110 zenon_H27 zenon_H124 zenon_H82 zenon_H23. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.29/10.45 apply (zenon_L897_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.29/10.45 apply (zenon_L269_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.29/10.45 apply (zenon_L906_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.29/10.45 apply (zenon_L616_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.29/10.45 apply (zenon_L867_); trivial. % 10.29/10.45 apply (zenon_L859_); trivial. % 10.29/10.45 apply (zenon_L521_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.29/10.45 apply (zenon_L901_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.29/10.45 apply (zenon_L892_); trivial. % 10.29/10.45 apply (zenon_L125_); trivial. % 10.29/10.45 (* end of lemma zenon_L907_ *) % 10.29/10.45 assert (zenon_L908_ : (~((op (e2) (op (e2) (e3))) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((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 (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e1) (e0)) = (e3)) -> (((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 (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 10.29/10.45 do 0 intro. intros zenon_H50 zenon_H45 zenon_H2b2 zenon_H25 zenon_H82 zenon_H10d zenon_H101 zenon_Hfe zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H105 zenon_H110 zenon_H124 zenon_H2b1 zenon_H2b4 zenon_H2ae zenon_H2c zenon_H30 zenon_H127 zenon_H1b9 zenon_H155 zenon_H12a zenon_H1d9 zenon_H14c zenon_H1cb zenon_H2ee zenon_H64 zenon_Ha9 zenon_H12c zenon_H83 zenon_Hef zenon_H2f7 zenon_H304 zenon_H113 zenon_Hf1 zenon_H130 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H16c zenon_H2fe zenon_H141 zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_Hae zenon_H9c zenon_H13d zenon_H13a zenon_H22d zenon_H22f zenon_H1e zenon_H272 zenon_H5f zenon_H187 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_H1c9 zenon_H2dd zenon_H12f zenon_H14b zenon_H7e zenon_H1f6 zenon_H1ec zenon_Hbe zenon_H22e zenon_H1d4 zenon_H23 zenon_H35f zenon_Hfd zenon_He2 zenon_H4d zenon_H73 zenon_H2c7 zenon_H89 zenon_Ha1 zenon_H27 zenon_Hd1 zenon_H2c4 zenon_H2f zenon_H2ac. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.29/10.45 apply (zenon_L29_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.29/10.45 apply (zenon_L809_); trivial. % 10.29/10.45 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.29/10.45 apply (zenon_L902_); trivial. % 10.29/10.45 apply (zenon_L390_); trivial. % 10.29/10.45 (* end of lemma zenon_L908_ *) % 10.29/10.45 assert (zenon_L909_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((((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)) = 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(e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (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) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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 (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.29/10.46 do 0 intro. intros zenon_H328 zenon_H338 zenon_H335 zenon_H33b zenon_H94 zenon_H73 zenon_H4d zenon_He2 zenon_Hfd zenon_H35f zenon_H23 zenon_H1d4 zenon_Hd1 zenon_H22e zenon_Hbe zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H1e zenon_H22f zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H130 zenon_Hf1 zenon_H113 zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H12a zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2c zenon_H2ae zenon_H2b4 zenon_H2b1 zenon_H124 zenon_H27 zenon_H110 zenon_H105 zenon_H2f zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_H101 zenon_H10d zenon_H82 zenon_H25. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.29/10.46 apply (zenon_L860_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.29/10.46 apply (zenon_L65_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.29/10.46 apply (zenon_L389_); trivial. % 10.29/10.46 apply (zenon_L901_); trivial. % 10.29/10.46 (* end of lemma zenon_L909_ *) % 10.29/10.46 assert (zenon_L910_ : ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.29/10.46 do 0 intro. intros zenon_Hd0 zenon_Hde zenon_H30. % 10.29/10.46 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H31 | zenon_intro zenon_H29 ]. % 10.29/10.46 cut (((e3) = (e3)) = ((e2) = (e3))). % 10.29/10.46 intro zenon_D_pnotp. % 10.29/10.46 apply zenon_H30. % 10.29/10.46 rewrite <- zenon_D_pnotp. % 10.29/10.46 exact zenon_H31. % 10.29/10.46 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.29/10.46 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 10.29/10.46 congruence. % 10.29/10.46 cut (((op (e0) (e2)) = (e2)) = ((e3) = (e2))). % 10.29/10.46 intro zenon_D_pnotp. % 10.29/10.46 apply zenon_H32. % 10.29/10.46 rewrite <- zenon_D_pnotp. % 10.29/10.46 exact zenon_Hd0. % 10.29/10.46 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.29/10.46 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_He0]. % 10.29/10.46 congruence. % 10.29/10.46 exact (zenon_He0 zenon_Hde). % 10.29/10.46 apply zenon_H22. apply refl_equal. % 10.29/10.46 apply zenon_H29. apply refl_equal. % 10.29/10.46 apply zenon_H29. apply refl_equal. % 10.29/10.46 (* end of lemma zenon_L910_ *) % 10.29/10.46 assert (zenon_L911_ : ((op (e0) (e2)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 10.29/10.46 do 0 intro. intros zenon_Hd0 zenon_H65 zenon_H335. % 10.29/10.46 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H336 | zenon_intro zenon_H9a ]. % 10.29/10.46 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e1)) = (op (e0) (e2)))). % 10.29/10.46 intro zenon_D_pnotp. % 10.29/10.46 apply zenon_H335. % 10.29/10.46 rewrite <- zenon_D_pnotp. % 10.29/10.46 exact zenon_H336. % 10.29/10.46 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 10.29/10.46 cut (((op (e0) (e2)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H337]. % 10.29/10.46 congruence. % 10.29/10.46 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e0) (e1)))). % 10.29/10.46 intro zenon_D_pnotp. % 10.29/10.46 apply zenon_H337. % 10.29/10.46 rewrite <- zenon_D_pnotp. % 10.29/10.46 exact zenon_Hd0. % 10.29/10.46 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 10.29/10.46 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 10.29/10.46 congruence. % 10.29/10.46 apply zenon_H9a. apply refl_equal. % 10.29/10.46 apply zenon_H66. apply sym_equal. exact zenon_H65. % 10.29/10.46 apply zenon_H9a. apply refl_equal. % 10.29/10.46 apply zenon_H9a. apply refl_equal. % 10.29/10.46 (* end of lemma zenon_L911_ *) % 10.29/10.46 assert (zenon_L912_ : ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (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) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.29/10.46 do 0 intro. intros zenon_Hd0 zenon_H2d4 zenon_H335 zenon_H33b zenon_H25 zenon_H124 zenon_H12a zenon_He2 zenon_Ha9 zenon_H101 zenon_Hfd zenon_H12c zenon_H27 zenon_H110 zenon_Ha2 zenon_H1ea zenon_H93 zenon_H35f zenon_H30 zenon_H2c zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H64 zenon_H2ee zenon_H1d9 zenon_H2ae zenon_H127 zenon_H155 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H304 zenon_H113 zenon_Hf1 zenon_H130 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H2fe zenon_H301 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H22f zenon_H1e zenon_H272 zenon_H5f zenon_H96 zenon_H11f zenon_H192 zenon_H1c9 zenon_Hd1 zenon_H1db zenon_H16c zenon_H1f5 zenon_H187 zenon_H1b9 zenon_H23 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1d4 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1ec zenon_Hbe zenon_H22e zenon_H105 zenon_H2f zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_H10d zenon_H73 zenon_H82 zenon_H141. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.29/10.46 apply (zenon_L911_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.29/10.46 apply (zenon_L871_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.29/10.46 apply (zenon_L27_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.29/10.46 apply (zenon_L65_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.29/10.46 apply (zenon_L738_); trivial. % 10.29/10.46 apply (zenon_L899_); trivial. % 10.29/10.46 apply (zenon_L358_); trivial. % 10.29/10.46 (* end of lemma zenon_L912_ *) % 10.29/10.46 assert (zenon_L913_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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) 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-> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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 (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.29/10.46 do 0 intro. intros zenon_H141 zenon_H94 zenon_Hd0 zenon_H2d4 zenon_H335 zenon_H33b zenon_H12a zenon_He2 zenon_Ha9 zenon_H12c zenon_H1ea zenon_H93 zenon_H35f zenon_H30 zenon_H2c zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H64 zenon_H2ee zenon_H1d9 zenon_H2ae zenon_H127 zenon_H155 zenon_H14c zenon_H1cb zenon_H2c7 zenon_H304 zenon_H113 zenon_Hf1 zenon_H130 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H2fe zenon_H301 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H22f zenon_H1e zenon_H272 zenon_H5f zenon_H96 zenon_H11f zenon_H192 zenon_H1c9 zenon_Hd1 zenon_H1db zenon_H16c zenon_H1f5 zenon_H187 zenon_H23 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1d4 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1ec zenon_Hbe zenon_H22e zenon_H73 zenon_Hd2 zenon_H4d zenon_H328 zenon_H338 zenon_H2b4 zenon_H69 zenon_H1b9 zenon_H13b zenon_H124 zenon_H27 zenon_H110 zenon_H105 zenon_H2f zenon_Heb zenon_H79 zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_H101 zenon_H10d zenon_H82 zenon_H25. % 10.29/10.46 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.29/10.46 apply (zenon_L197_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.29/10.46 apply (zenon_L893_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.29/10.46 apply (zenon_L912_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.29/10.46 apply (zenon_L892_); trivial. % 10.29/10.46 apply (zenon_L92_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.29/10.46 apply (zenon_L341_); trivial. % 10.29/10.46 apply (zenon_L892_); trivial. % 10.29/10.46 (* end of lemma zenon_L913_ *) % 10.29/10.46 assert (zenon_L914_ : ((op (e2) (e0)) = (e1)) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (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) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.29/10.46 do 0 intro. intros zenon_H2b2 zenon_H45 zenon_H50 zenon_H13b zenon_H69 zenon_Hd2 zenon_H73 zenon_H2d4 zenon_Hd0 zenon_H124 zenon_H27 zenon_H110 zenon_H105 zenon_H2f zenon_Heb zenon_H79 zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_H101 zenon_H10d zenon_H25 zenon_H4d zenon_He2 zenon_H35f zenon_H1d4 zenon_Hd1 zenon_H22e zenon_Hbe zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H1e zenon_H22f zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H130 zenon_Hf1 zenon_H113 zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H12a zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2c zenon_H2ae zenon_H2b4 zenon_H2b1 zenon_H328 zenon_H338 zenon_H335 zenon_H33b zenon_Ha2 zenon_H82 zenon_H23. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.29/10.46 apply (zenon_L900_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.29/10.46 apply (zenon_L913_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.29/10.46 apply (zenon_L907_); trivial. % 10.29/10.46 apply (zenon_L125_); trivial. % 10.29/10.46 (* end of lemma zenon_L914_ *) % 10.29/10.46 assert (zenon_L915_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.29/10.46 do 0 intro. intros zenon_H2ca zenon_H335 zenon_Hd0 zenon_Hf1 zenon_H69 zenon_H86 zenon_H2b1 zenon_H82 zenon_H141. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.29/10.46 apply (zenon_L911_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.29/10.46 apply (zenon_L163_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.29/10.46 apply (zenon_L342_); trivial. % 10.29/10.46 apply (zenon_L358_); trivial. % 10.29/10.46 (* end of lemma zenon_L915_ *) % 10.29/10.46 assert (zenon_L916_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.29/10.46 do 0 intro. intros zenon_H2a8 zenon_H141 zenon_H2b1 zenon_H86 zenon_Hf1 zenon_H335 zenon_H2ca zenon_H27 zenon_H25 zenon_Hd0 zenon_H13a zenon_H82 zenon_Hfe. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.29/10.46 apply (zenon_L915_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.29/10.46 apply (zenon_L5_); trivial. % 10.29/10.46 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.29/10.46 apply (zenon_L881_); trivial. % 10.29/10.46 apply (zenon_L313_); trivial. % 10.29/10.46 (* end of lemma zenon_L916_ *) % 10.29/10.46 assert (zenon_L917_ : ((op (e1) (e0)) = (e3)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.29/10.47 do 0 intro. intros zenon_H73 zenon_H1e zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H2c zenon_H30 zenon_H22f zenon_H105 zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H1ec zenon_Hbe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H7e zenon_H7a zenon_H74 zenon_H2fa zenon_H1b9 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H25 zenon_H23 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_Hef zenon_H1ce zenon_H127 zenon_H12c zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H101 zenon_H1ea zenon_H1f6 zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H20 zenon_H2f zenon_He2 zenon_H35f zenon_H27 zenon_H110 zenon_H82 zenon_Ha2 zenon_H1d5 zenon_H16c. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.29/10.47 apply (zenon_L27_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.29/10.47 apply (zenon_L8_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.29/10.47 apply (zenon_L389_); trivial. % 10.29/10.47 apply (zenon_L897_); trivial. % 10.29/10.47 (* end of lemma zenon_L917_ *) % 10.29/10.47 assert (zenon_L918_ : ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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 (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.29/10.47 do 0 intro. intros zenon_H65 zenon_H2b1 zenon_H328 zenon_H338 zenon_H335 zenon_H2b4 zenon_H33b zenon_H73 zenon_H1d5 zenon_H35f zenon_He2 zenon_H30 zenon_H2c zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H64 zenon_H2ee zenon_H1d9 zenon_H2ae zenon_H127 zenon_H155 zenon_H12a zenon_H14c zenon_H1cb zenon_H2c7 zenon_Ha9 zenon_H12c zenon_H304 zenon_H113 zenon_Hf1 zenon_H130 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H2fe zenon_H141 zenon_H301 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H22f zenon_H1e zenon_H272 zenon_H5f zenon_H96 zenon_H11f zenon_H192 zenon_H1c9 zenon_Hd1 zenon_H1db zenon_H16c zenon_H1f5 zenon_H1ea zenon_H187 zenon_H93 zenon_H1b9 zenon_H23 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1d4 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1ec zenon_Hbe zenon_H22e zenon_H124 zenon_H27 zenon_H110 zenon_H105 zenon_H2f zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_H101 zenon_H10d zenon_H82 zenon_H25. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.29/10.47 apply (zenon_L29_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.29/10.47 apply (zenon_L770_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.29/10.47 apply (zenon_L917_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.29/10.47 apply (zenon_L860_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.29/10.47 apply (zenon_L65_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.29/10.47 apply (zenon_L389_); trivial. % 10.29/10.47 apply (zenon_L898_); trivial. % 10.29/10.47 (* end of lemma zenon_L918_ *) % 10.29/10.47 assert (zenon_L919_ : ((op (e0) (e1)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((((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)) = 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(op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.29/10.47 do 0 intro. intros zenon_H89 zenon_H69 zenon_H25 zenon_H10d zenon_H101 zenon_Hfe zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H2f zenon_H105 zenon_H110 zenon_H27 zenon_H124 zenon_H22e zenon_Hbe zenon_H1ec zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1d4 zenon_H1f6 zenon_H7e zenon_H14b zenon_H23 zenon_H1b9 zenon_H93 zenon_H187 zenon_H1ea zenon_H1f5 zenon_H16c zenon_H1db zenon_Hd1 zenon_H1c9 zenon_H192 zenon_H11f zenon_H96 zenon_H5f zenon_H272 zenon_H1e zenon_H22f zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H301 zenon_H2fe zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H130 zenon_Hf1 zenon_H113 zenon_H304 zenon_H12c zenon_Ha9 zenon_H2c7 zenon_H1cb zenon_H14c zenon_H12a zenon_H155 zenon_H127 zenon_H2ae zenon_H1d9 zenon_H2ee zenon_H64 zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H2c zenon_H30 zenon_He2 zenon_H35f zenon_H1d5 zenon_H73 zenon_H82 zenon_H141. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.29/10.47 apply (zenon_L29_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.29/10.47 apply (zenon_L163_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.29/10.47 apply (zenon_L27_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.29/10.47 apply (zenon_L65_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.29/10.47 apply (zenon_L738_); trivial. % 10.29/10.47 apply (zenon_L898_); trivial. % 10.29/10.47 apply (zenon_L358_); trivial. % 10.29/10.47 (* end of lemma zenon_L919_ *) % 10.29/10.47 assert (zenon_L920_ : (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.29/10.47 do 0 intro. intros zenon_H335 zenon_Hd0 zenon_H16c zenon_H1d5 zenon_Ha2 zenon_H110 zenon_H27 zenon_H35f zenon_He2 zenon_H2f zenon_H20 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2c zenon_H2a zenon_H14b zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e zenon_H73 zenon_H82 zenon_H141. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.29/10.47 apply (zenon_L911_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.29/10.47 apply (zenon_L5_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.29/10.47 apply (zenon_L772_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.29/10.47 apply (zenon_L65_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.29/10.47 apply (zenon_L738_); trivial. % 10.29/10.47 apply (zenon_L897_); trivial. % 10.29/10.47 apply (zenon_L358_); trivial. % 10.29/10.47 (* end of lemma zenon_L920_ *) % 10.29/10.47 assert (zenon_L921_ : ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((((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) 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(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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) 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(e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.29/10.47 do 0 intro. intros zenon_Hd0 zenon_H2d4 zenon_H25 zenon_H10d zenon_H101 zenon_Hfe zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H2f zenon_H105 zenon_H110 zenon_H27 zenon_H124 zenon_H22e zenon_Hbe zenon_H1ec zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1d4 zenon_H1f6 zenon_H7e zenon_H14b zenon_H23 zenon_H1b9 zenon_H93 zenon_H187 zenon_H1ea zenon_H1f5 zenon_H16c zenon_H1db zenon_Hd1 zenon_H1c9 zenon_H192 zenon_H11f zenon_H96 zenon_H5f zenon_H272 zenon_H1e zenon_H22f zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H301 zenon_H2fe zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H130 zenon_Hf1 zenon_H113 zenon_H304 zenon_H12c zenon_Ha9 zenon_H2c7 zenon_H1cb zenon_H14c zenon_H12a zenon_H155 zenon_H127 zenon_H2ae zenon_H1d9 zenon_H2ee zenon_H64 zenon_H2ac zenon_H83 zenon_Hef zenon_H2f7 zenon_H2c zenon_H30 zenon_He2 zenon_H35f zenon_H1d5 zenon_H73 zenon_H94 zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H328 zenon_H82 zenon_H141. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.29/10.47 apply (zenon_L911_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.29/10.47 apply (zenon_L877_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.29/10.47 apply (zenon_L860_); trivial. % 10.29/10.47 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.29/10.48 apply (zenon_L65_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.29/10.48 apply (zenon_L738_); trivial. % 10.29/10.48 apply (zenon_L898_); trivial. % 10.29/10.48 apply (zenon_L358_); trivial. % 10.29/10.48 (* end of lemma zenon_L921_ *) % 10.29/10.48 assert (zenon_L922_ : (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((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) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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 (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.29/10.48 do 0 intro. intros zenon_H1e zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H30 zenon_H22f zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H16c zenon_H1ec zenon_Hbe zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H7e zenon_H7a zenon_H2fa zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H25 zenon_H23 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_Hef zenon_H1ce zenon_H127 zenon_H12c zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H101 zenon_H1ea zenon_H1f6 zenon_H1d9 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_Hf3 zenon_H82 zenon_H20 zenon_H35f zenon_H1d7 zenon_H22e zenon_H74 zenon_H27 zenon_H2c zenon_H1b9 zenon_H2f zenon_He2 zenon_H105. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.29/10.48 apply (zenon_L370_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.29/10.48 apply (zenon_L27_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.29/10.48 apply (zenon_L65_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.29/10.48 apply (zenon_L389_); trivial. % 10.29/10.48 apply (zenon_L896_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.29/10.48 apply (zenon_L161_); trivial. % 10.29/10.48 apply (zenon_L879_); trivial. % 10.29/10.48 (* end of lemma zenon_L922_ *) % 10.29/10.48 assert (zenon_L923_ : ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((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) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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 (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.29/10.48 do 0 intro. intros zenon_H1d5 zenon_H1e zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H30 zenon_H22f zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H16c zenon_H1ec zenon_Hbe zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H7e zenon_H7a zenon_H2fa zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H25 zenon_H23 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_Hef zenon_H1ce zenon_H127 zenon_H12c zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H101 zenon_H1ea zenon_H1f6 zenon_H1d9 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_Hf3 zenon_H82 zenon_H20 zenon_H35f zenon_H1d7 zenon_H22e zenon_H74 zenon_H27 zenon_H2c zenon_H1b9 zenon_H2f zenon_H105. % 10.29/10.48 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.29/10.48 apply (zenon_L7_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.29/10.48 apply (zenon_L772_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.29/10.48 apply (zenon_L259_); trivial. % 10.29/10.48 apply (zenon_L922_); trivial. % 10.29/10.48 (* end of lemma zenon_L923_ *) % 10.29/10.48 assert (zenon_L924_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.29/10.48 do 0 intro. intros zenon_H35f zenon_H50 zenon_H2f zenon_H12a zenon_Hf3 zenon_H16c zenon_H272 zenon_H7e zenon_H1f6 zenon_H1ec zenon_H5f zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H155 zenon_H23 zenon_Hb8 zenon_H1ce zenon_Ha9 zenon_H12c zenon_Hbe zenon_H13d zenon_H2a8 zenon_H1b9 zenon_H301 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H12f zenon_H11f zenon_Hd1 zenon_H1e zenon_H328 zenon_H22d zenon_H13a zenon_H2ac zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H22f zenon_H2fe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H1d4 zenon_H74 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H1ea zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H304 zenon_H30 zenon_H2c zenon_H2ae zenon_H338 zenon_H335 zenon_H2b4 zenon_H33b zenon_H27 zenon_H70 zenon_H14b zenon_H141 zenon_H10d zenon_H101 zenon_Hfe zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H105 zenon_H82 zenon_H25. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.29/10.48 apply (zenon_L923_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.29/10.48 apply (zenon_L269_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.29/10.48 apply (zenon_L864_); trivial. % 10.29/10.48 apply (zenon_L521_); trivial. % 10.29/10.48 (* end of lemma zenon_L924_ *) % 10.29/10.48 assert (zenon_L925_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((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) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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 (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.29/10.48 do 0 intro. intros zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H2ae zenon_H328 zenon_H272 zenon_H50 zenon_H1e zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H30 zenon_H22f zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H16c zenon_H1ec zenon_Hbe zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H7e zenon_H7a zenon_H2fa zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H25 zenon_H23 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_Hef zenon_H1ce zenon_H127 zenon_H12c zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H101 zenon_H1ea zenon_H1f6 zenon_H1d9 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_Hf3 zenon_H82 zenon_H20 zenon_H35f zenon_H1d7 zenon_H22e zenon_H74 zenon_H27 zenon_H2c zenon_H1b9 zenon_H2f zenon_H105. % 10.29/10.48 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.29/10.48 apply (zenon_L7_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.29/10.48 apply (zenon_L924_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.29/10.48 apply (zenon_L259_); trivial. % 10.29/10.48 apply (zenon_L922_); trivial. % 10.29/10.48 (* end of lemma zenon_L925_ *) % 10.29/10.48 assert (zenon_L926_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> False). % 10.29/10.48 do 0 intro. intros zenon_Hb4 zenon_H2dd. % 10.29/10.48 apply (zenon_and_s _ _ zenon_Hb4). zenon_intro zenon_H20. zenon_intro zenon_Hb5. % 10.29/10.48 apply (zenon_and_s _ _ zenon_Hb5). zenon_intro zenon_H20. zenon_intro zenon_Hb6. % 10.29/10.48 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 10.29/10.48 apply (zenon_L783_); trivial. % 10.29/10.48 (* end of lemma zenon_L926_ *) % 10.29/10.48 assert (zenon_L927_ : ((op (e0) (e3)) = (e0)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (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) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.48 do 0 intro. intros zenon_Hb7 zenon_H4d zenon_H50 zenon_H2f zenon_H27 zenon_H70 zenon_H82 zenon_H33b zenon_H335 zenon_H338 zenon_H328 zenon_H20 zenon_H25 zenon_H23 zenon_H1d4 zenon_Hd1 zenon_H22e zenon_Hbe zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_Heb zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H7a zenon_H1e zenon_H22f zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H105 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H110 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H12a zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2a zenon_H2c zenon_H2ae zenon_H2b4 zenon_H2b1 zenon_H101. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.29/10.48 apply (zenon_L7_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.29/10.48 apply (zenon_L27_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.29/10.48 apply (zenon_L161_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.29/10.48 apply (zenon_L794_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.29/10.48 apply (zenon_L770_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.29/10.48 apply (zenon_L23_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.29/10.48 apply (zenon_L8_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.29/10.48 apply (zenon_L174_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.29/10.48 apply (zenon_L783_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.29/10.48 apply (zenon_L869_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.29/10.48 apply (zenon_L341_); trivial. % 10.29/10.48 apply (zenon_L232_); trivial. % 10.29/10.48 apply (zenon_L887_); trivial. % 10.29/10.48 (* end of lemma zenon_L927_ *) % 10.29/10.48 assert (zenon_L928_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((((op (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 10.29/10.48 do 0 intro. intros zenon_Hbb zenon_H2f zenon_H50 zenon_H2d4 zenon_H65 zenon_H2b1 zenon_H4d zenon_H25 zenon_H16c zenon_Hfe zenon_Heb zenon_H272 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1ec zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H155 zenon_H23 zenon_Hb8 zenon_H1ce zenon_H101 zenon_Ha9 zenon_H12c zenon_Hbe zenon_H13d zenon_H2a8 zenon_H1b9 zenon_H105 zenon_H301 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_H1e zenon_H328 zenon_H22d zenon_H13a zenon_H2ac zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H141 zenon_H22f zenon_H2fe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H1d4 zenon_H7a zenon_H74 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H10d zenon_H304 zenon_H30 zenon_H2c zenon_H2ae zenon_H338 zenon_H335 zenon_H2b4 zenon_H33b zenon_H82 zenon_H27 zenon_Hb7 zenon_H1d9 zenon_H90. % 10.29/10.48 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.29/10.48 apply (zenon_L504_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.29/10.48 apply (zenon_L927_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.29/10.48 apply (zenon_L599_); trivial. % 10.29/10.48 apply (zenon_L891_); trivial. % 10.29/10.48 (* end of lemma zenon_L928_ *) % 10.29/10.48 assert (zenon_L929_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 10.29/10.48 do 0 intro. intros zenon_Hc3 zenon_Hbe zenon_H20. % 10.29/10.48 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_H89. zenon_intro zenon_Hc4. % 10.29/10.48 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_H9d. zenon_intro zenon_Hc5. % 10.29/10.48 apply (zenon_L794_); trivial. % 10.29/10.48 (* end of lemma zenon_L929_ *) % 10.29/10.48 assert (zenon_L930_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 10.29/10.48 do 0 intro. intros zenon_Hc9 zenon_Hbe zenon_H20. % 10.29/10.48 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H89. zenon_intro zenon_Hca. % 10.29/10.48 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_H9d. zenon_intro zenon_Hcb. % 10.29/10.48 apply (zenon_L794_); trivial. % 10.29/10.48 (* end of lemma zenon_L930_ *) % 10.29/10.48 assert (zenon_L931_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.29/10.48 do 0 intro. intros zenon_H172 zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H2f zenon_H105. % 10.29/10.48 apply (zenon_and_s _ _ zenon_H172). zenon_intro zenon_Hb7. zenon_intro zenon_H173. % 10.29/10.48 apply (zenon_and_s _ _ zenon_H173). zenon_intro zenon_H90. zenon_intro zenon_H174. % 10.29/10.48 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.29/10.48 apply (zenon_L807_); trivial. % 10.29/10.48 (* end of lemma zenon_L931_ *) % 10.29/10.48 assert (zenon_L932_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 10.29/10.48 do 0 intro. intros zenon_H17b zenon_H27 zenon_H5f. % 10.29/10.48 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H68. zenon_intro zenon_H17c. % 10.29/10.48 apply (zenon_and_s _ _ zenon_H17c). zenon_intro zenon_H5e. zenon_intro zenon_H6f. % 10.29/10.48 apply (zenon_L18_); trivial. % 10.29/10.48 (* end of lemma zenon_L932_ *) % 10.29/10.48 assert (zenon_L933_ : ((op (e0) (e1)) = (e2)) -> (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (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) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> False). % 10.29/10.48 do 0 intro. intros zenon_H65 zenon_H185 zenon_H50 zenon_H70 zenon_H82 zenon_H27 zenon_H2f zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H2ae zenon_H2c zenon_H30 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1ea zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H127 zenon_H2ee zenon_H156 zenon_H1dc zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H1d4 zenon_H2dd zenon_H2c4 zenon_H22e zenon_H2fe zenon_H22f zenon_H141 zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13a zenon_H22d zenon_H328 zenon_H1e zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_Hf1 zenon_H1c9 zenon_H130 zenon_H301 zenon_H105 zenon_H1b9 zenon_H2a8 zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hb8 zenon_H23 zenon_H155 zenon_H113 zenon_Hef zenon_H192 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H272 zenon_Heb zenon_Hfe zenon_H16c zenon_H25. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.29/10.48 apply (zenon_L7_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.29/10.48 apply (zenon_L27_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.29/10.48 apply (zenon_L161_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.29/10.48 apply (zenon_L29_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.29/10.48 apply (zenon_L268_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.29/10.48 apply (zenon_L870_); trivial. % 10.29/10.48 apply (zenon_L860_); trivial. % 10.29/10.48 (* end of lemma zenon_L933_ *) % 10.29/10.48 assert (zenon_L934_ : ((op (e1) (e0)) = (e3)) -> (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (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) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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 (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.29/10.48 do 0 intro. intros zenon_H73 zenon_H185 zenon_Hd2 zenon_H4d zenon_He2 zenon_Hfd zenon_H35f zenon_H23 zenon_H1d4 zenon_Hd1 zenon_H22e zenon_Hbe zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H1e zenon_H22f zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H2fe zenon_H16c zenon_Hb8 zenon_H74 zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H130 zenon_Hf1 zenon_H113 zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H64 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H12a zenon_H155 zenon_H1b9 zenon_H127 zenon_H30 zenon_H2c zenon_H2ae zenon_H2b4 zenon_H2b1 zenon_H124 zenon_H27 zenon_H110 zenon_H105 zenon_H2f zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_H101 zenon_H10d zenon_H82 zenon_H25. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.29/10.48 apply (zenon_L27_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.29/10.48 apply (zenon_L336_); trivial. % 10.29/10.48 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.29/10.48 apply (zenon_L738_); trivial. % 10.29/10.48 apply (zenon_L901_); trivial. % 10.29/10.48 (* end of lemma zenon_L934_ *) % 10.29/10.48 assert (zenon_L935_ : ((op (e1) (e0)) = (e3)) -> (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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 (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.29/10.48 do 0 intro. intros zenon_H73 zenon_H185 zenon_Hd2 zenon_H1d5 zenon_H35f zenon_He2 zenon_H30 zenon_H2c zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H64 zenon_H2ee zenon_H1d9 zenon_H2ae zenon_H127 zenon_H155 zenon_H12a zenon_H14c zenon_H1cb zenon_H2c7 zenon_Ha9 zenon_H12c zenon_H304 zenon_H113 zenon_Hf1 zenon_H130 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_H74 zenon_Hb8 zenon_H2fe zenon_H141 zenon_H301 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H22f zenon_H1e zenon_H272 zenon_H5f zenon_H96 zenon_H11f zenon_H192 zenon_H1c9 zenon_Hd1 zenon_H1db zenon_H16c zenon_H1f5 zenon_H1ea zenon_H187 zenon_H93 zenon_H1b9 zenon_H23 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1d4 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1ec zenon_Hbe zenon_H22e zenon_H124 zenon_H27 zenon_H110 zenon_H105 zenon_H2f zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_H101 zenon_H10d zenon_H82 zenon_H25. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.29/10.49 apply (zenon_L27_); trivial. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.29/10.49 apply (zenon_L336_); trivial. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.29/10.49 apply (zenon_L738_); trivial. % 10.29/10.49 apply (zenon_L898_); trivial. % 10.29/10.49 (* end of lemma zenon_L935_ *) % 10.29/10.49 assert (zenon_L936_ : ((op (e3) (e3)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (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) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> False). % 10.29/10.49 do 0 intro. intros zenon_H82 zenon_He2 zenon_H35f zenon_Hd2 zenon_H185 zenon_H73 zenon_H27 zenon_H2f zenon_H94 zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H2ae zenon_H2c zenon_H30 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1ea zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H127 zenon_H2ee zenon_H156 zenon_H1dc zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H1d4 zenon_H2dd zenon_H2c4 zenon_H22e zenon_H2fe zenon_H22f zenon_H141 zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13a zenon_H22d zenon_H328 zenon_H1e zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_Hf1 zenon_H1c9 zenon_H130 zenon_H301 zenon_H105 zenon_H1b9 zenon_H2a8 zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hb8 zenon_H23 zenon_H155 zenon_H113 zenon_Hef zenon_H192 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H272 zenon_Heb zenon_Hfe zenon_H16c zenon_H25. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.29/10.49 apply (zenon_L935_); trivial. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.29/10.49 apply (zenon_L269_); trivial. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.29/10.49 apply (zenon_L775_); trivial. % 10.29/10.49 apply (zenon_L859_); trivial. % 10.29/10.49 (* end of lemma zenon_L936_ *) % 10.29/10.49 assert (zenon_L937_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.29/10.49 do 0 intro. intros zenon_H141 zenon_H82 zenon_H328 zenon_H338 zenon_H335 zenon_H2b4 zenon_H33b zenon_H1d5 zenon_H35f zenon_H30 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H64 zenon_H2ee zenon_H1d9 zenon_H2ae zenon_H127 zenon_H155 zenon_H12a zenon_H14c zenon_H1cb zenon_H2c7 zenon_Ha9 zenon_H12c zenon_H304 zenon_H113 zenon_Hf1 zenon_H130 zenon_H22a zenon_H1d1 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H2a8 zenon_H118 zenon_H157 zenon_H154 zenon_H2fa zenon_Hb8 zenon_H2fe zenon_H301 zenon_H2ca zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H22f zenon_H1e zenon_H272 zenon_H5f zenon_H96 zenon_H11f zenon_H192 zenon_H1c9 zenon_Hd1 zenon_H1db zenon_H16c zenon_H1f5 zenon_H1ea zenon_H187 zenon_H93 zenon_H23 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1d4 zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1ec zenon_Hbe zenon_H124 zenon_H110 zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_H101 zenon_H10d zenon_H25 zenon_H2d4 zenon_Hd0 zenon_H2b1 zenon_H185 zenon_H1d7 zenon_H22e zenon_H74 zenon_H27 zenon_H2c zenon_H1b9 zenon_H2f zenon_H105. % 10.29/10.49 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.29/10.49 apply (zenon_L7_); trivial. % 10.29/10.49 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.29/10.49 apply (zenon_L772_); trivial. % 10.29/10.49 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.29/10.49 apply (zenon_L910_); trivial. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.29/10.49 apply (zenon_L370_); trivial. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.29/10.49 apply (zenon_L29_); trivial. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.29/10.49 apply (zenon_L118_); trivial. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.29/10.49 apply (zenon_L935_); trivial. % 10.29/10.49 apply (zenon_L390_); trivial. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.29/10.49 apply (zenon_L770_); trivial. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.29/10.49 apply (zenon_L920_); trivial. % 10.29/10.49 apply (zenon_L921_); trivial. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.29/10.49 apply (zenon_L161_); trivial. % 10.29/10.49 apply (zenon_L879_); trivial. % 10.29/10.49 (* end of lemma zenon_L937_ *) % 10.29/10.49 assert (zenon_L938_ : ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.29/10.49 do 0 intro. intros zenon_Hd0 zenon_H2d4 zenon_H25 zenon_H16c zenon_Hfe zenon_Heb zenon_H272 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1ec zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H155 zenon_H23 zenon_Hb8 zenon_H1ce zenon_H101 zenon_Ha9 zenon_H12c zenon_Hbe zenon_H13d zenon_H2a8 zenon_H1b9 zenon_H105 zenon_H301 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_H1e zenon_H328 zenon_H22d zenon_H13a zenon_H2ac zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H22f zenon_H2fe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H1d4 zenon_H7a zenon_H74 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H1ea zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H10d zenon_H304 zenon_H30 zenon_H2c zenon_H2ae zenon_H338 zenon_H335 zenon_H2b4 zenon_H33b zenon_H94 zenon_H2f zenon_H27 zenon_H73 zenon_H185 zenon_H35f zenon_He2 zenon_H82 zenon_H141. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.29/10.49 apply (zenon_L911_); trivial. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.29/10.49 apply (zenon_L877_); trivial. % 10.29/10.49 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.29/10.49 apply (zenon_L936_); trivial. % 10.29/10.49 apply (zenon_L358_); trivial. % 10.29/10.49 (* end of lemma zenon_L938_ *) % 10.29/10.49 assert (zenon_L939_ : (~((op (e2) (op (e2) (e0))) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e1) (e3)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H4d zenon_H2b1 zenon_H2b2 zenon_H45 zenon_H50 zenon_Hfd zenon_Hd0 zenon_H2d4 zenon_H25 zenon_H16c zenon_Hfe zenon_Heb zenon_H272 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1ec zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H155 zenon_H23 zenon_Hb8 zenon_H1ce zenon_H101 zenon_Ha9 zenon_H12c zenon_Hbe zenon_H13d zenon_H2a8 zenon_H1b9 zenon_H105 zenon_H301 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_H1e zenon_H328 zenon_H22d zenon_H13a zenon_H2ac zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H22f zenon_H2fe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H1d4 zenon_H7a zenon_H74 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H1ea zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H10d zenon_H304 zenon_H30 zenon_H2c zenon_H2ae zenon_H338 zenon_H335 zenon_H2b4 zenon_H33b zenon_H2f zenon_H27 zenon_H73 zenon_H185 zenon_H35f zenon_He2 zenon_H82 zenon_H141. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.29/10.50 apply (zenon_L911_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.29/10.50 apply (zenon_L809_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.29/10.50 apply (zenon_L934_); trivial. % 10.29/10.50 apply (zenon_L390_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.29/10.50 apply (zenon_L268_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.29/10.50 apply (zenon_L912_); trivial. % 10.29/10.50 apply (zenon_L938_); trivial. % 10.29/10.50 (* end of lemma zenon_L939_ *) % 10.29/10.50 assert (zenon_L940_ : ((op (e2) (e0)) = (e1)) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H2b2 zenon_H45 zenon_H50 zenon_Hd0 zenon_H2d4 zenon_H73 zenon_H185 zenon_Hd2 zenon_H82 zenon_H27 zenon_H2f zenon_H79 zenon_H20 zenon_H4d zenon_He2 zenon_H35f zenon_H272 zenon_H2ae zenon_H2b4 zenon_H2b1 zenon_H328 zenon_H338 zenon_H335 zenon_H33b zenon_Ha2 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2c zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.29/10.50 apply (zenon_L890_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.29/10.50 apply (zenon_L939_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.29/10.50 apply (zenon_L892_); trivial. % 10.29/10.50 apply (zenon_L108_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.29/10.50 apply (zenon_L936_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.29/10.50 apply (zenon_L907_); trivial. % 10.29/10.50 apply (zenon_L500_); trivial. % 10.29/10.50 (* end of lemma zenon_L940_ *) % 10.29/10.50 assert (zenon_L941_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H1a7 zenon_H2a8 zenon_H141 zenon_H2b1 zenon_Hf1 zenon_H335 zenon_H2ca zenon_H27 zenon_H25 zenon_H13a zenon_H82 zenon_Hfe. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H86. zenon_intro zenon_H1a8. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hd0. zenon_intro zenon_H6f. % 10.29/10.50 apply (zenon_L916_); trivial. % 10.29/10.50 (* end of lemma zenon_L941_ *) % 10.29/10.50 assert (zenon_L942_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 10.29/10.50 do 0 intro. intros zenon_H1a9 zenon_Hbe zenon_H20. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1a9). zenon_intro zenon_H86. zenon_intro zenon_H1aa. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_Hd0. zenon_intro zenon_Hb3. % 10.29/10.50 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H9d. zenon_intro zenon_H89. % 10.29/10.50 apply (zenon_L794_); trivial. % 10.29/10.50 (* end of lemma zenon_L942_ *) % 10.29/10.50 assert (zenon_L943_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H1d1 zenon_H20 zenon_H23 zenon_H25 zenon_H68 zenon_Hd2 zenon_H2b1 zenon_H82 zenon_H16c. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.29/10.50 apply (zenon_L4_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.29/10.50 apply (zenon_L20_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.29/10.50 apply (zenon_L342_); trivial. % 10.29/10.50 apply (zenon_L343_); trivial. % 10.29/10.50 (* end of lemma zenon_L943_ *) % 10.29/10.50 assert (zenon_L944_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H328 zenon_H1e zenon_H16c zenon_H155 zenon_H20 zenon_H23 zenon_H25 zenon_H2b1 zenon_Hd2 zenon_H35c zenon_H64 zenon_H1d1 zenon_Hd7 zenon_H13a zenon_H82 zenon_Hb8. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.29/10.50 apply (zenon_L2_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.29/10.50 apply (zenon_L943_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.29/10.50 apply (zenon_L4_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.29/10.50 apply (zenon_L873_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.29/10.50 apply (zenon_L881_); trivial. % 10.29/10.50 apply (zenon_L344_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.29/10.50 apply (zenon_L4_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.29/10.50 apply (zenon_L19_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.29/10.50 apply (zenon_L872_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.29/10.50 apply (zenon_L342_); trivial. % 10.29/10.50 apply (zenon_L613_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.29/10.50 apply (zenon_L881_); trivial. % 10.29/10.50 apply (zenon_L344_); trivial. % 10.29/10.50 (* end of lemma zenon_L944_ *) % 10.29/10.50 assert (zenon_L945_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H1b1 zenon_H328 zenon_H1e zenon_H16c zenon_H155 zenon_H20 zenon_H23 zenon_H25 zenon_H2b1 zenon_H35c zenon_H64 zenon_H1d1 zenon_H13a zenon_H82 zenon_Hb8. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_Hd2. zenon_intro zenon_H1b2. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_Hd7. zenon_intro zenon_Hc5. % 10.29/10.50 apply (zenon_L944_); trivial. % 10.29/10.50 (* end of lemma zenon_L945_ *) % 10.29/10.50 assert (zenon_L946_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H1e6 zenon_H22e zenon_H74 zenon_H27 zenon_H2c zenon_H1b9 zenon_H2f zenon_H105. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H72. zenon_intro zenon_H1e7. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_He2. zenon_intro zenon_H6f. % 10.29/10.50 apply (zenon_L879_); trivial. % 10.29/10.50 (* end of lemma zenon_L946_ *) % 10.29/10.50 assert (zenon_L947_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H1ff zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H2f zenon_H105. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1ff). zenon_intro zenon_H79. zenon_intro zenon_H200. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H200). zenon_intro zenon_H109. zenon_intro zenon_Hc5. % 10.29/10.50 apply (zenon_L807_); trivial. % 10.29/10.50 (* end of lemma zenon_L947_ *) % 10.29/10.50 assert (zenon_L948_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H203 zenon_H50. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H203). zenon_intro zenon_H7f. zenon_intro zenon_H204. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H204). zenon_intro zenon_H112. zenon_intro zenon_Hcf. % 10.29/10.50 apply (zenon_L368_); trivial. % 10.29/10.50 (* end of lemma zenon_L948_ *) % 10.29/10.50 assert (zenon_L949_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H22a zenon_H335 zenon_H65 zenon_Hb8 zenon_H82 zenon_H13a zenon_H1d1 zenon_H64 zenon_H35c zenon_Hd2 zenon_H2b1 zenon_H25 zenon_H23 zenon_H20 zenon_H155 zenon_H16c zenon_H1e zenon_H328 zenon_H30 zenon_H2f zenon_H5d. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.29/10.50 apply (zenon_L911_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.29/10.50 apply (zenon_L944_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.29/10.50 apply (zenon_L9_); trivial. % 10.29/10.50 apply (zenon_L208_); trivial. % 10.29/10.50 (* end of lemma zenon_L949_ *) % 10.29/10.50 assert (zenon_L950_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H1cb zenon_H2b2 zenon_H5d zenon_H328 zenon_H1e zenon_H16c zenon_H155 zenon_H20 zenon_H23 zenon_H25 zenon_H2b1 zenon_H35c zenon_H64 zenon_H1d1 zenon_H13a zenon_Hb8 zenon_H65 zenon_H335 zenon_H22a zenon_H30 zenon_H2f zenon_H82 zenon_Ha9. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.29/10.50 apply (zenon_L684_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.29/10.50 apply (zenon_L949_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.29/10.50 apply (zenon_L9_); trivial. % 10.29/10.50 apply (zenon_L255_); trivial. % 10.29/10.50 (* end of lemma zenon_L950_ *) % 10.29/10.50 assert (zenon_L951_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H2fa zenon_H68 zenon_H74 zenon_H5e zenon_H7a zenon_H2b3 zenon_H7e zenon_H82 zenon_H25. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.29/10.50 apply (zenon_L427_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.29/10.50 apply (zenon_L428_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.29/10.50 apply (zenon_L429_); trivial. % 10.29/10.50 apply (zenon_L521_); trivial. % 10.29/10.50 (* end of lemma zenon_L951_ *) % 10.29/10.50 assert (zenon_L952_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.29/10.50 do 0 intro. intros zenon_H301 zenon_H1d5 zenon_H74 zenon_H3c zenon_H1b9 zenon_H2b3 zenon_Hf6 zenon_H2d. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.29/10.50 apply (zenon_L427_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.29/10.50 apply (zenon_L12_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.29/10.50 apply (zenon_L432_); trivial. % 10.29/10.50 apply (zenon_L67_); trivial. % 10.29/10.50 (* end of lemma zenon_L952_ *) % 10.29/10.50 assert (zenon_L953_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.29/10.50 do 0 intro. intros zenon_H328 zenon_H20 zenon_H1e zenon_H25 zenon_H82 zenon_H7e zenon_H7a zenon_H5e zenon_H2fa zenon_H1d7 zenon_H301 zenon_H74 zenon_H3c zenon_H1b9 zenon_H2b3 zenon_Hf6 zenon_H2d. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.29/10.50 apply (zenon_L2_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.29/10.50 apply (zenon_L951_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.29/10.50 apply (zenon_L748_); trivial. % 10.29/10.50 apply (zenon_L952_); trivial. % 10.29/10.50 (* end of lemma zenon_L953_ *) % 10.29/10.50 assert (zenon_L954_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H2a8 zenon_H25 zenon_H68 zenon_H5f zenon_H65 zenon_H160 zenon_H82 zenon_Hfe. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.29/10.50 apply (zenon_L20_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.29/10.50 apply (zenon_L103_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.29/10.50 apply (zenon_L305_); trivial. % 10.29/10.50 apply (zenon_L313_); trivial. % 10.29/10.50 (* end of lemma zenon_L954_ *) % 10.29/10.50 assert (zenon_L955_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H2a8 zenon_H25 zenon_H68 zenon_H30 zenon_H2d zenon_Hd0 zenon_H13a zenon_H82 zenon_Hfe. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.29/10.50 apply (zenon_L20_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.29/10.50 apply (zenon_L38_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.29/10.50 apply (zenon_L881_); trivial. % 10.29/10.50 apply (zenon_L313_); trivial. % 10.29/10.50 (* end of lemma zenon_L955_ *) % 10.29/10.50 assert (zenon_L956_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.29/10.50 do 0 intro. intros zenon_H328 zenon_H20 zenon_H1e zenon_Hfe zenon_H82 zenon_H13a zenon_Hd0 zenon_H30 zenon_H25 zenon_H2a8 zenon_H1d7 zenon_H301 zenon_H74 zenon_H3c zenon_H1b9 zenon_H2b3 zenon_Hf6 zenon_H2d. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.29/10.50 apply (zenon_L2_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.29/10.50 apply (zenon_L955_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.29/10.50 apply (zenon_L748_); trivial. % 10.29/10.50 apply (zenon_L952_); trivial. % 10.29/10.50 (* end of lemma zenon_L956_ *) % 10.29/10.50 assert (zenon_L957_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H12f zenon_H11f zenon_H72 zenon_H2d zenon_Hd1 zenon_H2c zenon_H2b3 zenon_He2 zenon_H12a. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.29/10.50 apply (zenon_L78_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.29/10.50 apply (zenon_L79_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.29/10.50 apply (zenon_L438_); trivial. % 10.29/10.50 apply (zenon_L84_); trivial. % 10.29/10.50 (* end of lemma zenon_L957_ *) % 10.29/10.50 assert (zenon_L958_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H16f zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_H2c zenon_H2b3 zenon_H12a. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hb7. zenon_intro zenon_H170. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_H90. zenon_intro zenon_H171. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.29/10.50 apply (zenon_L957_); trivial. % 10.29/10.50 (* end of lemma zenon_L958_ *) % 10.29/10.50 assert (zenon_L959_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H175 zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H175). zenon_intro zenon_Hb7. zenon_intro zenon_H176. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H176). zenon_intro zenon_H90. zenon_intro zenon_H177. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.29/10.50 apply (zenon_L831_); trivial. % 10.29/10.50 (* end of lemma zenon_L959_ *) % 10.29/10.50 assert (zenon_L960_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H17b zenon_H2fa zenon_H74 zenon_H7a zenon_H2b3 zenon_H7e zenon_H82 zenon_H25. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H68. zenon_intro zenon_H17c. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H17c). zenon_intro zenon_H5e. zenon_intro zenon_H6f. % 10.29/10.50 apply (zenon_L951_); trivial. % 10.29/10.50 (* end of lemma zenon_L960_ *) % 10.29/10.50 assert (zenon_L961_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 10.29/10.50 do 0 intro. intros zenon_H17f zenon_H2dd zenon_H20. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H68. zenon_intro zenon_H180. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H5e. zenon_intro zenon_Hb6. % 10.29/10.50 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 10.29/10.50 apply (zenon_L783_); trivial. % 10.29/10.50 (* end of lemma zenon_L961_ *) % 10.29/10.50 assert (zenon_L962_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H19d zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_H2c zenon_H2b3 zenon_H12a. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_Hf7. zenon_intro zenon_H19e. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H171. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.29/10.50 apply (zenon_L957_); trivial. % 10.29/10.50 (* end of lemma zenon_L962_ *) % 10.29/10.50 assert (zenon_L963_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H1a3 zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_Hf7. zenon_intro zenon_H1a4. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1a4). zenon_intro zenon_H143. zenon_intro zenon_H177. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.29/10.50 apply (zenon_L831_); trivial. % 10.29/10.50 (* end of lemma zenon_L963_ *) % 10.29/10.50 assert (zenon_L964_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H1af zenon_H1d1 zenon_H20 zenon_H23 zenon_H25 zenon_H2b1 zenon_H82 zenon_H16c. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_Hd2. zenon_intro zenon_H1b0. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hd7. zenon_intro zenon_Hc2. % 10.29/10.50 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.29/10.50 apply (zenon_L943_); trivial. % 10.29/10.50 (* end of lemma zenon_L964_ *) % 10.29/10.50 assert (zenon_L965_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((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 (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H1e6 zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_H2c zenon_H2b3 zenon_H12a. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H72. zenon_intro zenon_H1e7. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_He2. zenon_intro zenon_H6f. % 10.29/10.50 apply (zenon_L957_); trivial. % 10.29/10.50 (* end of lemma zenon_L965_ *) % 10.29/10.50 assert (zenon_L966_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 10.29/10.50 do 0 intro. intros zenon_H1f9 zenon_H2dd zenon_H20. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1f9). zenon_intro zenon_H72. zenon_intro zenon_H1fa. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_He2. zenon_intro zenon_Hb6. % 10.29/10.50 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H9e. zenon_intro zenon_H97. % 10.29/10.50 apply (zenon_L783_); trivial. % 10.29/10.50 (* end of lemma zenon_L966_ *) % 10.29/10.50 assert (zenon_L967_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H1fb zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_H2c zenon_H2b3 zenon_H12a. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H72. zenon_intro zenon_H1fc. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_He2. zenon_intro zenon_Hbd. % 10.29/10.50 apply (zenon_L957_); trivial. % 10.29/10.50 (* end of lemma zenon_L967_ *) % 10.29/10.50 assert (zenon_L968_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H205 zenon_H160. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H7f. zenon_intro zenon_H206. % 10.29/10.50 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H112. zenon_intro zenon_Hd6. % 10.29/10.50 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd7. zenon_intro zenon_Hd2. % 10.29/10.50 apply (zenon_L305_); trivial. % 10.29/10.50 (* end of lemma zenon_L968_ *) % 10.29/10.50 assert (zenon_L969_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H5e zenon_H65 zenon_H25. % 10.29/10.50 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H6a | zenon_intro zenon_H22 ]. % 10.29/10.50 cut (((e2) = (e2)) = ((e1) = (e2))). % 10.29/10.50 intro zenon_D_pnotp. % 10.29/10.50 apply zenon_H25. % 10.29/10.50 rewrite <- zenon_D_pnotp. % 10.29/10.50 exact zenon_H6a. % 10.29/10.50 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.29/10.50 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 10.29/10.50 congruence. % 10.29/10.50 cut (((op (e0) (e1)) = (e1)) = ((e2) = (e1))). % 10.29/10.50 intro zenon_D_pnotp. % 10.29/10.50 apply zenon_H6b. % 10.29/10.50 rewrite <- zenon_D_pnotp. % 10.29/10.50 exact zenon_H5e. % 10.29/10.50 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.29/10.50 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 10.29/10.50 congruence. % 10.29/10.50 exact (zenon_H8b zenon_H65). % 10.29/10.50 apply zenon_H1d. apply refl_equal. % 10.29/10.50 apply zenon_H22. apply refl_equal. % 10.29/10.50 apply zenon_H22. apply refl_equal. % 10.29/10.50 (* end of lemma zenon_L969_ *) % 10.29/10.50 assert (zenon_L970_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H301 zenon_H25 zenon_H7e zenon_H7a zenon_H74 zenon_H2fa zenon_H5f zenon_H5e zenon_H1b9 zenon_H2b3 zenon_H2ca zenon_H335 zenon_Hd0 zenon_H30 zenon_H2d zenon_H101 zenon_H4f zenon_H87 zenon_H2c zenon_H2b4 zenon_H82 zenon_H141. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.29/10.50 apply (zenon_L951_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.29/10.50 apply (zenon_L18_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.29/10.50 apply (zenon_L432_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.29/10.50 apply (zenon_L911_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.29/10.50 apply (zenon_L38_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.29/10.50 apply (zenon_L379_); trivial. % 10.29/10.50 apply (zenon_L358_); trivial. % 10.29/10.50 (* end of lemma zenon_L970_ *) % 10.29/10.50 assert (zenon_L971_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H141 zenon_H82 zenon_H2b4 zenon_H4f zenon_H101 zenon_H30 zenon_Hd0 zenon_H335 zenon_H2ca zenon_H1b9 zenon_H5e zenon_H5f zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_H25 zenon_H301 zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_H2c zenon_H2b3 zenon_He2 zenon_H12a. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.29/10.50 apply (zenon_L370_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.29/10.50 apply (zenon_L65_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.29/10.50 apply (zenon_L970_); trivial. % 10.29/10.50 apply (zenon_L957_); trivial. % 10.29/10.50 (* end of lemma zenon_L971_ *) % 10.29/10.50 assert (zenon_L972_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H12c zenon_Hb7 zenon_Hf7 zenon_H101 zenon_Ha9 zenon_H82 zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H7f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.29/10.50 apply (zenon_L232_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.29/10.50 apply (zenon_L69_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.29/10.50 apply (zenon_L255_); trivial. % 10.29/10.50 apply (zenon_L831_); trivial. % 10.29/10.50 (* end of lemma zenon_L972_ *) % 10.29/10.50 assert (zenon_L973_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (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 (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H83 zenon_H50 zenon_Hde zenon_Heb zenon_Hd1 zenon_H11f zenon_H12f zenon_H93 zenon_H12a zenon_H130 zenon_Hef zenon_Hf1 zenon_H2d zenon_H113 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_Ha9 zenon_H101 zenon_Hf7 zenon_Hb7 zenon_H12c zenon_H82 zenon_H30. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.29/10.50 apply (zenon_L369_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.29/10.50 apply (zenon_L91_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.29/10.50 apply (zenon_L972_); trivial. % 10.29/10.50 apply (zenon_L26_); trivial. % 10.29/10.50 (* end of lemma zenon_L973_ *) % 10.29/10.50 assert (zenon_L974_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H301 zenon_H1d5 zenon_H74 zenon_H5e zenon_H1b9 zenon_H2b3 zenon_H2f7 zenon_H30 zenon_H93 zenon_H12f zenon_H11f zenon_Hd1 zenon_Heb zenon_H50 zenon_H83 zenon_H187 zenon_H1d7 zenon_H87 zenon_H12c zenon_Hb7 zenon_H101 zenon_Ha9 zenon_H82 zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.29/10.50 apply (zenon_L427_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.29/10.50 apply (zenon_L18_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.29/10.50 apply (zenon_L432_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.29/10.50 apply (zenon_L973_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.29/10.50 apply (zenon_L401_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.29/10.50 apply (zenon_L161_); trivial. % 10.29/10.50 apply (zenon_L972_); trivial. % 10.29/10.50 (* end of lemma zenon_L974_ *) % 10.29/10.50 assert (zenon_L975_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H118 zenon_H105 zenon_H82 zenon_Hfe zenon_Hf3 zenon_Hb7 zenon_H10d zenon_H2d zenon_H110 zenon_H113 zenon_H87 zenon_H7f zenon_H1ea. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_He2 | zenon_intro zenon_H119 ]. % 10.29/10.50 apply (zenon_L889_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H109 | zenon_intro zenon_H11a ]. % 10.29/10.50 apply (zenon_L73_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H112 | zenon_intro zenon_H52 ]. % 10.29/10.50 apply (zenon_L74_); trivial. % 10.29/10.50 apply (zenon_L299_); trivial. % 10.29/10.50 (* end of lemma zenon_L975_ *) % 10.29/10.50 assert (zenon_L976_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (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 (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H83 zenon_H11f zenon_H93 zenon_H1ea zenon_H87 zenon_H113 zenon_H110 zenon_H2d zenon_H10d zenon_Hb7 zenon_Hf3 zenon_Hfe zenon_H105 zenon_H118 zenon_H82 zenon_H30. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.29/10.50 apply (zenon_L78_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.29/10.50 apply (zenon_L91_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.29/10.50 apply (zenon_L975_); trivial. % 10.29/10.50 apply (zenon_L26_); trivial. % 10.29/10.50 (* end of lemma zenon_L976_ *) % 10.29/10.50 assert (zenon_L977_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H2fe zenon_H12a zenon_H2c zenon_H301 zenon_H74 zenon_H1b9 zenon_H2f7 zenon_H187 zenon_H1d7 zenon_H12c zenon_H101 zenon_Ha9 zenon_H1f5 zenon_H1c9 zenon_H2fa zenon_H7a zenon_H7e zenon_H25 zenon_H1e zenon_H328 zenon_H2b3 zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H50 zenon_Heb zenon_Hd1 zenon_H2d zenon_H11f zenon_H12f zenon_H83 zenon_H93 zenon_H1ea zenon_H113 zenon_H110 zenon_H118 zenon_H30 zenon_Hf1 zenon_Hef zenon_H130 zenon_H10d zenon_Hb7 zenon_Hfe zenon_H82 zenon_H105. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.29/10.50 apply (zenon_L2_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.29/10.50 apply (zenon_L2_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.29/10.50 apply (zenon_L951_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.29/10.50 apply (zenon_L748_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.29/10.50 apply (zenon_L7_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.29/10.50 apply (zenon_L59_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.29/10.50 apply (zenon_L7_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.29/10.50 apply (zenon_L65_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.29/10.50 apply (zenon_L974_); trivial. % 10.29/10.50 apply (zenon_L369_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.29/10.50 apply (zenon_L370_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.29/10.50 apply (zenon_L65_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.29/10.50 apply (zenon_L974_); trivial. % 10.29/10.50 apply (zenon_L957_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.29/10.50 apply (zenon_L434_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.29/10.50 apply (zenon_L7_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.29/10.50 apply (zenon_L59_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.29/10.50 apply (zenon_L64_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.29/10.50 apply (zenon_L65_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.29/10.50 apply (zenon_L976_); trivial. % 10.29/10.50 apply (zenon_L369_); trivial. % 10.29/10.50 apply (zenon_L889_); trivial. % 10.29/10.50 (* end of lemma zenon_L977_ *) % 10.29/10.50 assert (zenon_L978_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H12c zenon_Hfd zenon_H101 zenon_Hf3 zenon_Ha9 zenon_H82 zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H7f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.29/10.50 apply (zenon_L785_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.29/10.50 apply (zenon_L155_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.29/10.50 apply (zenon_L255_); trivial. % 10.29/10.50 apply (zenon_L831_); trivial. % 10.29/10.50 (* end of lemma zenon_L978_ *) % 10.29/10.50 assert (zenon_L979_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.29/10.50 do 0 intro. intros zenon_H83 zenon_H11f zenon_H87 zenon_H93 zenon_H12a zenon_H130 zenon_Hef zenon_Hf1 zenon_H2d zenon_H113 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_Ha9 zenon_Hf3 zenon_H101 zenon_Hfd zenon_H12c zenon_H82 zenon_H30. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.29/10.50 apply (zenon_L78_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.29/10.50 apply (zenon_L91_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.29/10.50 apply (zenon_L978_); trivial. % 10.29/10.50 apply (zenon_L26_); trivial. % 10.29/10.50 (* end of lemma zenon_L979_ *) % 10.29/10.50 assert (zenon_L980_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.29/10.50 do 0 intro. intros zenon_H10d zenon_Ha8 zenon_H101 zenon_H105 zenon_Hf3 zenon_Hfe zenon_H82 zenon_H110 zenon_H2d. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hfd | zenon_intro zenon_H10e ]. % 10.29/10.50 apply (zenon_L785_); trivial. % 10.29/10.50 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H10f ]. % 10.29/10.50 apply (zenon_L435_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H106 | zenon_intro zenon_H109 ]. % 10.29/10.51 apply (zenon_L313_); trivial. % 10.29/10.51 apply (zenon_L73_); trivial. % 10.29/10.51 (* end of lemma zenon_L980_ *) % 10.29/10.51 assert (zenon_L981_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.29/10.51 do 0 intro. intros zenon_H35f zenon_H118 zenon_H1ea zenon_H12f zenon_Hd1 zenon_Heb zenon_H50 zenon_H2b3 zenon_H328 zenon_H1e zenon_H25 zenon_H7e zenon_H7a zenon_H2fa zenon_H1c9 zenon_H1d7 zenon_H187 zenon_H2f7 zenon_H1b9 zenon_H74 zenon_H301 zenon_H2c zenon_H2fe zenon_H30 zenon_H12c zenon_Ha9 zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H113 zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a zenon_H93 zenon_H87 zenon_H11f zenon_H83 zenon_H2d zenon_H110 zenon_Hfe zenon_Hf3 zenon_H105 zenon_H101 zenon_H10d zenon_H82 zenon_H23. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.29/10.51 apply (zenon_L977_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.29/10.51 apply (zenon_L979_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.29/10.51 apply (zenon_L980_); trivial. % 10.29/10.51 apply (zenon_L125_); trivial. % 10.29/10.51 (* end of lemma zenon_L981_ *) % 10.29/10.51 assert (zenon_L982_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.51 do 0 intro. intros zenon_H2f7 zenon_Hb8 zenon_He2 zenon_H93 zenon_H12f zenon_H11f zenon_Hd1 zenon_Heb zenon_H50 zenon_H83 zenon_H30 zenon_Hd7 zenon_H1d7 zenon_H87 zenon_H12c zenon_Hfd zenon_H101 zenon_Hf3 zenon_Ha9 zenon_H82 zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.29/10.51 apply (zenon_L369_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.29/10.51 apply (zenon_L91_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.29/10.51 apply (zenon_L978_); trivial. % 10.29/10.51 apply (zenon_L229_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.29/10.51 apply (zenon_L251_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.29/10.51 apply (zenon_L161_); trivial. % 10.29/10.51 apply (zenon_L978_); trivial. % 10.29/10.51 (* end of lemma zenon_L982_ *) % 10.29/10.51 assert (zenon_L983_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.51 do 0 intro. intros zenon_Hfe zenon_H82 zenon_H35f zenon_H328 zenon_H20 zenon_H50 zenon_Hf3 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_H192 zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H16c zenon_H155 zenon_H5f zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_H22d zenon_H1e zenon_H68 zenon_H12f zenon_H11f zenon_H2d zenon_Hd1 zenon_H2c zenon_H2b3 zenon_He2 zenon_H12a. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.29/10.51 apply (zenon_L370_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.29/10.51 apply (zenon_L65_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.29/10.51 apply (zenon_L20_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.29/10.51 apply (zenon_L38_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.29/10.51 apply (zenon_L977_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.29/10.51 apply (zenon_L982_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.29/10.51 apply (zenon_L980_); trivial. % 10.29/10.51 apply (zenon_L500_); trivial. % 10.29/10.51 apply (zenon_L313_); trivial. % 10.29/10.51 apply (zenon_L957_); trivial. % 10.29/10.51 (* end of lemma zenon_L983_ *) % 10.29/10.51 assert (zenon_L984_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> ((op (e2) (e2)) = (e1)) -> False). % 10.29/10.51 do 0 intro. intros zenon_H1b5 zenon_H4f zenon_H2b3. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_Hd2. zenon_intro zenon_H1b6. % 10.29/10.51 apply (zenon_L378_); trivial. % 10.29/10.51 (* end of lemma zenon_L984_ *) % 10.29/10.51 assert (zenon_L985_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.29/10.51 do 0 intro. intros zenon_H207 zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H113 zenon_H2d zenon_Hf1 zenon_Hef zenon_H130 zenon_H12a. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H7f. zenon_intro zenon_H208. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H208). zenon_intro zenon_H112. zenon_intro zenon_H165. % 10.29/10.51 apply (zenon_L831_); trivial. % 10.29/10.51 (* end of lemma zenon_L985_ *) % 10.29/10.51 assert (zenon_L986_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.29/10.51 do 0 intro. intros zenon_H83 zenon_H2c zenon_H1d5 zenon_H2d zenon_H93 zenon_H5d zenon_H82 zenon_H30. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H72 | zenon_intro zenon_H84 ]. % 10.29/10.51 apply (zenon_L771_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H79 | zenon_intro zenon_H85 ]. % 10.29/10.51 apply (zenon_L91_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H7f | zenon_intro zenon_H52 ]. % 10.29/10.51 apply (zenon_L584_); trivial. % 10.29/10.51 apply (zenon_L26_); trivial. % 10.29/10.51 (* end of lemma zenon_L986_ *) % 10.29/10.51 assert (zenon_L987_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.29/10.51 do 0 intro. intros zenon_H2fa zenon_H105 zenon_H1b9 zenon_H2c zenon_H2d zenon_H74 zenon_H301 zenon_H5e zenon_H7a zenon_H2b3 zenon_H7e zenon_Hf3 zenon_Hb8. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.29/10.51 apply (zenon_L440_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.29/10.51 apply (zenon_L428_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.29/10.51 apply (zenon_L429_); trivial. % 10.29/10.51 apply (zenon_L712_); trivial. % 10.29/10.51 (* end of lemma zenon_L987_ *) % 10.29/10.51 assert (zenon_L988_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> False). % 10.29/10.51 do 0 intro. intros zenon_H362 zenon_Hb8 zenon_Hf3 zenon_H7e zenon_H7a zenon_H301 zenon_H74 zenon_H1b9 zenon_H105 zenon_H2fa zenon_H2d zenon_H2c zenon_H2ac zenon_H2b3 zenon_H5c. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H5e | zenon_intro zenon_H363 ]. % 10.29/10.51 apply (zenon_L987_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H363); [ zenon_intro zenon_H27 | zenon_intro zenon_H364 ]. % 10.29/10.51 apply (zenon_L8_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H364); [ zenon_intro zenon_H18c | zenon_intro zenon_H143 ]. % 10.29/10.51 apply (zenon_L455_); trivial. % 10.29/10.51 apply (zenon_L93_); trivial. % 10.29/10.51 (* end of lemma zenon_L988_ *) % 10.29/10.51 assert (zenon_L989_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 10.29/10.51 do 0 intro. intros zenon_Hd4 zenon_H2dd zenon_H20. % 10.29/10.51 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_H97. zenon_intro zenon_Hd5. % 10.29/10.51 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_H9e. zenon_intro zenon_Hd6. % 10.29/10.51 apply (zenon_L783_); trivial. % 10.29/10.51 (* end of lemma zenon_L989_ *) % 10.29/10.51 assert (zenon_L990_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.29/10.51 do 0 intro. intros zenon_H203 zenon_H5d zenon_H82. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H203). zenon_intro zenon_H7f. zenon_intro zenon_H204. % 10.29/10.51 apply (zenon_L584_); trivial. % 10.29/10.51 (* end of lemma zenon_L990_ *) % 10.29/10.51 assert (zenon_L991_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (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)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((~((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) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.29/10.51 do 0 intro. intros zenon_H1ea zenon_H93 zenon_H16c zenon_H25 zenon_H1b9 zenon_H110 zenon_H2dd zenon_H20 zenon_Hbe zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_Heb zenon_H1d1 zenon_H23 zenon_H2b1 zenon_H2fe zenon_H83 zenon_H1d7 zenon_H1e zenon_H328 zenon_H362 zenon_Hb8 zenon_H7e zenon_H7a zenon_H301 zenon_H74 zenon_H105 zenon_H2fa zenon_H2ac zenon_H5f zenon_H22f zenon_H35f zenon_H304 zenon_H22a zenon_H1d9 zenon_H1f6 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H157 zenon_H154 zenon_H192 zenon_H96 zenon_H1d4 zenon_H2c4 zenon_H22e zenon_H1ec zenon_H155 zenon_H14b zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H2b4 zenon_H335 zenon_Hfe zenon_H10d zenon_H118 zenon_H1c9 zenon_Ha9 zenon_H101 zenon_H12c zenon_H187 zenon_H2f7 zenon_H127 zenon_H130 zenon_Hef zenon_Hf1 zenon_H113 zenon_H1f5 zenon_H2a zenon_He8 zenon_H141 zenon_H2c zenon_H2b3 zenon_H82 zenon_H30. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.29/10.51 apply (zenon_L7_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.29/10.51 apply (zenon_L11_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H3c. zenon_intro zenon_H44. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H160. zenon_intro zenon_Hf6. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.29/10.51 apply (zenon_L2_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.29/10.51 apply (zenon_L953_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.29/10.51 apply (zenon_L434_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.29/10.51 apply (zenon_L154_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.29/10.51 apply (zenon_L424_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.29/10.51 apply (zenon_L954_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.29/10.51 apply (zenon_L956_); trivial. % 10.29/10.51 apply (zenon_L344_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.29/10.51 apply (zenon_L748_); trivial. % 10.29/10.51 apply (zenon_L440_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.29/10.51 apply (zenon_L795_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.29/10.51 apply (zenon_L926_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.29/10.51 apply (zenon_L2_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.29/10.51 apply (zenon_L953_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.29/10.51 apply (zenon_L434_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.29/10.51 apply (zenon_L154_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.29/10.51 apply (zenon_L503_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.29/10.51 apply (zenon_L954_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.29/10.51 apply (zenon_L955_); trivial. % 10.29/10.51 apply (zenon_L66_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.29/10.51 apply (zenon_L748_); trivial. % 10.29/10.51 apply (zenon_L440_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.29/10.51 apply (zenon_L302_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.29/10.51 apply (zenon_L321_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.29/10.51 apply (zenon_L303_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.29/10.51 apply (zenon_L304_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.29/10.51 apply (zenon_L55_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.29/10.51 apply (zenon_L306_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.29/10.51 apply (zenon_L446_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.29/10.51 apply (zenon_L256_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.29/10.51 apply (zenon_L958_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.29/10.51 apply (zenon_L308_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.29/10.51 apply (zenon_L959_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.29/10.51 apply (zenon_L263_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.29/10.51 apply (zenon_L960_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.29/10.51 apply (zenon_L309_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.29/10.51 apply (zenon_L961_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_H5e. zenon_intro zenon_Hbd. % 10.29/10.51 apply (zenon_L951_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.29/10.51 apply (zenon_L117_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.29/10.51 apply (zenon_L336_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.29/10.51 apply (zenon_L452_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.29/10.51 apply (zenon_L271_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.29/10.51 apply (zenon_L750_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.29/10.51 apply (zenon_L456_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.29/10.51 apply (zenon_L457_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.29/10.51 apply (zenon_L275_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.29/10.51 apply (zenon_L962_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.29/10.51 apply (zenon_L133_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.29/10.51 apply (zenon_L963_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.29/10.51 apply (zenon_L276_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H86. zenon_intro zenon_H1a8. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hd0. zenon_intro zenon_H6f. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H20. zenon_intro zenon_H20. % 10.29/10.51 apply (zenon_L956_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.29/10.51 apply (zenon_L361_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.29/10.51 apply (zenon_L138_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H86. zenon_intro zenon_H1ae. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_Hd0. zenon_intro zenon_Hbd. % 10.29/10.51 apply (zenon_L956_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.29/10.51 apply (zenon_L964_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.29/10.51 apply (zenon_L340_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.29/10.51 apply (zenon_L464_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.29/10.51 apply (zenon_L591_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.29/10.51 apply (zenon_L284_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.29/10.51 apply (zenon_L467_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.29/10.51 apply (zenon_L468_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.29/10.51 apply (zenon_L469_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.29/10.51 apply (zenon_L471_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.29/10.51 apply (zenon_L593_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.29/10.51 apply (zenon_L167_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.29/10.51 apply (zenon_L286_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.29/10.51 apply (zenon_L965_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.29/10.51 apply (zenon_L195_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.29/10.51 apply (zenon_L966_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.29/10.51 apply (zenon_L967_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.29/10.51 apply (zenon_L350_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.29/10.51 apply (zenon_L351_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.29/10.51 apply (zenon_L595_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.29/10.51 apply (zenon_L183_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H203). zenon_intro zenon_H7f. zenon_intro zenon_H204. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H204). zenon_intro zenon_H112. zenon_intro zenon_Hcf. % 10.29/10.51 apply (zenon_L831_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.29/10.51 apply (zenon_L968_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.29/10.51 apply (zenon_L491_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.29/10.51 apply (zenon_L187_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.29/10.51 apply (zenon_L296_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.29/10.51 apply (zenon_L357_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.29/10.51 apply (zenon_L300_); trivial. % 10.29/10.51 apply (zenon_L301_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.29/10.51 apply (zenon_L2_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.29/10.51 apply (zenon_L424_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.29/10.51 apply (zenon_L969_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.29/10.51 apply (zenon_L7_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.29/10.51 apply (zenon_L59_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.29/10.51 apply (zenon_L64_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.29/10.51 apply (zenon_L65_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.29/10.51 apply (zenon_L970_); trivial. % 10.29/10.51 apply (zenon_L369_); trivial. % 10.29/10.51 apply (zenon_L971_); trivial. % 10.29/10.51 apply (zenon_L344_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.29/10.51 apply (zenon_L434_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.29/10.51 apply (zenon_L154_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.29/10.51 apply (zenon_L21_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.29/10.51 apply (zenon_L59_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.29/10.51 apply (zenon_L64_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.29/10.51 apply (zenon_L65_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.29/10.51 apply (zenon_L981_); trivial. % 10.29/10.51 apply (zenon_L369_); trivial. % 10.29/10.51 apply (zenon_L983_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.29/10.51 apply (zenon_L748_); trivial. % 10.29/10.51 apply (zenon_L440_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.29/10.51 apply (zenon_L795_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.29/10.51 apply (zenon_L926_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.29/10.51 apply (zenon_and_s _ _ zenon_Hbb). zenon_intro zenon_H20. zenon_intro zenon_Hbc. % 10.29/10.51 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_H20. zenon_intro zenon_Hbd. % 10.29/10.51 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.29/10.51 apply (zenon_L977_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.29/10.51 apply (zenon_L246_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.29/10.51 apply (zenon_L321_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.29/10.51 apply (zenon_L364_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.29/10.51 apply (zenon_L930_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.29/10.51 apply (zenon_L55_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.29/10.51 apply (zenon_L372_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.29/10.51 apply (zenon_L446_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.29/10.51 apply (zenon_L198_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.29/10.51 apply (zenon_L958_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.29/10.51 apply (zenon_L328_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.29/10.51 apply (zenon_L596_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.29/10.51 apply (zenon_L263_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.29/10.51 apply (zenon_L960_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.29/10.51 apply (zenon_L264_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.29/10.51 apply (zenon_L597_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_H5e. zenon_intro zenon_Hbd. % 10.29/10.51 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.29/10.51 apply (zenon_L977_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.29/10.51 apply (zenon_L117_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.29/10.51 apply (zenon_L336_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.29/10.51 apply (zenon_L121_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.29/10.51 apply (zenon_L271_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.29/10.51 apply (zenon_L694_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.29/10.51 apply (zenon_L374_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.29/10.51 apply (zenon_L457_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.29/10.51 apply (zenon_L375_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.29/10.51 apply (zenon_L962_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.29/10.51 apply (zenon_L133_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.29/10.51 apply (zenon_L963_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.29/10.51 apply (zenon_L276_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H86. zenon_intro zenon_H1a8. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hd0. zenon_intro zenon_H6f. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H20. zenon_intro zenon_H20. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.29/10.51 apply (zenon_L277_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.29/10.51 apply (zenon_L526_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.29/10.51 apply (zenon_L59_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.29/10.51 apply (zenon_L526_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.29/10.51 apply (zenon_L65_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.29/10.51 apply (zenon_L970_); trivial. % 10.29/10.51 apply (zenon_L369_); trivial. % 10.29/10.51 apply (zenon_L971_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.29/10.51 apply (zenon_L434_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.29/10.51 apply (zenon_L154_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.29/10.51 apply (zenon_L526_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.29/10.51 apply (zenon_L59_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.29/10.51 apply (zenon_L526_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.29/10.51 apply (zenon_L65_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.29/10.51 apply (zenon_L981_); trivial. % 10.29/10.51 apply (zenon_L369_); trivial. % 10.29/10.51 apply (zenon_L983_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.29/10.51 apply (zenon_L684_); trivial. % 10.29/10.51 apply (zenon_L440_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.29/10.51 apply (zenon_L942_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.29/10.51 apply (zenon_L138_); trivial. % 10.29/10.51 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.29/10.51 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H86. zenon_intro zenon_H1ae. % 10.40/10.51 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_Hd0. zenon_intro zenon_Hbd. % 10.40/10.51 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.40/10.51 apply (zenon_L977_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.40/10.51 apply (zenon_L752_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.40/10.51 apply (zenon_L340_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.40/10.51 apply (zenon_L377_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.40/10.51 apply (zenon_L984_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.40/10.51 apply (zenon_L284_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.40/10.51 apply (zenon_L146_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.40/10.51 apply (zenon_L468_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.40/10.51 apply (zenon_L149_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.40/10.51 apply (zenon_L471_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.40/10.51 apply (zenon_L346_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.40/10.51 apply (zenon_L167_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.40/10.51 apply (zenon_L286_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.40/10.51 apply (zenon_L965_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.40/10.51 apply (zenon_L858_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.40/10.51 apply (zenon_L204_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.40/10.51 apply (zenon_L967_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.40/10.51 apply (zenon_L350_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.40/10.51 apply (zenon_L351_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.40/10.51 apply (zenon_L206_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.40/10.51 apply (zenon_L183_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.40/10.51 apply (zenon_L948_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.40/10.51 apply (zenon_L753_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.40/10.51 apply (zenon_L985_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.40/10.51 apply (zenon_L187_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.40/10.51 apply (zenon_L296_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.40/10.51 apply (zenon_L298_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.40/10.51 apply (zenon_L300_); trivial. % 10.40/10.51 apply (zenon_L301_); trivial. % 10.40/10.51 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.40/10.51 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 10.40/10.51 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H51. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.51 apply (zenon_L39_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.40/10.51 apply (zenon_L39_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.40/10.51 apply (zenon_L951_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.40/10.51 apply (zenon_L748_); trivial. % 10.40/10.51 apply (zenon_L986_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.51 apply (zenon_L434_); trivial. % 10.40/10.51 apply (zenon_L988_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.40/10.51 apply (zenon_L795_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.40/10.51 apply (zenon_L926_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.40/10.51 apply (zenon_L502_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.40/10.51 apply (zenon_L246_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.40/10.51 apply (zenon_L321_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.40/10.51 apply (zenon_L433_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.40/10.51 apply (zenon_L207_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.40/10.51 apply (zenon_L55_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.40/10.51 apply (zenon_L989_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.40/10.51 apply (zenon_L446_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.40/10.51 apply (zenon_L209_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.40/10.51 apply (zenon_L700_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.40/10.51 apply (zenon_L328_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.40/10.51 apply (zenon_L701_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.40/10.51 apply (zenon_L263_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.40/10.51 apply (zenon_L960_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.40/10.51 apply (zenon_L264_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.40/10.51 apply (zenon_L961_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.40/10.51 apply (zenon_L553_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.40/10.51 apply (zenon_L117_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.40/10.51 apply (zenon_L336_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.40/10.51 apply (zenon_L452_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.40/10.51 apply (zenon_L583_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.40/10.51 apply (zenon_L750_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.40/10.51 apply (zenon_L456_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.40/10.51 apply (zenon_L457_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.40/10.51 apply (zenon_L211_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.40/10.51 apply (zenon_L703_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.40/10.51 apply (zenon_L133_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.40/10.51 apply (zenon_L585_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.40/10.51 apply (zenon_L276_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.51 apply (zenon_L277_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.40/10.51 apply (zenon_L277_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.40/10.51 apply (zenon_L951_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.40/10.51 apply (zenon_L748_); trivial. % 10.40/10.51 apply (zenon_L986_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.51 apply (zenon_L434_); trivial. % 10.40/10.51 apply (zenon_L988_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.40/10.51 apply (zenon_L942_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.40/10.51 apply (zenon_L138_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.40/10.51 apply (zenon_L578_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.40/10.51 apply (zenon_L964_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.40/10.51 apply (zenon_L340_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.40/10.51 apply (zenon_L464_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.40/10.51 apply (zenon_L586_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.40/10.51 apply (zenon_L284_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.40/10.51 apply (zenon_L467_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.40/10.51 apply (zenon_L468_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.40/10.51 apply (zenon_L213_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.40/10.51 apply (zenon_L704_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.40/10.51 apply (zenon_L346_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.40/10.51 apply (zenon_L167_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.40/10.51 apply (zenon_L286_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.40/10.51 apply (zenon_L965_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.40/10.51 apply (zenon_L858_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.40/10.51 apply (zenon_L966_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.40/10.51 apply (zenon_L579_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.40/10.51 apply (zenon_L350_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.40/10.51 apply (zenon_L351_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.40/10.51 apply (zenon_L490_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.40/10.51 apply (zenon_L183_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.40/10.51 apply (zenon_L990_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.40/10.51 apply (zenon_L706_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.40/10.51 apply (zenon_L491_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.40/10.51 apply (zenon_L187_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.40/10.51 apply (zenon_L296_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.40/10.51 apply (zenon_L357_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.40/10.51 apply (zenon_L300_); trivial. % 10.40/10.51 apply (zenon_L301_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.40/10.51 apply (zenon_L438_); trivial. % 10.40/10.51 apply (zenon_L26_); trivial. % 10.40/10.51 (* end of lemma zenon_L991_ *) % 10.40/10.51 assert (zenon_L992_ : ((op (e2) (e2)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((((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) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> False). % 10.40/10.51 do 0 intro. intros zenon_H2f zenon_H65 zenon_H35c zenon_H5d zenon_H27 zenon_H30 zenon_H2c zenon_H141 zenon_He8 zenon_H2a zenon_H1f5 zenon_H113 zenon_Hf1 zenon_Hef zenon_H130 zenon_H127 zenon_H2f7 zenon_H187 zenon_H12c zenon_H101 zenon_Ha9 zenon_H1c9 zenon_H118 zenon_H10d zenon_Hfe zenon_H335 zenon_H2b4 zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H14b zenon_H155 zenon_H1ec zenon_H22e zenon_H2c4 zenon_H1d4 zenon_H96 zenon_H192 zenon_H154 zenon_H157 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1f6 zenon_H1d9 zenon_H22a zenon_H304 zenon_H35f zenon_H22f zenon_H5f zenon_H2ac zenon_H2fa zenon_H105 zenon_H74 zenon_H301 zenon_H7a zenon_H7e zenon_Hb8 zenon_H362 zenon_H328 zenon_H1e zenon_H1d7 zenon_H83 zenon_H2fe zenon_H2b1 zenon_H23 zenon_H1d1 zenon_Heb zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_Hbe zenon_H20 zenon_H2dd zenon_H110 zenon_H1b9 zenon_H25 zenon_H16c zenon_H93 zenon_H1ea zenon_Ha2 zenon_H82. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b5 ]. % 10.40/10.51 apply (zenon_L950_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H18c | zenon_intro zenon_H2b6 ]. % 10.40/10.51 apply (zenon_L388_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H102 ]. % 10.40/10.51 apply (zenon_L991_); trivial. % 10.40/10.51 apply (zenon_L867_); trivial. % 10.40/10.51 (* end of lemma zenon_L992_ *) % 10.40/10.51 assert (zenon_L993_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.40/10.51 do 0 intro. intros zenon_H16c zenon_H338 zenon_H23 zenon_H1d4 zenon_Hbe zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H12f zenon_H2dd zenon_H2c4 zenon_H1c9 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H187 zenon_H5f zenon_H272 zenon_H1e zenon_H22f zenon_H22d zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H141 zenon_H2fe zenon_H2fa zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H1dc zenon_H156 zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d7 zenon_H22a zenon_H130 zenon_Hf1 zenon_H113 zenon_H304 zenon_H2f7 zenon_Hef zenon_H83 zenon_H2ac zenon_H12c zenon_Ha9 zenon_H110 zenon_H2ee zenon_H2c7 zenon_H1cb zenon_H14c zenon_H1d9 zenon_H12a zenon_H155 zenon_H127 zenon_H2ae zenon_H2b1 zenon_H2b4 zenon_H35c zenon_H64 zenon_H1d1 zenon_Hd1 zenon_H2d4 zenon_H10d zenon_H101 zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H33b zenon_H335 zenon_H5d zenon_H35f zenon_H362 zenon_H328 zenon_H30 zenon_H22e zenon_H74 zenon_H2c zenon_H1b9 zenon_H2f zenon_H105 zenon_Hfe zenon_H13a zenon_H25 zenon_H27 zenon_H68 zenon_H2a8 zenon_H82 zenon_Hb8. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.51 apply (zenon_L4_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.51 apply (zenon_L19_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.51 apply (zenon_L20_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.51 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.51 apply (zenon_L7_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.51 apply (zenon_L29_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.51 apply (zenon_L770_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.51 apply (zenon_L992_); trivial. % 10.40/10.51 apply (zenon_L860_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.51 apply (zenon_L599_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.51 apply (zenon_L370_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.51 apply (zenon_L29_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.51 apply (zenon_L231_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.51 apply (zenon_L992_); trivial. % 10.40/10.51 apply (zenon_L878_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.51 apply (zenon_L28_); trivial. % 10.40/10.51 apply (zenon_L879_); trivial. % 10.40/10.51 apply (zenon_L343_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.51 apply (zenon_L882_); trivial. % 10.40/10.51 apply (zenon_L344_); trivial. % 10.40/10.51 (* end of lemma zenon_L993_ *) % 10.40/10.51 assert (zenon_L994_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 10.40/10.51 do 0 intro. intros zenon_H33b zenon_Ha2 zenon_Ha1 zenon_H2d4 zenon_H5d zenon_H2f zenon_H30 zenon_H328 zenon_H1e zenon_H16c zenon_H155 zenon_H20 zenon_H23 zenon_H25 zenon_H2b1 zenon_Hd2 zenon_H35c zenon_H64 zenon_H1d1 zenon_H13a zenon_H82 zenon_Hb8 zenon_H335 zenon_H22a zenon_H79 zenon_H7a. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H89 | zenon_intro zenon_H33c ]. % 10.40/10.51 apply (zenon_L41_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H33c); [ zenon_intro zenon_H5e | zenon_intro zenon_H33d ]. % 10.40/10.51 apply (zenon_L776_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H33d); [ zenon_intro zenon_H65 | zenon_intro zenon_H70 ]. % 10.40/10.51 apply (zenon_L949_); trivial. % 10.40/10.51 apply (zenon_L24_); trivial. % 10.40/10.51 (* end of lemma zenon_L994_ *) % 10.40/10.51 assert (zenon_L995_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 10.40/10.51 do 0 intro. intros zenon_H33b zenon_H94 zenon_H5f zenon_H27 zenon_H5d zenon_H2f zenon_H30 zenon_H328 zenon_H1e zenon_H16c zenon_H155 zenon_H20 zenon_H23 zenon_H25 zenon_H2b1 zenon_Hd2 zenon_H35c zenon_H64 zenon_H1d1 zenon_H13a zenon_H82 zenon_Hb8 zenon_H335 zenon_H22a zenon_H79 zenon_H7a. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H89 | zenon_intro zenon_H33c ]. % 10.40/10.51 apply (zenon_L382_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H33c); [ zenon_intro zenon_H5e | zenon_intro zenon_H33d ]. % 10.40/10.51 apply (zenon_L18_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H33d); [ zenon_intro zenon_H65 | zenon_intro zenon_H70 ]. % 10.40/10.51 apply (zenon_L949_); trivial. % 10.40/10.51 apply (zenon_L24_); trivial. % 10.40/10.51 (* end of lemma zenon_L995_ *) % 10.40/10.51 assert (zenon_L996_ : (((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)) = (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) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.40/10.51 do 0 intro. intros zenon_H35f zenon_H12a zenon_He2 zenon_Ha9 zenon_H12c zenon_H105 zenon_H2f zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_H82 zenon_Hfe zenon_Hf3 zenon_H101 zenon_H10d zenon_H1f6 zenon_H1ea zenon_H1d5 zenon_H1f5 zenon_H5d zenon_H14b zenon_H79. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.40/10.51 apply (zenon_L889_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.40/10.51 apply (zenon_L895_); trivial. % 10.40/10.51 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.40/10.51 apply (zenon_L862_); trivial. % 10.40/10.51 apply (zenon_L216_); trivial. % 10.40/10.51 (* end of lemma zenon_L996_ *) % 10.40/10.51 assert (zenon_L997_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (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)) = (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) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 10.40/10.51 do 0 intro. intros zenon_H2ee zenon_H7e zenon_H73 zenon_H74 zenon_H93 zenon_H2c zenon_H83 zenon_H30 zenon_Hd2 zenon_H35f zenon_H12a zenon_He2 zenon_Ha9 zenon_H12c zenon_H105 zenon_H2f zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_H82 zenon_Hfe zenon_Hf3 zenon_H101 zenon_H10d zenon_H1f6 zenon_H1ea zenon_H1d5 zenon_H1f5 zenon_H5d zenon_H14b. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.52 apply (zenon_L27_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.52 apply (zenon_L986_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.52 apply (zenon_L738_); trivial. % 10.40/10.52 apply (zenon_L996_); trivial. % 10.40/10.52 (* end of lemma zenon_L997_ *) % 10.40/10.52 assert (zenon_L998_ : (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (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 (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.40/10.52 do 0 intro. intros zenon_H64 zenon_H130 zenon_H1c9 zenon_H14b zenon_H5d zenon_H1f5 zenon_H1d5 zenon_H1ea zenon_H1f6 zenon_H10d zenon_H101 zenon_Hf3 zenon_Hfe zenon_H82 zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H12c zenon_Ha9 zenon_H12a zenon_H35f zenon_Hd2 zenon_H30 zenon_H83 zenon_H93 zenon_H7e zenon_H2ee zenon_H1d7 zenon_H22e zenon_H74 zenon_H27 zenon_H2c zenon_H1b9 zenon_H2f zenon_H105. % 10.40/10.52 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.52 apply (zenon_L7_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.52 apply (zenon_L772_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.52 apply (zenon_L259_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.52 apply (zenon_L370_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.52 apply (zenon_L997_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.52 apply (zenon_L161_); trivial. % 10.40/10.52 apply (zenon_L879_); trivial. % 10.40/10.52 (* end of lemma zenon_L998_ *) % 10.40/10.52 assert (zenon_L999_ : ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (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) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> False). % 10.40/10.52 do 0 intro. intros zenon_H27 zenon_Hd2 zenon_H35f zenon_H5d zenon_H5c zenon_H2f zenon_H82 zenon_Hf3 zenon_Ha8 zenon_H98 zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H2ae zenon_H2c zenon_H30 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1ea zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H127 zenon_H2ee zenon_H156 zenon_H1dc zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H1d4 zenon_H2dd zenon_H2c4 zenon_H22e zenon_H2fe zenon_H22f zenon_H141 zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13a zenon_H22d zenon_H328 zenon_H1e zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_Hf1 zenon_H1c9 zenon_H130 zenon_H301 zenon_H105 zenon_H1b9 zenon_H2a8 zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hb8 zenon_H23 zenon_H155 zenon_H113 zenon_Hef zenon_H192 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H272 zenon_Heb zenon_Hfe zenon_H16c zenon_H25. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.40/10.52 apply (zenon_L998_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.40/10.52 apply (zenon_L93_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.40/10.52 apply (zenon_L904_); trivial. % 10.40/10.52 apply (zenon_L859_); trivial. % 10.40/10.52 (* end of lemma zenon_L999_ *) % 10.40/10.52 assert (zenon_L1000_ : ((op (e1) (e0)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((((op (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.40/10.52 do 0 intro. intros zenon_H73 zenon_H2d4 zenon_H89 zenon_H5a zenon_H35c zenon_H2b1 zenon_H25 zenon_H16c zenon_Hfe zenon_Heb zenon_H272 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1ec zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H155 zenon_Hb8 zenon_H1ce zenon_H101 zenon_Ha9 zenon_H12c zenon_Hbe zenon_H13d zenon_H2a8 zenon_H1b9 zenon_H105 zenon_H301 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_H1e zenon_H328 zenon_H22d zenon_H13a zenon_H2ac zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H141 zenon_H22f zenon_H2fe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H1d4 zenon_H7a zenon_H74 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H1ea zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H10d zenon_H304 zenon_H30 zenon_H2c zenon_H2ae zenon_H338 zenon_H335 zenon_H2b4 zenon_H33b zenon_H2f zenon_H27 zenon_Hd2 zenon_H35f zenon_H5d zenon_H5c zenon_H82 zenon_H23. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.52 apply (zenon_L27_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.52 apply (zenon_L8_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.52 apply (zenon_L738_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.40/10.52 apply (zenon_L783_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.40/10.52 apply (zenon_L994_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.40/10.52 apply (zenon_L501_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.40/10.52 apply (zenon_L381_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.40/10.52 apply (zenon_L995_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.40/10.52 apply (zenon_L999_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.40/10.52 apply (zenon_L616_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.40/10.52 apply (zenon_L875_); trivial. % 10.40/10.52 apply (zenon_L859_); trivial. % 10.40/10.52 apply (zenon_L125_); trivial. % 10.40/10.52 (* end of lemma zenon_L1000_ *) % 10.40/10.52 assert (zenon_L1001_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (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 (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.40/10.52 do 0 intro. intros zenon_H2fa zenon_H105 zenon_H1b9 zenon_H2c zenon_H27 zenon_H74 zenon_H22e zenon_H1d7 zenon_H2ee zenon_H7e zenon_H93 zenon_H83 zenon_H30 zenon_Hd2 zenon_H35f zenon_H12a zenon_Ha9 zenon_H12c zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_Hf3 zenon_H101 zenon_H10d zenon_H1f6 zenon_H1ea zenon_H1f5 zenon_H5d zenon_H14b zenon_H1c9 zenon_H130 zenon_H64 zenon_H5c zenon_H2f zenon_H94 zenon_H82 zenon_H25. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.40/10.52 apply (zenon_L998_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.40/10.52 apply (zenon_L93_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.40/10.52 apply (zenon_L775_); trivial. % 10.40/10.52 apply (zenon_L521_); trivial. % 10.40/10.52 (* end of lemma zenon_L1001_ *) % 10.40/10.52 assert (zenon_L1002_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (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))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.40/10.52 do 0 intro. intros zenon_H2ca zenon_H335 zenon_Hd0 zenon_Hf1 zenon_H69 zenon_H25 zenon_H94 zenon_H2f zenon_H5c zenon_H64 zenon_H130 zenon_H1c9 zenon_H14b zenon_H5d zenon_H1f5 zenon_H1ea zenon_H1f6 zenon_H10d zenon_H101 zenon_Hf3 zenon_Hfe zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H12c zenon_Ha9 zenon_H12a zenon_H35f zenon_H30 zenon_H83 zenon_H93 zenon_H7e zenon_H2ee zenon_H1d7 zenon_H22e zenon_H74 zenon_H27 zenon_H2c zenon_H1b9 zenon_H105 zenon_H2fa zenon_H82 zenon_H141. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.52 apply (zenon_L911_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.52 apply (zenon_L163_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.52 apply (zenon_L1001_); trivial. % 10.40/10.52 apply (zenon_L358_); trivial. % 10.40/10.52 (* end of lemma zenon_L1002_ *) % 10.40/10.52 assert (zenon_L1003_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.40/10.52 do 0 intro. intros zenon_H12c zenon_Hfd zenon_Hf3 zenon_H12a zenon_Ha9 zenon_H82 zenon_H109 zenon_H101. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.40/10.52 apply (zenon_L785_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.40/10.52 apply (zenon_L155_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.40/10.52 apply (zenon_L255_); trivial. % 10.40/10.52 apply (zenon_L80_); trivial. % 10.40/10.52 (* end of lemma zenon_L1003_ *) % 10.40/10.52 assert (zenon_L1004_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> False). % 10.40/10.52 do 0 intro. intros zenon_H35f zenon_H109 zenon_H2f zenon_H20 zenon_H82 zenon_Hf3 zenon_H1ed zenon_H98 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2c zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.40/10.52 apply (zenon_L906_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.40/10.52 apply (zenon_L1003_); trivial. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.40/10.52 apply (zenon_L904_); trivial. % 10.40/10.52 apply (zenon_L500_); trivial. % 10.40/10.52 (* end of lemma zenon_L1004_ *) % 10.40/10.52 assert (zenon_L1005_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.40/10.52 do 0 intro. intros zenon_H272 zenon_H27 zenon_H5d zenon_H5c zenon_H69 zenon_Hd0 zenon_H335 zenon_H1e zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H2c zenon_H30 zenon_H22f zenon_H105 zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H16c zenon_H1ec zenon_Hbe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H7e zenon_H7a zenon_H74 zenon_H2fa zenon_H1b9 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H25 zenon_H23 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_Hef zenon_H1ce zenon_H127 zenon_H12c zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H101 zenon_H1ea zenon_H1f6 zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H1ed zenon_Hf3 zenon_H82 zenon_H20 zenon_H2f zenon_H109 zenon_H35f zenon_H5a zenon_H72. % 10.40/10.52 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.40/10.53 apply (zenon_L381_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.40/10.53 apply (zenon_L1002_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.40/10.53 apply (zenon_L1004_); trivial. % 10.40/10.53 apply (zenon_L98_); trivial. % 10.40/10.53 (* end of lemma zenon_L1005_ *) % 10.40/10.53 assert (zenon_L1006_ : ((op (e3) (e0)) = (e3)) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> False). % 10.40/10.53 do 0 intro. intros zenon_H72 zenon_H5a zenon_H35f zenon_H109 zenon_H2f zenon_Hf3 zenon_H1ed zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2c zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H13d zenon_Hfe zenon_H22d zenon_H335 zenon_H69 zenon_H5c zenon_H27 zenon_H272 zenon_Hb8 zenon_H82 zenon_H13a zenon_H1d1 zenon_H64 zenon_H35c zenon_H2b1 zenon_H25 zenon_H23 zenon_H20 zenon_H155 zenon_H16c zenon_H1e zenon_H328 zenon_H2ac zenon_Hd2 zenon_H5d. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.40/10.53 apply (zenon_L1005_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.40/10.53 apply (zenon_L944_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.40/10.53 apply (zenon_L668_); trivial. % 10.40/10.53 apply (zenon_L208_); trivial. % 10.40/10.53 (* end of lemma zenon_L1006_ *) % 10.40/10.53 assert (zenon_L1007_ : (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.40/10.53 do 0 intro. intros zenon_H5d zenon_Hd2 zenon_H2ac zenon_H328 zenon_H1e zenon_H16c zenon_H155 zenon_H20 zenon_H23 zenon_H25 zenon_H2b1 zenon_H35c zenon_H64 zenon_H1d1 zenon_H13a zenon_Hb8 zenon_H272 zenon_H27 zenon_H5c zenon_H69 zenon_H335 zenon_H22d zenon_Hfe zenon_H13d zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H30 zenon_H22f zenon_H105 zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H1ec zenon_Hbe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_H7e zenon_H7a zenon_H74 zenon_H2fa zenon_H1b9 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_Hef zenon_H1ce zenon_H127 zenon_H12c zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H101 zenon_H1f6 zenon_H1d9 zenon_H1d7 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H2f zenon_H35f zenon_H5a zenon_H72 zenon_H2c zenon_H109 zenon_H82 zenon_Ha2 zenon_H1ed zenon_H1ea. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.40/10.53 apply (zenon_L1006_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.40/10.53 apply (zenon_L132_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.40/10.53 apply (zenon_L867_); trivial. % 10.40/10.53 apply (zenon_L777_); trivial. % 10.40/10.53 (* end of lemma zenon_L1007_ *) % 10.40/10.53 assert (zenon_L1008_ : ((op (e0) (e1)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = 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(e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.40/10.53 do 0 intro. intros zenon_H70 zenon_H1ea zenon_Ha2 zenon_H109 zenon_H2c zenon_H72 zenon_H5a zenon_H35f zenon_H2f zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H13d zenon_Hfe zenon_H22d zenon_H335 zenon_H69 zenon_H5c zenon_H27 zenon_H272 zenon_Hb8 zenon_H13a zenon_H1d1 zenon_H64 zenon_H35c zenon_H2b1 zenon_H23 zenon_H20 zenon_H155 zenon_H16c zenon_H1e zenon_H328 zenon_H2ac zenon_Hd2 zenon_H5d zenon_H82 zenon_H25. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.40/10.53 apply (zenon_L772_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.40/10.53 apply (zenon_L93_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.40/10.53 apply (zenon_L1007_); trivial. % 10.40/10.53 apply (zenon_L521_); trivial. % 10.40/10.53 (* end of lemma zenon_L1008_ *) % 10.40/10.53 assert (zenon_L1009_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((~((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) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.40/10.53 do 0 intro. intros zenon_H272 zenon_H2ae zenon_H1ea zenon_H93 zenon_H16c zenon_H25 zenon_H1b9 zenon_H110 zenon_H2dd zenon_H20 zenon_Hbe zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_Heb zenon_H1d1 zenon_H23 zenon_H2b1 zenon_H2fe zenon_H83 zenon_H1d7 zenon_H1e zenon_H328 zenon_H362 zenon_Hb8 zenon_H7e zenon_H7a zenon_H301 zenon_H74 zenon_H105 zenon_H2fa zenon_H2ac zenon_H5f zenon_H22f zenon_H35f zenon_H304 zenon_H22a zenon_H1d9 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H157 zenon_H154 zenon_H192 zenon_H96 zenon_H1d4 zenon_H2c4 zenon_H22e zenon_H1ec zenon_H155 zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H2b4 zenon_H335 zenon_Hfe zenon_H10d zenon_H118 zenon_H1c9 zenon_Ha9 zenon_H101 zenon_H12c zenon_H187 zenon_H2f7 zenon_H127 zenon_H130 zenon_Hef zenon_Hf1 zenon_H113 zenon_H2a zenon_He8 zenon_H141 zenon_H2c zenon_H30 zenon_H27 zenon_H35c zenon_H65 zenon_H2f zenon_H1f6 zenon_H14b zenon_H1d5 zenon_H1f5 zenon_H5d zenon_H82. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.53 apply (zenon_L29_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.53 apply (zenon_L770_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.53 apply (zenon_L992_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H98 | zenon_intro zenon_H1f7 ]. % 10.40/10.53 apply (zenon_L833_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1f8 ]. % 10.40/10.53 apply (zenon_L215_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H166 | zenon_intro zenon_H7f ]. % 10.40/10.53 apply (zenon_L208_); trivial. % 10.40/10.53 apply (zenon_L584_); trivial. % 10.40/10.53 (* end of lemma zenon_L1009_ *) % 10.40/10.53 assert (zenon_L1010_ : (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = 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(e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (((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 (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 10.40/10.53 do 0 intro. intros zenon_H23 zenon_H82 zenon_H5c zenon_H5d zenon_H35f zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H2ae zenon_H2c zenon_H30 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1ea zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H127 zenon_H2ee zenon_H156 zenon_H1dc zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H1d4 zenon_H2dd zenon_H22e zenon_H2fe zenon_H22f zenon_H141 zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_H110 zenon_H13a zenon_H22d zenon_H328 zenon_H1e zenon_H12a zenon_H11f zenon_H12f zenon_Hf1 zenon_H1c9 zenon_H130 zenon_H301 zenon_H105 zenon_H1b9 zenon_H2a8 zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hb8 zenon_H155 zenon_H113 zenon_Hef zenon_H192 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H272 zenon_Heb zenon_Hfe zenon_H16c zenon_H25 zenon_H2b1 zenon_H35c zenon_H5a zenon_H2d4 zenon_H73 zenon_H2c7 zenon_H89 zenon_Ha1 zenon_H27 zenon_Hd1 zenon_H2c4 zenon_H2f zenon_H2ac. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.53 apply (zenon_L29_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.53 apply (zenon_L5_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.53 apply (zenon_L1000_); trivial. % 10.40/10.53 apply (zenon_L390_); trivial. % 10.40/10.53 (* end of lemma zenon_L1010_ *) % 10.40/10.53 assert (zenon_L1011_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 10.40/10.53 do 0 intro. intros zenon_H2ee zenon_H7e zenon_H74 zenon_H83 zenon_Hf1 zenon_H73 zenon_H33b zenon_Ha2 zenon_Ha1 zenon_H2d4 zenon_H5d zenon_H2f zenon_H30 zenon_H328 zenon_H1e zenon_H16c zenon_H155 zenon_H20 zenon_H23 zenon_H25 zenon_H2b1 zenon_Hd2 zenon_H35c zenon_H64 zenon_H1d1 zenon_H13a zenon_H82 zenon_Hb8 zenon_H335 zenon_H22a zenon_H7a. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.53 apply (zenon_L27_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.53 apply (zenon_L65_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.53 apply (zenon_L738_); trivial. % 10.40/10.53 apply (zenon_L994_); trivial. % 10.40/10.53 (* end of lemma zenon_L1011_ *) % 10.40/10.53 assert (zenon_L1012_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.40/10.53 do 0 intro. intros zenon_H2ca zenon_Hd0 zenon_H27 zenon_H7a zenon_H22a zenon_H335 zenon_Hb8 zenon_H13a zenon_H1d1 zenon_H64 zenon_H35c zenon_H2b1 zenon_H25 zenon_H23 zenon_H20 zenon_H155 zenon_H16c zenon_H1e zenon_H328 zenon_H30 zenon_H2f zenon_H5d zenon_H2d4 zenon_Ha1 zenon_Ha2 zenon_H33b zenon_H73 zenon_Hf1 zenon_H83 zenon_H74 zenon_H7e zenon_H2ee zenon_H82 zenon_H141. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.53 apply (zenon_L911_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.53 apply (zenon_L5_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.53 apply (zenon_L1011_); trivial. % 10.40/10.53 apply (zenon_L358_); trivial. % 10.40/10.53 (* end of lemma zenon_L1012_ *) % 10.40/10.53 assert (zenon_L1013_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 10.40/10.53 do 0 intro. intros zenon_H2ee zenon_H7e zenon_H74 zenon_H83 zenon_Hf1 zenon_H73 zenon_H33b zenon_H94 zenon_H5f zenon_H27 zenon_H5d zenon_H2f zenon_H30 zenon_H328 zenon_H1e zenon_H16c zenon_H155 zenon_H20 zenon_H23 zenon_H25 zenon_H2b1 zenon_Hd2 zenon_H35c zenon_H64 zenon_H1d1 zenon_H13a zenon_H82 zenon_Hb8 zenon_H335 zenon_H22a zenon_H7a. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.53 apply (zenon_L27_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.53 apply (zenon_L65_); trivial. % 10.40/10.53 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.54 apply (zenon_L738_); trivial. % 10.40/10.54 apply (zenon_L995_); trivial. % 10.40/10.54 (* end of lemma zenon_L1013_ *) % 10.40/10.54 assert (zenon_L1014_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.40/10.54 do 0 intro. intros zenon_H2ac zenon_H2c4 zenon_Hd1 zenon_H2c7 zenon_H5a zenon_Hfe zenon_Heb zenon_H272 zenon_H14b zenon_H1f6 zenon_H1ec zenon_He8 zenon_H2a zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H1ce zenon_H101 zenon_Ha9 zenon_H12c zenon_Hbe zenon_H13d zenon_H2a8 zenon_H301 zenon_H130 zenon_H1c9 zenon_H12f zenon_H11f zenon_H12a zenon_H22d zenon_H110 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H1db zenon_H14c zenon_H22f zenon_H2fe zenon_H2dd zenon_H1d4 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H1dc zenon_H156 zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d9 zenon_H1d7 zenon_H10d zenon_H304 zenon_H2c zenon_H2ae zenon_H338 zenon_H2b4 zenon_H35f zenon_H5c zenon_Ha1 zenon_H2ca zenon_Hd0 zenon_He2 zenon_H22e zenon_H1b9 zenon_H105 zenon_H2d4 zenon_H7a zenon_H22a zenon_H335 zenon_Hb8 zenon_H13a zenon_H1d1 zenon_H64 zenon_H35c zenon_H2b1 zenon_H25 zenon_H23 zenon_H20 zenon_H155 zenon_H16c zenon_H1e zenon_H328 zenon_H30 zenon_H2f zenon_H5d zenon_H27 zenon_H5f zenon_H33b zenon_H73 zenon_Hf1 zenon_H83 zenon_H74 zenon_H7e zenon_H2ee zenon_H82 zenon_H141. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.54 apply (zenon_L1010_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.54 apply (zenon_L231_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.54 apply (zenon_L1012_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.54 apply (zenon_L911_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.54 apply (zenon_L877_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.54 apply (zenon_L1013_); trivial. % 10.40/10.54 apply (zenon_L358_); trivial. % 10.40/10.54 (* end of lemma zenon_L1014_ *) % 10.40/10.54 assert (zenon_L1015_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (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) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> (~((op (e0) (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 (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.40/10.54 do 0 intro. intros zenon_H6d zenon_H362 zenon_H105 zenon_H2f zenon_H1b9 zenon_H2c zenon_H27 zenon_H74 zenon_H22e zenon_H1d7 zenon_H2ac zenon_H2c4 zenon_Hd1 zenon_H2c7 zenon_H5a zenon_Hfe zenon_Heb zenon_H272 zenon_H14b zenon_H1f6 zenon_H1ec zenon_He8 zenon_H2a zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H1ce zenon_H101 zenon_Ha9 zenon_H12c zenon_Hbe zenon_H13d zenon_H2a8 zenon_H301 zenon_H130 zenon_H1c9 zenon_H12f zenon_H11f zenon_H12a zenon_H22d zenon_H110 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H1db zenon_H14c zenon_H22f zenon_H2fe zenon_H2dd zenon_H1d4 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H1dc zenon_H156 zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1ea zenon_H1d9 zenon_H10d zenon_H304 zenon_H2ae zenon_H338 zenon_H2b4 zenon_H35f zenon_H5c zenon_Ha1 zenon_H2ca zenon_H2d4 zenon_H7a zenon_H22a zenon_H335 zenon_H13a zenon_H1d1 zenon_H64 zenon_H35c zenon_H2b1 zenon_H25 zenon_H23 zenon_H20 zenon_H155 zenon_H16c zenon_H1e zenon_H328 zenon_H30 zenon_H5d zenon_H5f zenon_H33b zenon_Hf1 zenon_H83 zenon_H7e zenon_H2ee zenon_H141 zenon_H1d5 zenon_H82 zenon_Hb8. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.54 apply (zenon_L424_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.54 apply (zenon_L1009_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.54 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.54 apply (zenon_L7_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.54 apply (zenon_L772_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.54 apply (zenon_L599_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.54 apply (zenon_L370_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.54 apply (zenon_L1014_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.54 apply (zenon_L161_); trivial. % 10.40/10.54 apply (zenon_L879_); trivial. % 10.40/10.54 apply (zenon_L344_); trivial. % 10.40/10.54 (* end of lemma zenon_L1015_ *) % 10.40/10.54 assert (zenon_L1016_ : ((op (e2) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((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) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.40/10.54 do 0 intro. intros zenon_Ha8 zenon_H1e zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H2c zenon_H30 zenon_H22f zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H16c zenon_H1ec zenon_Hbe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_H7e zenon_H7a zenon_H74 zenon_H2fa zenon_H1b9 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H25 zenon_H23 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_Hef zenon_H1ce zenon_H127 zenon_H12c zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H101 zenon_H1ea zenon_H1f6 zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_H98 zenon_H1ed zenon_H20 zenon_H2f zenon_H35f zenon_Hb8 zenon_H82 zenon_H109 zenon_H105. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H1cf ]. % 10.40/10.54 apply (zenon_L232_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1d0 ]. % 10.40/10.54 apply (zenon_L1004_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hf4 | zenon_intro zenon_He2 ]. % 10.40/10.54 apply (zenon_L344_); trivial. % 10.40/10.54 apply (zenon_L71_); trivial. % 10.40/10.54 (* end of lemma zenon_L1016_ *) % 10.40/10.54 assert (zenon_L1017_ : (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (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) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> False). % 10.40/10.54 do 0 intro. intros zenon_H5d zenon_H2b1 zenon_H35c zenon_H2d4 zenon_H5c zenon_H5a zenon_H362 zenon_H6d zenon_H27 zenon_H109 zenon_H82 zenon_H35f zenon_H2f zenon_H98 zenon_Ha8 zenon_H33b zenon_H2b4 zenon_H335 zenon_H338 zenon_H2ae zenon_H2c zenon_H30 zenon_H304 zenon_H10d zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1ea zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H127 zenon_H2ee zenon_H156 zenon_H1dc zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H93 zenon_H96 zenon_H2fa zenon_H74 zenon_H7a zenon_H1d4 zenon_H2dd zenon_H2c4 zenon_H22e zenon_H2fe zenon_H22f zenon_H141 zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H110 zenon_H2ac zenon_H13a zenon_H22d zenon_H328 zenon_H1e zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_Hf1 zenon_H1c9 zenon_H130 zenon_H301 zenon_H105 zenon_H1b9 zenon_H2a8 zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_Hb8 zenon_H23 zenon_H155 zenon_H113 zenon_Hef zenon_H192 zenon_H1f5 zenon_H5f zenon_H2a zenon_H20 zenon_He8 zenon_H1ec zenon_H1f6 zenon_H7e zenon_H14b zenon_H272 zenon_Heb zenon_Hfe zenon_H16c zenon_H25. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.40/10.54 apply (zenon_L1015_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.40/10.54 apply (zenon_L269_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.40/10.54 apply (zenon_L1016_); trivial. % 10.40/10.54 apply (zenon_L859_); trivial. % 10.40/10.54 (* end of lemma zenon_L1017_ *) % 10.40/10.54 assert (zenon_L1018_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 10.40/10.54 do 0 intro. intros zenon_H2ee zenon_H1d5 zenon_H1d7 zenon_H83 zenon_H74 zenon_H7e zenon_H130 zenon_H2c zenon_H2ac zenon_H33b zenon_H94 zenon_H5f zenon_H27 zenon_H5d zenon_H2f zenon_H30 zenon_H328 zenon_H1e zenon_H16c zenon_H155 zenon_H20 zenon_H23 zenon_H25 zenon_H2b1 zenon_Hd2 zenon_H35c zenon_H64 zenon_H1d1 zenon_H13a zenon_H82 zenon_Hb8 zenon_H335 zenon_H22a zenon_H7a. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.54 apply (zenon_L772_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.54 apply (zenon_L8_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.54 apply (zenon_L389_); trivial. % 10.40/10.54 apply (zenon_L995_); trivial. % 10.40/10.54 (* end of lemma zenon_L1018_ *) % 10.40/10.54 assert (zenon_L1019_ : ((op (e2) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.40/10.54 do 0 intro. intros zenon_H2b2 zenon_H25 zenon_H16c zenon_Hfe zenon_Heb zenon_H272 zenon_H14b zenon_H7e zenon_H1f6 zenon_H1ec zenon_He8 zenon_H20 zenon_H2a zenon_H5f zenon_H1f5 zenon_H192 zenon_Hef zenon_H113 zenon_H155 zenon_H23 zenon_Hb8 zenon_H1ce zenon_H101 zenon_Ha9 zenon_H12c zenon_Hbe zenon_H13d zenon_H2a8 zenon_H1b9 zenon_H105 zenon_H301 zenon_H130 zenon_H1c9 zenon_Hf1 zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_H1e zenon_H328 zenon_H22d zenon_H13a zenon_H2ac zenon_H110 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H22f zenon_H2fe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H1d4 zenon_H7a zenon_H74 zenon_H2fa zenon_H96 zenon_H93 zenon_H154 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H127 zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H1ea zenon_H1d9 zenon_H1d7 zenon_H1d1 zenon_H22a zenon_H10d zenon_H304 zenon_H30 zenon_H2c zenon_H2ae zenon_H338 zenon_H335 zenon_H2b4 zenon_H33b zenon_H94 zenon_H2f zenon_H5c zenon_H27 zenon_H5d zenon_H2b1 zenon_H35c zenon_H82 zenon_H141. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.54 apply (zenon_L950_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.54 apply (zenon_L5_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.40/10.54 apply (zenon_L1018_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.40/10.54 apply (zenon_L93_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.40/10.54 apply (zenon_L775_); trivial. % 10.40/10.54 apply (zenon_L859_); trivial. % 10.40/10.54 apply (zenon_L358_); trivial. % 10.40/10.54 (* end of lemma zenon_L1019_ *) % 10.40/10.54 assert (zenon_L1020_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (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)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((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) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((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 (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (op (e3) (e0))) = (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 (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.40/10.54 do 0 intro. intros zenon_H141 zenon_H82 zenon_H2ee zenon_H7e zenon_H83 zenon_Hf1 zenon_H33b zenon_H5f zenon_H5d zenon_H30 zenon_H328 zenon_H1e zenon_H16c zenon_H155 zenon_H20 zenon_H23 zenon_H25 zenon_H2b1 zenon_H35c zenon_H64 zenon_H1d1 zenon_H13a zenon_Hb8 zenon_H335 zenon_H22a zenon_H7a zenon_H2d4 zenon_Hd0 zenon_H2ca zenon_Ha1 zenon_H5c zenon_H35f zenon_H2b4 zenon_H338 zenon_H2ae zenon_H304 zenon_H10d zenon_H1d7 zenon_H1d9 zenon_H1ea zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H127 zenon_H156 zenon_H1dc zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_H93 zenon_H96 zenon_H2fa zenon_H1d4 zenon_H2dd zenon_H2fe zenon_H22f zenon_H14c zenon_H1db zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_H110 zenon_H22d zenon_H12a zenon_H11f zenon_H12f zenon_H1c9 zenon_H130 zenon_H301 zenon_H2a8 zenon_H13d zenon_Hbe zenon_H12c zenon_Ha9 zenon_H101 zenon_H1ce zenon_H113 zenon_Hef zenon_H192 zenon_H1f5 zenon_H2a zenon_He8 zenon_H1ec zenon_H1f6 zenon_H14b zenon_H272 zenon_Heb zenon_Hfe zenon_H5a zenon_H2c7 zenon_Hd1 zenon_H2c4 zenon_H2ac zenon_H2b2 zenon_H22e zenon_H74 zenon_H27 zenon_H2c zenon_H1b9 zenon_H2f zenon_He2 zenon_H105. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.54 apply (zenon_L370_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.54 apply (zenon_L1014_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.54 apply (zenon_L365_); trivial. % 10.40/10.54 apply (zenon_L879_); trivial. % 10.40/10.54 (* end of lemma zenon_L1020_ *) % 10.40/10.54 assert (zenon_L1021_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.40/10.54 do 0 intro. intros zenon_H2fa zenon_H68 zenon_H74 zenon_H5e zenon_H7a zenon_H2b3 zenon_H7e zenon_H52 zenon_H2c. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.40/10.54 apply (zenon_L427_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.40/10.54 apply (zenon_L428_); trivial. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.40/10.54 apply (zenon_L429_); trivial. % 10.40/10.54 apply (zenon_L505_); trivial. % 10.40/10.54 (* end of lemma zenon_L1021_ *) % 10.40/10.54 assert (zenon_L1022_ : ((op (e2) (e0)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (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)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((~((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) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 10.40/10.54 do 0 intro. intros zenon_H86 zenon_H26 zenon_Hd0 zenon_H1ea zenon_H93 zenon_H16c zenon_H25 zenon_H1b9 zenon_H110 zenon_H2dd zenon_H20 zenon_Hbe zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_Heb zenon_H1d1 zenon_H23 zenon_H2b1 zenon_H2fe zenon_H83 zenon_H1d7 zenon_H1e zenon_H328 zenon_H362 zenon_Hb8 zenon_H7e zenon_H7a zenon_H301 zenon_H74 zenon_H105 zenon_H2fa zenon_H2ac zenon_H5f zenon_H22f zenon_H35f zenon_H304 zenon_H22a zenon_H1d9 zenon_H1f6 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H157 zenon_H154 zenon_H192 zenon_H96 zenon_H1d4 zenon_H2c4 zenon_H22e zenon_H1ec zenon_H155 zenon_H14b zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H2b4 zenon_H335 zenon_Hfe zenon_H10d zenon_H118 zenon_H1c9 zenon_Ha9 zenon_H101 zenon_H12c zenon_H187 zenon_H2f7 zenon_H127 zenon_H130 zenon_Hef zenon_Hf1 zenon_H113 zenon_H1f5 zenon_H2a zenon_He8 zenon_H141 zenon_H2c zenon_H2b3 zenon_H30. % 10.40/10.54 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.40/10.55 apply (zenon_L123_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.40/10.55 apply (zenon_L124_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.40/10.55 apply (zenon_L104_); trivial. % 10.40/10.55 apply (zenon_L991_); trivial. % 10.40/10.55 (* end of lemma zenon_L1022_ *) % 10.40/10.55 assert (zenon_L1023_ : (~((e2) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((((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) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.40/10.55 do 0 intro. intros zenon_H30 zenon_H2b3 zenon_H2c zenon_H141 zenon_He8 zenon_H2a zenon_H1f5 zenon_H113 zenon_Hf1 zenon_Hef zenon_H130 zenon_H127 zenon_H2f7 zenon_H187 zenon_H12c zenon_H101 zenon_Ha9 zenon_H1c9 zenon_H118 zenon_H10d zenon_Hfe zenon_H335 zenon_H2b4 zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H14b zenon_H155 zenon_H1ec zenon_H22e zenon_H2c4 zenon_H1d4 zenon_H96 zenon_H192 zenon_H154 zenon_H157 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1f6 zenon_H1d9 zenon_H22a zenon_H304 zenon_H35f zenon_H22f zenon_H5f zenon_H2ac zenon_H2fa zenon_H105 zenon_H74 zenon_H301 zenon_H7a zenon_H7e zenon_Hb8 zenon_H362 zenon_H328 zenon_H1e zenon_H1d7 zenon_H83 zenon_H2fe zenon_H2b1 zenon_H23 zenon_H1d1 zenon_Heb zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_Hbe zenon_H20 zenon_H2dd zenon_H110 zenon_H1b9 zenon_H16c zenon_H93 zenon_H1ea zenon_Hd0 zenon_H26 zenon_H1d5 zenon_H25. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.55 apply (zenon_L4_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.55 apply (zenon_L163_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.55 apply (zenon_L1022_); trivial. % 10.40/10.55 apply (zenon_L613_); trivial. % 10.40/10.55 (* end of lemma zenon_L1023_ *) % 10.40/10.55 assert (zenon_L1024_ : ((op (e2) (e2)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 10.40/10.55 do 0 intro. intros zenon_H2e zenon_H86 zenon_H1d7. % 10.40/10.55 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hec | zenon_intro zenon_H81 ]. % 10.40/10.55 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H1d7. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_Hec. % 10.40/10.55 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.40/10.55 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d8]. % 10.40/10.55 congruence. % 10.40/10.55 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e0)))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H1d8. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_H2e. % 10.40/10.55 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2de]. % 10.40/10.55 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 10.40/10.55 congruence. % 10.40/10.55 apply zenon_H81. apply refl_equal. % 10.40/10.55 apply zenon_H2de. apply sym_equal. exact zenon_H86. % 10.40/10.55 apply zenon_H81. apply refl_equal. % 10.40/10.55 apply zenon_H81. apply refl_equal. % 10.40/10.55 (* end of lemma zenon_L1024_ *) % 10.40/10.55 assert (zenon_L1025_ : (~((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> False). % 10.40/10.55 do 0 intro. intros zenon_H365 zenon_H26. % 10.40/10.55 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 10.40/10.55 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H366]. % 10.40/10.55 congruence. % 10.40/10.55 exact (zenon_H366 zenon_H26). % 10.40/10.55 apply zenon_H1d. apply refl_equal. % 10.40/10.55 (* end of lemma zenon_L1025_ *) % 10.40/10.55 assert (zenon_L1026_ : ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((e3) = (op (op (e1) (e1)) (e1)))) -> False). % 10.40/10.55 do 0 intro. intros zenon_H121 zenon_H26 zenon_H276. % 10.40/10.55 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H277 | zenon_intro zenon_H278 ]. % 10.40/10.55 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e3) = (op (op (e1) (e1)) (e1)))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H276. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_H277. % 10.40/10.55 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 10.40/10.55 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 10.40/10.55 congruence. % 10.40/10.55 cut (((op (e2) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H279. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_H121. % 10.40/10.55 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.40/10.55 cut (((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H367]. % 10.40/10.55 congruence. % 10.40/10.55 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H277 | zenon_intro zenon_H278 ]. % 10.40/10.55 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H367. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_H277. % 10.40/10.55 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 10.40/10.55 cut (((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H365]. % 10.40/10.55 congruence. % 10.40/10.55 apply (zenon_L1025_); trivial. % 10.40/10.55 apply zenon_H278. apply refl_equal. % 10.40/10.55 apply zenon_H278. apply refl_equal. % 10.40/10.55 apply zenon_H29. apply refl_equal. % 10.40/10.55 apply zenon_H278. apply refl_equal. % 10.40/10.55 apply zenon_H278. apply refl_equal. % 10.40/10.55 (* end of lemma zenon_L1026_ *) % 10.40/10.55 assert (zenon_L1027_ : ((op (e2) (e3)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> False). % 10.40/10.55 do 0 intro. intros zenon_Ha8 zenon_H121 zenon_H26. % 10.40/10.55 apply (zenon_notand_s _ _ ax9); [ zenon_intro zenon_H34f | zenon_intro zenon_H368 ]. % 10.40/10.55 elim (classic ((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))); [ zenon_intro zenon_H27d | zenon_intro zenon_H27e ]. % 10.40/10.55 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1)))) = ((e0) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H34f. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_H27d. % 10.40/10.55 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H27e]. % 10.40/10.55 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H350]. % 10.40/10.55 congruence. % 10.40/10.55 cut (((op (e2) (e3)) = (e0)) = ((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (e0))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H350. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_Ha8. % 10.40/10.55 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.40/10.55 cut (((op (e2) (e3)) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H369]. % 10.40/10.55 congruence. % 10.40/10.55 elim (classic ((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))); [ zenon_intro zenon_H27d | zenon_intro zenon_H27e ]. % 10.40/10.55 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1)))) = ((op (e2) (e3)) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H369. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_H27d. % 10.40/10.55 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (op (e1) (e1)) (op (op (e1) (e1)) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H27e]. % 10.40/10.55 cut (((op (op (e1) (e1)) (op (op (e1) (e1)) (e1))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H36a]. % 10.40/10.55 congruence. % 10.40/10.55 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 10.40/10.55 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H366]. % 10.40/10.55 congruence. % 10.40/10.55 exact (zenon_H366 zenon_H26). % 10.40/10.55 cut (((op (e2) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H279. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_H121. % 10.40/10.55 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.40/10.55 cut (((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H367]. % 10.40/10.55 congruence. % 10.40/10.55 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H277 | zenon_intro zenon_H278 ]. % 10.40/10.55 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H367. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_H277. % 10.40/10.55 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 10.40/10.55 cut (((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H365]. % 10.40/10.55 congruence. % 10.40/10.55 apply (zenon_L1025_); trivial. % 10.40/10.55 apply zenon_H278. apply refl_equal. % 10.40/10.55 apply zenon_H278. apply refl_equal. % 10.40/10.55 apply zenon_H29. apply refl_equal. % 10.40/10.55 apply zenon_H27e. apply refl_equal. % 10.40/10.55 apply zenon_H27e. apply refl_equal. % 10.40/10.55 apply zenon_H34. apply refl_equal. % 10.40/10.55 apply zenon_H27e. apply refl_equal. % 10.40/10.55 apply zenon_H27e. apply refl_equal. % 10.40/10.55 apply (zenon_notand_s _ _ zenon_H368); [ zenon_intro zenon_H36b | zenon_intro zenon_H276 ]. % 10.40/10.55 apply zenon_H36b. apply sym_equal. exact zenon_H26. % 10.40/10.55 apply (zenon_L1026_); trivial. % 10.40/10.55 (* end of lemma zenon_L1027_ *) % 10.40/10.55 assert (zenon_L1028_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.40/10.55 do 0 intro. intros zenon_H12c zenon_H26 zenon_H121 zenon_Hfe zenon_H105 zenon_H101 zenon_Hb7 zenon_H10d zenon_H12a zenon_Hf4 zenon_H52 zenon_Ha9. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.40/10.55 apply (zenon_L1027_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.40/10.55 apply (zenon_L237_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.40/10.55 apply (zenon_L105_); trivial. % 10.40/10.55 apply (zenon_L233_); trivial. % 10.40/10.55 (* end of lemma zenon_L1028_ *) % 10.40/10.55 assert (zenon_L1029_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.40/10.55 do 0 intro. intros zenon_H155 zenon_H20 zenon_H23 zenon_H25 zenon_H5e zenon_H166 zenon_H96 zenon_H128 zenon_H12a. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.55 apply (zenon_L4_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.55 apply (zenon_L969_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.55 apply (zenon_L104_); trivial. % 10.40/10.55 apply (zenon_L105_); trivial. % 10.40/10.55 (* end of lemma zenon_L1029_ *) % 10.40/10.55 assert (zenon_L1030_ : (((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) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.40/10.55 do 0 intro. intros zenon_H12c zenon_Hfd zenon_H101 zenon_H2b3 zenon_H127 zenon_H12a zenon_H96 zenon_H166 zenon_H5e zenon_H25 zenon_H23 zenon_H20 zenon_H155 zenon_H52 zenon_Ha9. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.40/10.55 apply (zenon_L785_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.40/10.55 apply (zenon_L735_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.40/10.55 apply (zenon_L1029_); trivial. % 10.40/10.55 apply (zenon_L233_); trivial. % 10.40/10.55 (* end of lemma zenon_L1030_ *) % 10.40/10.55 assert (zenon_L1031_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e2) (e2)) = (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 (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e2))) -> False). % 10.40/10.55 do 0 intro. intros zenon_H35f zenon_Hf4 zenon_H10d zenon_H52 zenon_H20 zenon_H5e zenon_H166 zenon_H127 zenon_H101 zenon_H12c zenon_H26 zenon_H121 zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H2c zenon_H30 zenon_H22f zenon_H105 zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H16c zenon_H1ec zenon_Hbe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H1e zenon_H7e zenon_H7a zenon_H74 zenon_H2fa zenon_H1b9 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H25 zenon_H2b3 zenon_H23. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.40/10.55 apply (zenon_L1028_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.40/10.55 apply (zenon_L1030_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.40/10.55 apply (zenon_L1027_); trivial. % 10.40/10.55 apply (zenon_L499_); trivial. % 10.40/10.55 (* end of lemma zenon_L1031_ *) % 10.40/10.55 assert (zenon_L1032_ : (~((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e1)) -> False). % 10.40/10.55 do 0 intro. intros zenon_H36c zenon_H2b3. % 10.40/10.55 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 10.40/10.55 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H36d]. % 10.40/10.55 congruence. % 10.40/10.55 exact (zenon_H36d zenon_H2b3). % 10.40/10.55 apply zenon_H22. apply refl_equal. % 10.40/10.55 (* end of lemma zenon_L1032_ *) % 10.40/10.55 assert (zenon_L1033_ : ((op (e1) (e2)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> (~((e3) = (op (op (e2) (e2)) (e2)))) -> False). % 10.40/10.55 do 0 intro. intros zenon_H1f0 zenon_H2b3 zenon_H30c. % 10.40/10.55 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H30d | zenon_intro zenon_H30e ]. % 10.40/10.55 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e3) = (op (op (e2) (e2)) (e2)))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H30c. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_H30d. % 10.40/10.55 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H30e]. % 10.40/10.55 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H30f]. % 10.40/10.55 congruence. % 10.40/10.55 cut (((op (e1) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H30f. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_H1f0. % 10.40/10.55 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.40/10.55 cut (((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H36e]. % 10.40/10.55 congruence. % 10.40/10.55 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H30d | zenon_intro zenon_H30e ]. % 10.40/10.55 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H36e. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_H30d. % 10.40/10.55 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H30e]. % 10.40/10.55 cut (((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H36c]. % 10.40/10.55 congruence. % 10.40/10.55 apply (zenon_L1032_); trivial. % 10.40/10.55 apply zenon_H30e. apply refl_equal. % 10.40/10.55 apply zenon_H30e. apply refl_equal. % 10.40/10.55 apply zenon_H29. apply refl_equal. % 10.40/10.55 apply zenon_H30e. apply refl_equal. % 10.40/10.55 apply zenon_H30e. apply refl_equal. % 10.40/10.55 (* end of lemma zenon_L1033_ *) % 10.40/10.55 assert (zenon_L1034_ : ((op (e1) (e3)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> False). % 10.40/10.55 do 0 intro. intros zenon_Hfd zenon_H1f0 zenon_H2b3. % 10.40/10.55 apply (zenon_notand_s _ _ ax7); [ zenon_intro zenon_H330 | zenon_intro zenon_H36f ]. % 10.40/10.55 elim (classic ((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))); [ zenon_intro zenon_H313 | zenon_intro zenon_H314 ]. % 10.40/10.55 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2)))) = ((e0) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H330. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_H313. % 10.40/10.55 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H314]. % 10.40/10.55 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H331]. % 10.40/10.55 congruence. % 10.40/10.55 cut (((op (e1) (e3)) = (e0)) = ((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (e0))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H331. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_Hfd. % 10.40/10.55 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 10.40/10.55 cut (((op (e1) (e3)) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H370]. % 10.40/10.55 congruence. % 10.40/10.55 elim (classic ((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))); [ zenon_intro zenon_H313 | zenon_intro zenon_H314 ]. % 10.40/10.55 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2)))) = ((op (e1) (e3)) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H370. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_H313. % 10.40/10.55 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (op (e2) (e2)) (op (op (e2) (e2)) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H314]. % 10.40/10.55 cut (((op (op (e2) (e2)) (op (op (e2) (e2)) (e2))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H371]. % 10.40/10.55 congruence. % 10.40/10.55 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H30f]. % 10.40/10.55 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H36d]. % 10.40/10.55 congruence. % 10.40/10.55 exact (zenon_H36d zenon_H2b3). % 10.40/10.55 cut (((op (e1) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H30f. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_H1f0. % 10.40/10.55 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 10.40/10.55 cut (((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H36e]. % 10.40/10.55 congruence. % 10.40/10.55 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H30d | zenon_intro zenon_H30e ]. % 10.40/10.55 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))). % 10.40/10.55 intro zenon_D_pnotp. % 10.40/10.55 apply zenon_H36e. % 10.40/10.55 rewrite <- zenon_D_pnotp. % 10.40/10.55 exact zenon_H30d. % 10.40/10.55 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H30e]. % 10.40/10.55 cut (((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H36c]. % 10.40/10.55 congruence. % 10.40/10.55 apply (zenon_L1032_); trivial. % 10.40/10.55 apply zenon_H30e. apply refl_equal. % 10.40/10.55 apply zenon_H30e. apply refl_equal. % 10.40/10.55 apply zenon_H29. apply refl_equal. % 10.40/10.55 apply zenon_H314. apply refl_equal. % 10.40/10.55 apply zenon_H314. apply refl_equal. % 10.40/10.55 apply zenon_H34. apply refl_equal. % 10.40/10.55 apply zenon_H314. apply refl_equal. % 10.40/10.55 apply zenon_H314. apply refl_equal. % 10.40/10.55 apply (zenon_notand_s _ _ zenon_H36f); [ zenon_intro zenon_H372 | zenon_intro zenon_H30c ]. % 10.40/10.55 apply zenon_H372. apply sym_equal. exact zenon_H2b3. % 10.40/10.55 apply (zenon_L1033_); trivial. % 10.40/10.55 (* end of lemma zenon_L1034_ *) % 10.40/10.55 assert (zenon_L1035_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.40/10.55 do 0 intro. intros zenon_H10d zenon_Ha8 zenon_H105 zenon_Hf3 zenon_H101 zenon_H128 zenon_H52 zenon_Hfe. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hfd | zenon_intro zenon_H10e ]. % 10.40/10.55 apply (zenon_L785_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H10f ]. % 10.40/10.55 apply (zenon_L435_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H106 | zenon_intro zenon_H109 ]. % 10.40/10.55 apply (zenon_L241_); trivial. % 10.40/10.55 apply (zenon_L236_); trivial. % 10.40/10.55 (* end of lemma zenon_L1035_ *) % 10.40/10.55 assert (zenon_L1036_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.40/10.55 do 0 intro. intros zenon_H35f zenon_H2b3 zenon_H1f0 zenon_Hfe zenon_H128 zenon_H101 zenon_Hf3 zenon_H105 zenon_H10d zenon_H52 zenon_H2a. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.40/10.55 apply (zenon_L611_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.40/10.55 apply (zenon_L1034_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.40/10.55 apply (zenon_L1035_); trivial. % 10.40/10.55 apply (zenon_L75_); trivial. % 10.40/10.55 (* end of lemma zenon_L1036_ *) % 10.40/10.55 assert (zenon_L1037_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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) (e0)) = (op (e3) (e0)))) -> (~((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 (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((((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)) = 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(e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.40/10.55 do 0 intro. intros zenon_H1ea zenon_H52 zenon_H2b3 zenon_H2c zenon_H35f zenon_Hfe zenon_H101 zenon_H105 zenon_H10d zenon_H2a zenon_H30 zenon_H2f7 zenon_Heb zenon_Hd1 zenon_H26 zenon_H93 zenon_H16c zenon_H1b9 zenon_H110 zenon_H2dd zenon_H20 zenon_Hbe zenon_H12f zenon_H11f zenon_H12a zenon_H1d1 zenon_H23 zenon_H2b1 zenon_H2fe zenon_H83 zenon_H1d7 zenon_H1e zenon_H328 zenon_H362 zenon_Hb8 zenon_H7e zenon_H7a zenon_H301 zenon_H74 zenon_H2fa zenon_H2ac zenon_H5f zenon_H22f zenon_H304 zenon_H22a zenon_H1d9 zenon_H1f6 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H157 zenon_H154 zenon_H192 zenon_H96 zenon_H1d4 zenon_H2c4 zenon_H22e zenon_H1ec zenon_H155 zenon_H14b zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H2b4 zenon_H335 zenon_H118 zenon_H1c9 zenon_Ha9 zenon_H12c zenon_H187 zenon_H127 zenon_H130 zenon_Hef zenon_Hf1 zenon_H113 zenon_H1f5 zenon_He8 zenon_H141 zenon_Hf3 zenon_H25. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.55 apply (zenon_L4_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.55 apply (zenon_L103_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.40/10.55 apply (zenon_L1022_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.40/10.55 apply (zenon_L56_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.40/10.55 apply (zenon_L63_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.40/10.55 apply (zenon_L910_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.40/10.55 apply (zenon_L1036_); trivial. % 10.40/10.55 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.40/10.55 apply (zenon_L438_); trivial. % 10.40/10.55 apply (zenon_L299_); trivial. % 10.40/10.55 apply (zenon_L66_); trivial. % 10.40/10.55 (* end of lemma zenon_L1037_ *) % 10.40/10.55 assert (zenon_L1038_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H1cb zenon_H91 zenon_H11f zenon_H26 zenon_Hd1 zenon_H25 zenon_H2b3 zenon_Hf4 zenon_H12a. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.40/10.56 apply (zenon_L123_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.40/10.56 apply (zenon_L56_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.40/10.56 apply (zenon_L445_); trivial. % 10.40/10.56 apply (zenon_L105_); trivial. % 10.40/10.56 (* end of lemma zenon_L1038_ *) % 10.40/10.56 assert (zenon_L1039_ : ((op (e0) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (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)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((~((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) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H5e zenon_H90 zenon_H1ea zenon_H93 zenon_H16c zenon_H1b9 zenon_H110 zenon_H2dd zenon_Hbe zenon_Heb zenon_H2b1 zenon_H2fe zenon_H83 zenon_H1d7 zenon_H1e zenon_H328 zenon_H362 zenon_Hb8 zenon_H7e zenon_H7a zenon_H301 zenon_H74 zenon_H2fa zenon_H2ac zenon_H5f zenon_H22f zenon_H35f zenon_H304 zenon_H22a zenon_H1d9 zenon_H1f6 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H157 zenon_H154 zenon_H192 zenon_H96 zenon_H1d4 zenon_H2c4 zenon_H22e zenon_H1ec zenon_H155 zenon_H14b zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H2b4 zenon_H335 zenon_H118 zenon_H1c9 zenon_H187 zenon_H2f7 zenon_H127 zenon_H130 zenon_Hef zenon_H113 zenon_H1f5 zenon_H2a zenon_He8 zenon_H141 zenon_H1d1 zenon_H20 zenon_H23 zenon_Hf1 zenon_Ha9 zenon_H52 zenon_H2c zenon_H12c zenon_Hfe zenon_H105 zenon_H101 zenon_Hb7 zenon_H10d zenon_H30 zenon_H12f zenon_H1cb zenon_H11f zenon_H26 zenon_Hd1 zenon_H25 zenon_H2b3 zenon_H12a. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.56 apply (zenon_L4_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.56 apply (zenon_L969_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.56 apply (zenon_L4_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.56 apply (zenon_L163_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.56 apply (zenon_L1022_); trivial. % 10.40/10.56 apply (zenon_L35_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.56 apply (zenon_L4_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.56 apply (zenon_L163_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.40/10.56 apply (zenon_L28_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.40/10.56 apply (zenon_L1028_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.40/10.56 apply (zenon_L438_); trivial. % 10.40/10.56 apply (zenon_L233_); trivial. % 10.40/10.56 apply (zenon_L1038_); trivial. % 10.40/10.56 (* end of lemma zenon_L1039_ *) % 10.40/10.56 assert (zenon_L1040_ : ((op (e0) (e3)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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) (e0)) = (op (e3) (e0)))) -> (~((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 (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = 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(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) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> False). % 10.40/10.56 do 0 intro. intros zenon_Hb7 zenon_H90 zenon_H1ea zenon_H52 zenon_H2b3 zenon_H2c zenon_H35f zenon_Hfe zenon_H101 zenon_H105 zenon_H10d zenon_H2a zenon_H30 zenon_H2f7 zenon_Heb zenon_Hd1 zenon_H26 zenon_H93 zenon_H16c zenon_H1b9 zenon_H110 zenon_H2dd zenon_H20 zenon_Hbe zenon_H12f zenon_H11f zenon_H12a zenon_H1d1 zenon_H23 zenon_H2b1 zenon_H2fe zenon_H83 zenon_H1d7 zenon_H1e zenon_H328 zenon_H362 zenon_Hb8 zenon_H7e zenon_H7a zenon_H301 zenon_H74 zenon_H2fa zenon_H2ac zenon_H5f zenon_H22f zenon_H304 zenon_H22a zenon_H1d9 zenon_H1f6 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H157 zenon_H154 zenon_H192 zenon_H96 zenon_H1d4 zenon_H2c4 zenon_H22e zenon_H1ec zenon_H155 zenon_H14b zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H2b4 zenon_H335 zenon_H118 zenon_H1c9 zenon_Ha9 zenon_H12c zenon_H187 zenon_H127 zenon_H130 zenon_Hef zenon_Hf1 zenon_H113 zenon_H1f5 zenon_He8 zenon_H141 zenon_H25. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.56 apply (zenon_L2_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.56 apply (zenon_L1039_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.56 apply (zenon_L434_); trivial. % 10.40/10.56 apply (zenon_L1037_); trivial. % 10.40/10.56 (* end of lemma zenon_L1040_ *) % 10.40/10.56 assert (zenon_L1041_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 10.40/10.56 do 0 intro. intros zenon_H169 zenon_H2dd zenon_H20. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H169). zenon_intro zenon_H97. zenon_intro zenon_H16a. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H16a). zenon_intro zenon_H9e. zenon_intro zenon_H16b. % 10.40/10.56 apply (zenon_L783_); trivial. % 10.40/10.56 (* end of lemma zenon_L1041_ *) % 10.40/10.56 assert (zenon_L1042_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H16f zenon_H52 zenon_H16c. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hb7. zenon_intro zenon_H170. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_H90. zenon_intro zenon_H171. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.40/10.56 apply (zenon_L295_); trivial. % 10.40/10.56 (* end of lemma zenon_L1042_ *) % 10.40/10.56 assert (zenon_L1043_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H17b zenon_H2fa zenon_H74 zenon_H7a zenon_H2b3 zenon_H7e zenon_H52 zenon_H2c. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H68. zenon_intro zenon_H17c. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H17c). zenon_intro zenon_H5e. zenon_intro zenon_H6f. % 10.40/10.56 apply (zenon_L1021_); trivial. % 10.40/10.56 (* end of lemma zenon_L1043_ *) % 10.40/10.56 assert (zenon_L1044_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H181 zenon_H2fa zenon_H74 zenon_H7a zenon_H2b3 zenon_H7e zenon_H52 zenon_H2c. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_H5e. zenon_intro zenon_Hbd. % 10.40/10.56 apply (zenon_L1021_); trivial. % 10.40/10.56 (* end of lemma zenon_L1044_ *) % 10.40/10.56 assert (zenon_L1045_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H19d zenon_H52 zenon_H16c. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_Hf7. zenon_intro zenon_H19e. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H171. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.40/10.56 apply (zenon_L295_); trivial. % 10.40/10.56 (* end of lemma zenon_L1045_ *) % 10.40/10.56 assert (zenon_L1046_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H1a3 zenon_H52 zenon_H1ea. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_Hf7. zenon_intro zenon_H1a4. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1a4). zenon_intro zenon_H143. zenon_intro zenon_H177. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.40/10.56 apply (zenon_L299_); trivial. % 10.40/10.56 (* end of lemma zenon_L1046_ *) % 10.40/10.56 assert (zenon_L1047_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H1a5 zenon_H2fe zenon_H20 zenon_H1e zenon_H7a zenon_Heb zenon_H2b3 zenon_H105. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_Hf7. zenon_intro zenon_H1a6. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1a6). zenon_intro zenon_H143. zenon_intro zenon_H17a. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.56 apply (zenon_L2_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.56 apply (zenon_L428_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.56 apply (zenon_L434_); trivial. % 10.40/10.56 apply (zenon_L435_); trivial. % 10.40/10.56 (* end of lemma zenon_L1047_ *) % 10.40/10.56 assert (zenon_L1048_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (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) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (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)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((~((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) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H1a7 zenon_H26 zenon_H1ea zenon_H93 zenon_H16c zenon_H25 zenon_H1b9 zenon_H110 zenon_H2dd zenon_Hbe zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_Heb zenon_H1d1 zenon_H23 zenon_H2b1 zenon_H2fe zenon_H83 zenon_H1d7 zenon_H1e zenon_H328 zenon_H362 zenon_Hb8 zenon_H7e zenon_H7a zenon_H301 zenon_H74 zenon_H105 zenon_H2fa zenon_H2ac zenon_H5f zenon_H22f zenon_H35f zenon_H304 zenon_H22a zenon_H1d9 zenon_H1f6 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H157 zenon_H154 zenon_H192 zenon_H96 zenon_H1d4 zenon_H2c4 zenon_H22e zenon_H1ec zenon_H155 zenon_H14b zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H2b4 zenon_H335 zenon_Hfe zenon_H10d zenon_H118 zenon_H1c9 zenon_Ha9 zenon_H101 zenon_H12c zenon_H187 zenon_H2f7 zenon_H127 zenon_H130 zenon_Hef zenon_Hf1 zenon_H113 zenon_H1f5 zenon_H2a zenon_He8 zenon_H141 zenon_H2c zenon_H2b3 zenon_H30. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H86. zenon_intro zenon_H1a8. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hd0. zenon_intro zenon_H6f. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H20. zenon_intro zenon_H20. % 10.40/10.56 apply (zenon_L1022_); trivial. % 10.40/10.56 (* end of lemma zenon_L1048_ *) % 10.40/10.56 assert (zenon_L1049_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (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)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((~((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) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H1ad zenon_H26 zenon_H1ea zenon_H93 zenon_H16c zenon_H25 zenon_H1b9 zenon_H110 zenon_H2dd zenon_H20 zenon_Hbe zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_Heb zenon_H1d1 zenon_H23 zenon_H2b1 zenon_H2fe zenon_H83 zenon_H1d7 zenon_H1e zenon_H328 zenon_H362 zenon_Hb8 zenon_H7e zenon_H7a zenon_H301 zenon_H74 zenon_H105 zenon_H2fa zenon_H2ac zenon_H5f zenon_H22f zenon_H35f zenon_H304 zenon_H22a zenon_H1d9 zenon_H1f6 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H157 zenon_H154 zenon_H192 zenon_H96 zenon_H1d4 zenon_H2c4 zenon_H22e zenon_H1ec zenon_H155 zenon_H14b zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H2b4 zenon_H335 zenon_Hfe zenon_H10d zenon_H118 zenon_H1c9 zenon_Ha9 zenon_H101 zenon_H12c zenon_H187 zenon_H2f7 zenon_H127 zenon_H130 zenon_Hef zenon_Hf1 zenon_H113 zenon_H1f5 zenon_H2a zenon_He8 zenon_H141 zenon_H2c zenon_H2b3 zenon_H30. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H86. zenon_intro zenon_H1ae. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_Hd0. zenon_intro zenon_Hbd. % 10.40/10.56 apply (zenon_L1022_); trivial. % 10.40/10.56 (* end of lemma zenon_L1049_ *) % 10.40/10.56 assert (zenon_L1050_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H1c2 zenon_H52 zenon_H16c. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H128. zenon_intro zenon_H1c3. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1c3). zenon_intro zenon_H166. zenon_intro zenon_H171. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.40/10.56 apply (zenon_L295_); trivial. % 10.40/10.56 (* end of lemma zenon_L1050_ *) % 10.40/10.56 assert (zenon_L1051_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H1e6 zenon_H52 zenon_Hb8. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H72. zenon_intro zenon_H1e7. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_He2. zenon_intro zenon_H6f. % 10.40/10.56 apply (zenon_L229_); trivial. % 10.40/10.56 (* end of lemma zenon_L1051_ *) % 10.40/10.56 assert (zenon_L1052_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H1fb zenon_H52 zenon_Hb8. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H72. zenon_intro zenon_H1fc. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_He2. zenon_intro zenon_Hbd. % 10.40/10.56 apply (zenon_L229_); trivial. % 10.40/10.56 (* end of lemma zenon_L1052_ *) % 10.40/10.56 assert (zenon_L1053_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H1fd zenon_H2fa zenon_H74 zenon_H7a zenon_H2b3 zenon_H7e zenon_H52 zenon_H2c. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H79. zenon_intro zenon_H1fe. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H109. zenon_intro zenon_Hc2. % 10.40/10.56 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H5e. zenon_intro zenon_H68. % 10.40/10.56 apply (zenon_L1021_); trivial. % 10.40/10.56 (* end of lemma zenon_L1053_ *) % 10.40/10.56 assert (zenon_L1054_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (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)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H35f zenon_Hf4 zenon_H10d zenon_H105 zenon_Hfe zenon_Ha9 zenon_H52 zenon_H155 zenon_H20 zenon_H23 zenon_H25 zenon_H5e zenon_H166 zenon_H96 zenon_H12a zenon_H127 zenon_H2b3 zenon_H101 zenon_H12c zenon_H26 zenon_H121 zenon_H211 zenon_H2a. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.40/10.56 apply (zenon_L1028_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.40/10.56 apply (zenon_L1030_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.40/10.56 apply (zenon_L1027_); trivial. % 10.40/10.56 apply (zenon_L191_); trivial. % 10.40/10.56 (* end of lemma zenon_L1054_ *) % 10.40/10.56 assert (zenon_L1055_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H12c zenon_H101 zenon_H2b3 zenon_H127 zenon_Hb8 zenon_H52 zenon_H12a zenon_Hf7 zenon_H105 zenon_Hfd zenon_H1ce zenon_H50. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H12d ]. % 10.40/10.56 apply (zenon_L785_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H102 | zenon_intro zenon_H12e ]. % 10.40/10.56 apply (zenon_L735_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H128 | zenon_intro zenon_H112 ]. % 10.40/10.56 apply (zenon_L682_); trivial. % 10.40/10.56 apply (zenon_L368_); trivial. % 10.40/10.56 (* end of lemma zenon_L1055_ *) % 10.40/10.56 assert (zenon_L1056_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (op (e2) (e3))) = (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 (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H35f zenon_Ha9 zenon_Hf4 zenon_H10d zenon_Hfe zenon_H50 zenon_H1ce zenon_H105 zenon_Hf7 zenon_H12a zenon_Hb8 zenon_H127 zenon_H2b3 zenon_H101 zenon_H12c zenon_H26 zenon_H121 zenon_H52 zenon_H2a. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.40/10.56 apply (zenon_L1028_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.40/10.56 apply (zenon_L1055_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.40/10.56 apply (zenon_L1027_); trivial. % 10.40/10.56 apply (zenon_L75_); trivial. % 10.40/10.56 (* end of lemma zenon_L1056_ *) % 10.40/10.56 assert (zenon_L1057_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H2f7 zenon_H30 zenon_Hd0 zenon_H2b3 zenon_Hfd zenon_H128 zenon_H50 zenon_H52 zenon_H1ea. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f8 ]. % 10.40/10.56 apply (zenon_L910_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H2f9 ]. % 10.40/10.56 apply (zenon_L1034_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H2f | zenon_intro zenon_H7f ]. % 10.40/10.56 apply (zenon_L199_); trivial. % 10.40/10.56 apply (zenon_L299_); trivial. % 10.40/10.56 (* end of lemma zenon_L1057_ *) % 10.40/10.56 assert (zenon_L1058_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e2))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H35f zenon_H1ea zenon_H50 zenon_Hd0 zenon_H52 zenon_H128 zenon_H101 zenon_Hf3 zenon_H10d zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H2c zenon_H30 zenon_H22f zenon_H105 zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H16c zenon_H1ec zenon_Hbe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H1e zenon_H7e zenon_H7a zenon_H74 zenon_H2fa zenon_H1b9 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H25 zenon_H2b3 zenon_H23. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.40/10.56 apply (zenon_L611_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.40/10.56 apply (zenon_L1057_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.40/10.56 apply (zenon_L1035_); trivial. % 10.40/10.56 apply (zenon_L499_); trivial. % 10.40/10.56 (* end of lemma zenon_L1058_ *) % 10.40/10.56 assert (zenon_L1059_ : ((op (e3) (e0)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e2))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H91 zenon_H26 zenon_H35f zenon_H1ea zenon_H50 zenon_Hd0 zenon_H52 zenon_H101 zenon_Hf3 zenon_H10d zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H2c zenon_H30 zenon_H22f zenon_H105 zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H16c zenon_H1ec zenon_Hbe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H1e zenon_H7e zenon_H7a zenon_H74 zenon_H2fa zenon_H1b9 zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H25 zenon_H2b3 zenon_H23. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.40/10.56 apply (zenon_L123_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.40/10.56 apply (zenon_L56_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.40/10.56 apply (zenon_L445_); trivial. % 10.40/10.56 apply (zenon_L1058_); trivial. % 10.40/10.56 (* end of lemma zenon_L1059_ *) % 10.40/10.56 assert (zenon_L1060_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H301 zenon_H1d5 zenon_H74 zenon_H26 zenon_H25 zenon_H1b9 zenon_H2b3 zenon_Hf3 zenon_H105. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.40/10.56 apply (zenon_L427_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.40/10.56 apply (zenon_L5_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.40/10.56 apply (zenon_L432_); trivial. % 10.40/10.56 apply (zenon_L435_); trivial. % 10.40/10.56 (* end of lemma zenon_L1060_ *) % 10.40/10.56 assert (zenon_L1061_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((~((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)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (op (e2) (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) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((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) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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 (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.40/10.56 do 0 intro. intros zenon_He8 zenon_H113 zenon_Hf1 zenon_Hef zenon_H130 zenon_H127 zenon_H12c zenon_H1c9 zenon_H118 zenon_H335 zenon_H2b4 zenon_H157 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1f6 zenon_H1d9 zenon_H22a zenon_H304 zenon_H362 zenon_H328 zenon_H83 zenon_H2b1 zenon_H1d1 zenon_H20 zenon_H35f zenon_H1ea zenon_H50 zenon_H52 zenon_H101 zenon_H10d zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H2c zenon_H30 zenon_H22f zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H16c zenon_H1ec zenon_Hbe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H1e zenon_H7e zenon_H7a zenon_H2fa zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H23 zenon_H1d7 zenon_H301 zenon_H74 zenon_H26 zenon_H25 zenon_H1b9 zenon_H2b3 zenon_Hf3 zenon_H105. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.40/10.56 apply (zenon_L154_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.56 apply (zenon_L4_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.56 apply (zenon_L103_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.56 apply (zenon_L152_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.56 apply (zenon_L20_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.56 apply (zenon_L1022_); trivial. % 10.40/10.56 apply (zenon_L1059_); trivial. % 10.40/10.56 apply (zenon_L66_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.40/10.56 apply (zenon_L748_); trivial. % 10.40/10.56 apply (zenon_L1060_); trivial. % 10.40/10.56 (* end of lemma zenon_L1061_ *) % 10.40/10.56 assert (zenon_L1062_ : ((op (e0) (e3)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((~((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)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (op (e2) (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) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((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) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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 (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.40/10.56 do 0 intro. intros zenon_Hb7 zenon_H90 zenon_He8 zenon_H113 zenon_Hf1 zenon_Hef zenon_H130 zenon_H127 zenon_H12c zenon_H1c9 zenon_H118 zenon_H335 zenon_H2b4 zenon_H157 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1f6 zenon_H1d9 zenon_H22a zenon_H304 zenon_H362 zenon_H328 zenon_H83 zenon_H2b1 zenon_H1d1 zenon_H20 zenon_H35f zenon_H1ea zenon_H50 zenon_H52 zenon_H101 zenon_H10d zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H2c zenon_H30 zenon_H22f zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H16c zenon_H1ec zenon_Hbe zenon_H22e zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H1e zenon_H7e zenon_H7a zenon_H2fa zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H23 zenon_H1d7 zenon_H301 zenon_H74 zenon_H26 zenon_H25 zenon_H1b9 zenon_H2b3 zenon_H105. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.56 apply (zenon_L2_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.56 apply (zenon_L1039_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.56 apply (zenon_L434_); trivial. % 10.40/10.56 apply (zenon_L1061_); trivial. % 10.40/10.56 (* end of lemma zenon_L1062_ *) % 10.40/10.56 assert (zenon_L1063_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H207 zenon_H52 zenon_Ha9. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H7f. zenon_intro zenon_H208. % 10.40/10.56 apply (zenon_and_s _ _ zenon_H208). zenon_intro zenon_H112. zenon_intro zenon_H165. % 10.40/10.56 apply (zenon_L233_); trivial. % 10.40/10.56 (* end of lemma zenon_L1063_ *) % 10.40/10.56 assert (zenon_L1064_ : (((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) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H192 zenon_H86 zenon_H11f zenon_H26 zenon_H93 zenon_Hd0 zenon_H96 zenon_H211 zenon_H30. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H91 | zenon_intro zenon_H193 ]. % 10.40/10.56 apply (zenon_L123_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H149 | zenon_intro zenon_H194 ]. % 10.40/10.56 apply (zenon_L124_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H166 | zenon_intro zenon_H82 ]. % 10.40/10.56 apply (zenon_L104_); trivial. % 10.40/10.56 apply (zenon_L301_); trivial. % 10.40/10.56 (* end of lemma zenon_L1064_ *) % 10.40/10.56 assert (zenon_L1065_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H1d1 zenon_H20 zenon_H23 zenon_Hf1 zenon_H30 zenon_H211 zenon_H96 zenon_Hd0 zenon_H93 zenon_H26 zenon_H11f zenon_H192 zenon_H1d5 zenon_H25. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.56 apply (zenon_L4_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.56 apply (zenon_L163_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.56 apply (zenon_L1064_); trivial. % 10.40/10.56 apply (zenon_L613_); trivial. % 10.40/10.56 (* end of lemma zenon_L1065_ *) % 10.40/10.56 assert (zenon_L1066_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> False). % 10.40/10.56 do 0 intro. intros zenon_H301 zenon_H1d5 zenon_H74 zenon_H26 zenon_H25 zenon_H1b9 zenon_H12c zenon_H101 zenon_H2b3 zenon_H127 zenon_Hb8 zenon_H52 zenon_H12a zenon_H105 zenon_Hfd zenon_H1ce zenon_H50. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.40/10.56 apply (zenon_L427_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.40/10.56 apply (zenon_L5_); trivial. % 10.40/10.56 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.40/10.57 apply (zenon_L432_); trivial. % 10.40/10.57 apply (zenon_L1055_); trivial. % 10.40/10.57 (* end of lemma zenon_L1066_ *) % 10.40/10.57 assert (zenon_L1067_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (op (e2) (e3))) = (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 (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> False). % 10.40/10.57 do 0 intro. intros zenon_H35f zenon_Ha9 zenon_Hf4 zenon_H10d zenon_Hfe zenon_H50 zenon_H1ce zenon_H105 zenon_H12a zenon_H52 zenon_Hb8 zenon_H127 zenon_H2b3 zenon_H101 zenon_H12c zenon_H1b9 zenon_H25 zenon_H74 zenon_H1d5 zenon_H301 zenon_H26 zenon_H121 zenon_H211 zenon_H2a. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.40/10.57 apply (zenon_L1028_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.40/10.57 apply (zenon_L1066_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.40/10.57 apply (zenon_L1027_); trivial. % 10.40/10.57 apply (zenon_L191_); trivial. % 10.40/10.57 (* end of lemma zenon_L1067_ *) % 10.40/10.57 assert (zenon_L1068_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((((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)) = 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-> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 10.40/10.57 do 0 intro. intros zenon_H1ea zenon_H93 zenon_H16c zenon_H25 zenon_H1b9 zenon_H110 zenon_H2dd zenon_H20 zenon_Hbe zenon_H12f zenon_H11f zenon_Hd1 zenon_H12a zenon_Heb zenon_H1d1 zenon_H23 zenon_H2b1 zenon_H2fe zenon_H83 zenon_H1d7 zenon_H1e zenon_H328 zenon_H362 zenon_Hb8 zenon_H7e zenon_H7a zenon_H301 zenon_H74 zenon_H105 zenon_H2fa zenon_H2ac zenon_H5f zenon_H22f zenon_H35f zenon_H304 zenon_H22a zenon_H1d9 zenon_H1f6 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H157 zenon_H154 zenon_H192 zenon_H96 zenon_H1d4 zenon_H2c4 zenon_H22e zenon_H1ec zenon_H155 zenon_H14b zenon_H14c zenon_H1db zenon_H2ca zenon_H64 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_H13d zenon_H13a zenon_H22d zenon_H2b4 zenon_H335 zenon_Hfe zenon_H10d zenon_H118 zenon_H1c9 zenon_Ha9 zenon_H101 zenon_H12c zenon_H187 zenon_H2f7 zenon_H127 zenon_H130 zenon_Hef zenon_Hf1 zenon_H113 zenon_H1f5 zenon_H2a zenon_He8 zenon_H141 zenon_H2c zenon_H2b3 zenon_H30. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H24 | zenon_intro zenon_H230 ]. % 10.40/10.57 apply (zenon_L4_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H26 | zenon_intro zenon_H231 ]. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.40/10.57 apply (zenon_L7_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.40/10.57 apply (zenon_L38_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.40/10.57 apply (zenon_L438_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.40/10.57 apply (zenon_L11_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H3c. zenon_intro zenon_H44. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H160. zenon_intro zenon_Hf6. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.57 apply (zenon_L39_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.40/10.57 apply (zenon_L39_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.40/10.57 apply (zenon_L1021_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.40/10.57 apply (zenon_L748_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.57 apply (zenon_L4_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.57 apply (zenon_L969_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.57 apply (zenon_L1023_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.57 apply (zenon_L424_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.57 apply (zenon_L163_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.40/10.57 apply (zenon_L1023_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.40/10.57 apply (zenon_L173_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.40/10.57 apply (zenon_L1024_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.40/10.57 apply (zenon_L28_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.40/10.57 apply (zenon_L1031_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.40/10.57 apply (zenon_L438_); trivial. % 10.40/10.57 apply (zenon_L233_); trivial. % 10.40/10.57 apply (zenon_L613_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.57 apply (zenon_L434_); trivial. % 10.40/10.57 apply (zenon_L1037_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.40/10.57 apply (zenon_L795_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.40/10.57 apply (zenon_L926_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.40/10.57 apply (zenon_and_s _ _ zenon_Hbb). zenon_intro zenon_H20. zenon_intro zenon_Hbc. % 10.40/10.57 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_H20. zenon_intro zenon_Hbd. % 10.40/10.57 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.40/10.57 apply (zenon_L1040_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.40/10.57 apply (zenon_L302_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.40/10.57 apply (zenon_L51_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.40/10.57 apply (zenon_L303_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.40/10.57 apply (zenon_L304_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.40/10.57 apply (zenon_L55_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.40/10.57 apply (zenon_L306_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.40/10.57 apply (zenon_L446_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.40/10.57 apply (zenon_L1041_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.40/10.57 apply (zenon_L1042_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.40/10.57 apply (zenon_L308_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H175). zenon_intro zenon_Hb7. zenon_intro zenon_H176. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H176). zenon_intro zenon_H90. zenon_intro zenon_H177. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H112. zenon_intro zenon_H7f. % 10.40/10.57 apply (zenon_L299_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H178). zenon_intro zenon_Hb7. zenon_intro zenon_H179. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H179). zenon_intro zenon_H90. zenon_intro zenon_H17a. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 10.40/10.57 apply (zenon_L1040_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.40/10.57 apply (zenon_L1043_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.40/10.57 apply (zenon_L309_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.40/10.57 apply (zenon_L961_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.40/10.57 apply (zenon_L1044_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.40/10.57 apply (zenon_L117_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.40/10.57 apply (zenon_L118_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.40/10.57 apply (zenon_L452_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.40/10.57 apply (zenon_L271_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.40/10.57 apply (zenon_L750_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.40/10.57 apply (zenon_L456_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.40/10.57 apply (zenon_L457_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.40/10.57 apply (zenon_L802_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.40/10.57 apply (zenon_L1045_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.40/10.57 apply (zenon_L133_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.40/10.57 apply (zenon_L1046_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.40/10.57 apply (zenon_L1047_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.40/10.57 apply (zenon_L1048_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.40/10.57 apply (zenon_L361_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.40/10.57 apply (zenon_L138_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.40/10.57 apply (zenon_L1049_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.40/10.57 apply (zenon_L140_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.40/10.57 apply (zenon_L141_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.40/10.57 apply (zenon_L464_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.40/10.57 apply (zenon_L591_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.40/10.57 apply (zenon_L284_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.40/10.57 apply (zenon_L467_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.40/10.57 apply (zenon_L468_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.40/10.57 apply (zenon_L469_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.40/10.57 apply (zenon_L1050_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.40/10.57 apply (zenon_L593_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.40/10.57 apply (zenon_L167_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H1e4). zenon_intro zenon_H128. zenon_intro zenon_H1e5. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H1e5). zenon_intro zenon_H166. zenon_intro zenon_H17a. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.57 apply (zenon_L106_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.57 apply (zenon_L1029_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.57 apply (zenon_L434_); trivial. % 10.40/10.57 apply (zenon_L1037_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.40/10.57 apply (zenon_L1051_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.40/10.57 apply (zenon_L195_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.40/10.57 apply (zenon_L966_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.40/10.57 apply (zenon_L1052_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.40/10.57 apply (zenon_L1053_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.40/10.57 apply (zenon_L182_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.40/10.57 apply (zenon_L595_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.40/10.57 apply (zenon_L183_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H203). zenon_intro zenon_H7f. zenon_intro zenon_H204. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H204). zenon_intro zenon_H112. zenon_intro zenon_Hcf. % 10.40/10.57 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd0. zenon_intro zenon_H86. % 10.40/10.57 apply (zenon_L1022_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.40/10.57 apply (zenon_L968_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.40/10.57 apply (zenon_L491_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.40/10.57 apply (zenon_L187_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.40/10.57 apply (zenon_L296_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.40/10.57 apply (zenon_L298_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.40/10.57 apply (zenon_L300_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.57 apply (zenon_L2_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.40/10.57 apply (zenon_L2_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.40/10.57 apply (zenon_L1021_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.40/10.57 apply (zenon_L748_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.57 apply (zenon_L4_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.57 apply (zenon_L103_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.57 apply (zenon_L1023_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.57 apply (zenon_L4_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.57 apply (zenon_L163_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H22b ]. % 10.40/10.57 apply (zenon_L1022_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H22c ]. % 10.40/10.57 apply (zenon_L305_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H2e | zenon_intro zenon_H166 ]. % 10.40/10.57 apply (zenon_L1024_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.40/10.57 apply (zenon_L28_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.40/10.57 apply (zenon_L1054_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.40/10.57 apply (zenon_L438_); trivial. % 10.40/10.57 apply (zenon_L233_); trivial. % 10.40/10.57 apply (zenon_L1038_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.57 apply (zenon_L434_); trivial. % 10.40/10.57 apply (zenon_L1037_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.57 apply (zenon_L39_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.40/10.57 apply (zenon_L39_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.40/10.57 apply (zenon_L1021_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.40/10.57 apply (zenon_L748_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.57 apply (zenon_L4_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.57 apply (zenon_L103_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.57 apply (zenon_L1023_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.57 apply (zenon_L424_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.57 apply (zenon_L163_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H68 | zenon_intro zenon_H302 ]. % 10.40/10.57 apply (zenon_L1021_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H27 | zenon_intro zenon_H303 ]. % 10.40/10.57 apply (zenon_L18_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H188 | zenon_intro zenon_Hf7 ]. % 10.40/10.57 apply (zenon_L432_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.40/10.57 apply (zenon_L28_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.40/10.57 apply (zenon_L1056_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.40/10.57 apply (zenon_L438_); trivial. % 10.40/10.57 apply (zenon_L233_); trivial. % 10.40/10.57 apply (zenon_L1038_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.57 apply (zenon_L434_); trivial. % 10.40/10.57 apply (zenon_L1061_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.40/10.57 apply (zenon_L795_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.40/10.57 apply (zenon_L926_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.40/10.57 apply (zenon_and_s _ _ zenon_Hbb). zenon_intro zenon_H20. zenon_intro zenon_Hbc. % 10.40/10.57 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_H20. zenon_intro zenon_Hbd. % 10.40/10.57 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.40/10.57 apply (zenon_L1062_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.40/10.57 apply (zenon_L246_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.40/10.57 apply (zenon_L51_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.40/10.57 apply (zenon_L364_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.40/10.57 apply (zenon_L930_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.40/10.57 apply (zenon_L55_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.40/10.57 apply (zenon_L372_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.40/10.57 apply (zenon_L446_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.40/10.57 apply (zenon_L198_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.40/10.57 apply (zenon_L1042_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H172). zenon_intro zenon_Hb7. zenon_intro zenon_H173. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H173). zenon_intro zenon_H90. zenon_intro zenon_H174. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.40/10.57 apply (zenon_L297_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.40/10.57 apply (zenon_L596_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H178). zenon_intro zenon_Hb7. zenon_intro zenon_H179. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H179). zenon_intro zenon_H90. zenon_intro zenon_H17a. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 10.40/10.57 apply (zenon_L1062_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.40/10.57 apply (zenon_L1043_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.40/10.57 apply (zenon_L264_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.40/10.57 apply (zenon_L597_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.40/10.57 apply (zenon_L1044_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.40/10.57 apply (zenon_L117_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.40/10.57 apply (zenon_L118_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.40/10.57 apply (zenon_L121_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.40/10.57 apply (zenon_L122_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.40/10.57 apply (zenon_L694_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.40/10.57 apply (zenon_L374_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.40/10.57 apply (zenon_L457_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.40/10.57 apply (zenon_L375_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.40/10.57 apply (zenon_L1045_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.40/10.57 apply (zenon_L133_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.40/10.57 apply (zenon_L1046_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.40/10.57 apply (zenon_L1047_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.40/10.57 apply (zenon_L1048_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.40/10.57 apply (zenon_L942_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.40/10.57 apply (zenon_L138_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.40/10.57 apply (zenon_L1049_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.40/10.57 apply (zenon_L752_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.40/10.57 apply (zenon_L141_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.40/10.57 apply (zenon_L377_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.40/10.57 apply (zenon_L984_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.40/10.57 apply (zenon_L284_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.40/10.57 apply (zenon_L193_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.40/10.57 apply (zenon_L468_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.40/10.57 apply (zenon_L149_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.40/10.57 apply (zenon_L1050_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H21c). zenon_intro zenon_H128. zenon_intro zenon_H21d. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H166. zenon_intro zenon_H174. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.40/10.57 apply (zenon_L297_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.40/10.57 apply (zenon_L167_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H1e4). zenon_intro zenon_H128. zenon_intro zenon_H1e5. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H1e5). zenon_intro zenon_H166. zenon_intro zenon_H17a. % 10.40/10.57 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H52. zenon_intro zenon_H52. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.57 apply (zenon_L106_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.57 apply (zenon_L1029_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.57 apply (zenon_L434_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.57 apply (zenon_L4_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.57 apply (zenon_L103_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.57 apply (zenon_L1058_); trivial. % 10.40/10.57 apply (zenon_L66_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.40/10.57 apply (zenon_L1051_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.40/10.57 apply (zenon_L858_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.40/10.57 apply (zenon_L204_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.40/10.57 apply (zenon_L1052_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.40/10.57 apply (zenon_L1053_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.40/10.57 apply (zenon_L182_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.40/10.57 apply (zenon_L206_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.40/10.57 apply (zenon_L183_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.40/10.57 apply (zenon_L948_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.40/10.57 apply (zenon_L753_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.40/10.57 apply (zenon_L1063_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.40/10.57 apply (zenon_L187_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.40/10.57 apply (zenon_L296_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.40/10.57 apply (zenon_L298_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.40/10.57 apply (zenon_L300_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.57 apply (zenon_L2_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.40/10.57 apply (zenon_L2_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.40/10.57 apply (zenon_L1021_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.40/10.57 apply (zenon_L748_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.57 apply (zenon_L4_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.57 apply (zenon_L969_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.57 apply (zenon_L1065_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.57 apply (zenon_L4_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.57 apply (zenon_L163_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H87 | zenon_intro zenon_H133 ]. % 10.40/10.57 apply (zenon_L28_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H121 | zenon_intro zenon_H134 ]. % 10.40/10.57 apply (zenon_L1067_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H2f | zenon_intro zenon_H112 ]. % 10.40/10.57 apply (zenon_L438_); trivial. % 10.40/10.57 apply (zenon_L233_); trivial. % 10.40/10.57 apply (zenon_L1038_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.57 apply (zenon_L434_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.40/10.57 apply (zenon_L154_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.57 apply (zenon_L4_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.57 apply (zenon_L103_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.57 apply (zenon_L152_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.57 apply (zenon_L20_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.57 apply (zenon_L1064_); trivial. % 10.40/10.57 apply (zenon_L1059_); trivial. % 10.40/10.57 apply (zenon_L66_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.40/10.57 apply (zenon_L748_); trivial. % 10.40/10.57 apply (zenon_L1060_); trivial. % 10.40/10.57 apply (zenon_L17_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H2e | zenon_intro zenon_H82 ]. % 10.40/10.57 apply (zenon_L445_); trivial. % 10.40/10.57 apply (zenon_L991_); trivial. % 10.40/10.57 (* end of lemma zenon_L1068_ *) % 10.40/10.57 assert (zenon_L1069_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op 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(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) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.40/10.57 do 0 intro. intros zenon_H35c zenon_H30 zenon_H2c zenon_H141 zenon_He8 zenon_H2a zenon_H1f5 zenon_H113 zenon_Hf1 zenon_Hef zenon_H130 zenon_H127 zenon_H2f7 zenon_H187 zenon_H12c zenon_H101 zenon_Ha9 zenon_H1c9 zenon_H118 zenon_H10d zenon_H335 zenon_H2b4 zenon_H22d zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H14b zenon_H155 zenon_H1ec zenon_H22e zenon_H2c4 zenon_H1d4 zenon_H96 zenon_H192 zenon_H154 zenon_H157 zenon_H124 zenon_H2c7 zenon_H1dc zenon_H156 zenon_H2ee zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1f6 zenon_H1d9 zenon_H22a zenon_H304 zenon_H35f zenon_H22f zenon_H5f zenon_H2ac zenon_H2fa zenon_H105 zenon_H74 zenon_H301 zenon_H7a zenon_H7e zenon_Hb8 zenon_H362 zenon_H328 zenon_H1e zenon_H1d7 zenon_H83 zenon_H2fe zenon_H2b1 zenon_H23 zenon_H1d1 zenon_Heb zenon_Hd1 zenon_H11f zenon_H12f zenon_Hbe zenon_H20 zenon_H2dd zenon_H110 zenon_H1b9 zenon_H16c zenon_H93 zenon_H1ea zenon_H12a zenon_Hfe zenon_H82 zenon_H13a zenon_H27 zenon_H68 zenon_H2a8 zenon_Hf3 zenon_H25. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.57 apply (zenon_L4_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H69 | zenon_intro zenon_H2a9 ]. % 10.40/10.57 apply (zenon_L20_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H26 | zenon_intro zenon_H2aa ]. % 10.40/10.57 apply (zenon_L103_); trivial. % 10.40/10.57 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H106 ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b5 ]. % 10.40/10.58 apply (zenon_L873_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H18c | zenon_intro zenon_H2b6 ]. % 10.40/10.58 apply (zenon_L388_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H102 ]. % 10.40/10.58 apply (zenon_L1068_); trivial. % 10.40/10.58 apply (zenon_L155_); trivial. % 10.40/10.58 apply (zenon_L313_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.58 apply (zenon_L882_); trivial. % 10.40/10.58 apply (zenon_L66_); trivial. % 10.40/10.58 (* end of lemma zenon_L1069_ *) % 10.40/10.58 assert (zenon_L1070_ : ((op (e0) (e1)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.40/10.58 do 0 intro. intros zenon_H70 zenon_H72 zenon_H5a zenon_H35f zenon_H109 zenon_H2f zenon_H20 zenon_Hf3 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2c zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e zenon_H335 zenon_Hd0 zenon_H69 zenon_H5c zenon_H5d zenon_H27 zenon_H272 zenon_H82 zenon_H25. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.40/10.58 apply (zenon_L772_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.40/10.58 apply (zenon_L269_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.40/10.58 apply (zenon_L1005_); trivial. % 10.40/10.58 apply (zenon_L521_); trivial. % 10.40/10.58 (* end of lemma zenon_L1070_ *) % 10.40/10.58 assert (zenon_L1071_ : (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((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)) = 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= (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> 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(e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.40/10.58 do 0 intro. intros zenon_H1e zenon_H22d zenon_Hfe zenon_H13a zenon_H13d zenon_H2ac zenon_H110 zenon_Ha9 zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H2f7 zenon_H187 zenon_H64 zenon_H2ca zenon_H1f5 zenon_H301 zenon_H1db zenon_H14c zenon_H141 zenon_H14b zenon_H2a zenon_H30 zenon_H22f zenon_Heb zenon_H2fe zenon_H12a zenon_H5f zenon_H155 zenon_H16c zenon_H1ec zenon_Hbe zenon_H2c4 zenon_H2dd zenon_H12f zenon_H1d4 zenon_Hb8 zenon_H7e zenon_H7a zenon_H2fa zenon_H96 zenon_H93 zenon_H11f zenon_H192 zenon_Hd1 zenon_H154 zenon_H25 zenon_H23 zenon_H157 zenon_H118 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_Hef zenon_H1ce zenon_H127 zenon_H12c zenon_H2f1 zenon_H1c9 zenon_H1f2 zenon_H2f4 zenon_H83 zenon_H101 zenon_H1ea zenon_H1f6 zenon_H1d9 zenon_H1d1 zenon_H22a zenon_He8 zenon_H130 zenon_Hf1 zenon_H113 zenon_H10d zenon_H304 zenon_Hf3 zenon_H82 zenon_H20 zenon_H35f zenon_Hd2 zenon_H1d7 zenon_H22e zenon_H74 zenon_H27 zenon_H2c zenon_H1b9 zenon_H2f zenon_He2 zenon_H105. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.58 apply (zenon_L370_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.58 apply (zenon_L27_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.58 apply (zenon_L8_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.58 apply (zenon_L738_); trivial. % 10.40/10.58 apply (zenon_L896_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.58 apply (zenon_L161_); trivial. % 10.40/10.58 apply (zenon_L879_); trivial. % 10.40/10.58 (* end of lemma zenon_L1071_ *) % 10.40/10.58 assert (zenon_L1072_ : (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.40/10.58 do 0 intro. intros zenon_H335 zenon_Hd0 zenon_H105 zenon_He2 zenon_H2f zenon_H1b9 zenon_H2c zenon_H27 zenon_H74 zenon_H22e zenon_H1d7 zenon_H35f zenon_H20 zenon_Hf3 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H2fa zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_Hbe zenon_H1ec zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H22f zenon_H30 zenon_H2a zenon_H14b zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e zenon_H82 zenon_H141. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.58 apply (zenon_L911_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.58 apply (zenon_L5_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.58 apply (zenon_L1071_); trivial. % 10.40/10.58 apply (zenon_L358_); trivial. % 10.40/10.58 (* end of lemma zenon_L1072_ *) % 10.40/10.58 assert (zenon_L1073_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.40/10.58 do 0 intro. intros zenon_H2ca zenon_H335 zenon_Hd0 zenon_H27 zenon_H25 zenon_H14b zenon_H5d zenon_H1f5 zenon_H1d5 zenon_H1ea zenon_H1f6 zenon_H10d zenon_H101 zenon_Hf3 zenon_Hfe zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H2f zenon_H105 zenon_H12c zenon_Ha9 zenon_He2 zenon_H12a zenon_H35f zenon_H30 zenon_H83 zenon_H2c zenon_H93 zenon_H74 zenon_H73 zenon_H7e zenon_H2ee zenon_H82 zenon_H141. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.58 apply (zenon_L911_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.58 apply (zenon_L5_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.58 apply (zenon_L997_); trivial. % 10.40/10.58 apply (zenon_L358_); trivial. % 10.40/10.58 (* end of lemma zenon_L1073_ *) % 10.40/10.58 assert (zenon_L1074_ : (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.40/10.58 do 0 intro. intros zenon_H64 zenon_H130 zenon_H1c9 zenon_H141 zenon_H82 zenon_H2ee zenon_H7e zenon_H93 zenon_H83 zenon_H30 zenon_H35f zenon_H12a zenon_Ha9 zenon_H12c zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_Hfe zenon_Hf3 zenon_H101 zenon_H10d zenon_H1f6 zenon_H1ea zenon_H1d5 zenon_H1f5 zenon_H5d zenon_H14b zenon_H25 zenon_Hd0 zenon_H335 zenon_H2ca zenon_H1d7 zenon_H22e zenon_H74 zenon_H27 zenon_H2c zenon_H1b9 zenon_H2f zenon_H105. % 10.40/10.58 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.58 apply (zenon_L7_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.58 apply (zenon_L772_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.58 apply (zenon_L259_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.58 apply (zenon_L370_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.58 apply (zenon_L1073_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.58 apply (zenon_L161_); trivial. % 10.40/10.58 apply (zenon_L879_); trivial. % 10.40/10.58 (* end of lemma zenon_L1074_ *) % 10.40/10.58 assert (zenon_L1075_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.40/10.58 do 0 intro. intros zenon_H272 zenon_H5d zenon_H5c zenon_H69 zenon_H5a zenon_H185 zenon_H2b2 zenon_H335 zenon_Hd0 zenon_H105 zenon_H2f zenon_H1b9 zenon_H2c zenon_H27 zenon_H74 zenon_H22e zenon_H1d7 zenon_H35f zenon_H20 zenon_Hf3 zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d1 zenon_H1d9 zenon_H1f6 zenon_H1ea zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H23 zenon_H25 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H2fa zenon_H7a zenon_H7e zenon_Hb8 zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_Hbe zenon_H1ec zenon_H16c zenon_H155 zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H22f zenon_H30 zenon_H2a zenon_H14b zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H64 zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H2ac zenon_H13d zenon_H13a zenon_Hfe zenon_H22d zenon_H1e zenon_H82 zenon_H141. % 10.40/10.58 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.58 apply (zenon_L7_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.58 apply (zenon_L22_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.58 apply (zenon_L27_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.58 apply (zenon_L365_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.40/10.58 apply (zenon_L27_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.40/10.58 apply (zenon_L336_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.40/10.58 apply (zenon_L174_); trivial. % 10.40/10.58 apply (zenon_L1070_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.58 apply (zenon_L910_); trivial. % 10.40/10.58 apply (zenon_L1072_); trivial. % 10.40/10.58 (* end of lemma zenon_L1075_ *) % 10.40/10.58 assert (zenon_L1076_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((((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) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((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 (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.40/10.58 do 0 intro. intros zenon_H35c zenon_Hd2 zenon_H2d4 zenon_H33b zenon_H89 zenon_H1d5 zenon_H272 zenon_H5d zenon_H5c zenon_H69 zenon_H5a zenon_H185 zenon_Hd0 zenon_H27 zenon_H30 zenon_H2c zenon_H141 zenon_H1f5 zenon_H113 zenon_Hf1 zenon_Hef zenon_H130 zenon_H127 zenon_H2f7 zenon_H187 zenon_H12c zenon_Ha9 zenon_H1c9 zenon_H118 zenon_H335 zenon_H2b4 zenon_H22d zenon_H13a zenon_H13d zenon_Ha1 zenon_H9c zenon_Hae zenon_H1cb zenon_H64 zenon_H2ca zenon_H1db zenon_H14c zenon_H14b zenon_H155 zenon_H1ec zenon_H22e zenon_H2c4 zenon_H1d4 zenon_H96 zenon_H192 zenon_H154 zenon_H157 zenon_H124 zenon_H2c7 zenon_H2a8 zenon_H1dc zenon_H156 zenon_H2ee zenon_H1ce zenon_H2f1 zenon_H1f2 zenon_H2f4 zenon_H1f6 zenon_H1d9 zenon_H22a zenon_H304 zenon_H35f zenon_H22f zenon_H5f zenon_H2ac zenon_H2fa zenon_H74 zenon_H301 zenon_H7e zenon_Hb8 zenon_H362 zenon_H328 zenon_H1e zenon_H1d7 zenon_H83 zenon_H2fe zenon_H2b1 zenon_H23 zenon_H1d1 zenon_H12a zenon_Hd1 zenon_H11f zenon_H12f zenon_Hbe zenon_H2dd zenon_H110 zenon_H1b9 zenon_H25 zenon_H16c zenon_H93 zenon_H1ea zenon_H10d zenon_H101 zenon_Hfe zenon_H82 zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H2f zenon_H105. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.58 apply (zenon_L772_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.58 apply (zenon_L8_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.58 apply (zenon_L738_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.40/10.58 apply (zenon_L783_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.40/10.58 apply (zenon_L994_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.40/10.58 apply (zenon_L501_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b5 ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H125 ]. % 10.40/10.58 apply (zenon_L1075_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H126 ]. % 10.40/10.58 apply (zenon_L616_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H102 | zenon_intro zenon_H11b ]. % 10.40/10.58 apply (zenon_L875_); trivial. % 10.40/10.58 apply (zenon_L793_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H18c | zenon_intro zenon_H2b6 ]. % 10.40/10.58 apply (zenon_L388_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H102 ]. % 10.40/10.58 apply (zenon_L991_); trivial. % 10.40/10.58 apply (zenon_L875_); trivial. % 10.40/10.58 (* end of lemma zenon_L1076_ *) % 10.40/10.58 assert (zenon_L1077_ : (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (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 (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (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) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((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 (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (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)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((~((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) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (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) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (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 (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.40/10.58 do 0 intro. intros zenon_H25 zenon_H1d5 zenon_H2a8 zenon_H141 zenon_H2b1 zenon_Hf1 zenon_H335 zenon_H2ca zenon_H27 zenon_H13a zenon_Hfe zenon_H2ee zenon_H83 zenon_H7e zenon_H130 zenon_H2ac zenon_H33b zenon_H5f zenon_H5d zenon_H30 zenon_H328 zenon_H1e zenon_H16c zenon_H155 zenon_H20 zenon_H23 zenon_H35c zenon_H64 zenon_H1d1 zenon_H22a zenon_H7a zenon_H2d4 zenon_Ha1 zenon_Heb zenon_H2a zenon_He8 zenon_H101 zenon_H10d zenon_H1ea zenon_H93 zenon_H110 zenon_H2dd zenon_Hbe zenon_H12f zenon_H11f zenon_H12a zenon_H2fe zenon_H362 zenon_H301 zenon_H2fa zenon_H22f zenon_H35f zenon_H304 zenon_H1d9 zenon_H1f6 zenon_H2f4 zenon_H1f2 zenon_H2f1 zenon_H1ce zenon_H156 zenon_H1dc zenon_H124 zenon_H157 zenon_H154 zenon_H192 zenon_H96 zenon_H1d4 zenon_H1ec zenon_H14b zenon_H14c zenon_H1db zenon_H1cb zenon_Hae zenon_H9c zenon_H13d zenon_H22d zenon_H2b4 zenon_H118 zenon_H1c9 zenon_Ha9 zenon_H12c zenon_H187 zenon_H2f7 zenon_H127 zenon_Hef zenon_H113 zenon_H1f5 zenon_H185 zenon_H5a zenon_H5c zenon_H272 zenon_H2c7 zenon_Hd1 zenon_H2c4 zenon_H2ae zenon_H1d7 zenon_H22e zenon_H74 zenon_H2c zenon_H1b9 zenon_H2f zenon_H105 zenon_H82 zenon_Hb8. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.58 apply (zenon_L4_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.58 apply (zenon_L1009_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.58 apply (zenon_L152_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.58 apply (zenon_L7_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.58 apply (zenon_L772_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.58 apply (zenon_L910_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.58 apply (zenon_L370_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.58 apply (zenon_L911_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.58 apply (zenon_L163_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.58 apply (zenon_L1076_); trivial. % 10.40/10.58 apply (zenon_L390_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.58 apply (zenon_L231_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.58 apply (zenon_L1012_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.58 apply (zenon_L911_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.58 apply (zenon_L877_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.58 apply (zenon_L1018_); trivial. % 10.40/10.58 apply (zenon_L358_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.58 apply (zenon_L161_); trivial. % 10.40/10.58 apply (zenon_L879_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.58 apply (zenon_L916_); trivial. % 10.40/10.58 apply (zenon_L613_); trivial. % 10.40/10.58 apply (zenon_L344_); trivial. % 10.40/10.58 (* end of lemma zenon_L1077_ *) % 10.40/10.58 assert (zenon_L1078_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (((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 (e0) (e2)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (op (e0) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = 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(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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.40/10.58 do 0 intro. intros zenon_H2ae zenon_H185 zenon_H2b4 zenon_H362 zenon_H2d4 zenon_H33b zenon_H1ea zenon_Ha2 zenon_H109 zenon_H2c zenon_H72 zenon_H5a zenon_H35f zenon_H2f zenon_H304 zenon_H10d zenon_H113 zenon_Hf1 zenon_H130 zenon_He8 zenon_H22a zenon_H1d7 zenon_H1d9 zenon_H1f6 zenon_H101 zenon_H83 zenon_H2f4 zenon_H1f2 zenon_H1c9 zenon_H2f1 zenon_H12c zenon_H127 zenon_H1ce zenon_Hef zenon_H2ee zenon_H156 zenon_H1dc zenon_H2a8 zenon_H2c7 zenon_H124 zenon_H118 zenon_H157 zenon_H154 zenon_Hd1 zenon_H192 zenon_H11f zenon_H93 zenon_H96 zenon_H1b9 zenon_H2fa zenon_H74 zenon_H7a zenon_H7e zenon_H1d4 zenon_H12f zenon_H2dd zenon_H2c4 zenon_H22e zenon_Hbe zenon_H1ec zenon_H5f zenon_H12a zenon_H2fe zenon_Heb zenon_H105 zenon_H22f zenon_H30 zenon_H2a zenon_H14b zenon_H141 zenon_H14c zenon_H1db zenon_H301 zenon_H1f5 zenon_H2ca zenon_H187 zenon_H2f7 zenon_H1cb zenon_Hae zenon_H9c zenon_Ha1 zenon_Ha9 zenon_H110 zenon_H13d zenon_Hfe zenon_H22d zenon_H335 zenon_H69 zenon_H5c zenon_H27 zenon_H272 zenon_Hb8 zenon_H13a zenon_H1d1 zenon_H64 zenon_H35c zenon_H2b1 zenon_H23 zenon_H20 zenon_H155 zenon_H16c zenon_H1e zenon_H328 zenon_H2ac zenon_Hd2 zenon_H5d zenon_H82 zenon_H25. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.40/10.58 apply (zenon_L1077_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.40/10.58 apply (zenon_L269_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.40/10.58 apply (zenon_L1007_); trivial. % 10.40/10.58 apply (zenon_L521_); trivial. % 10.40/10.58 (* end of lemma zenon_L1078_ *) % 10.40/10.58 assert (zenon_L1079_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (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)) = (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) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 10.40/10.58 do 0 intro. intros zenon_H2ee zenon_H30 zenon_H7e zenon_H73 zenon_H74 zenon_H83 zenon_H2c zenon_H185 zenon_H2ac zenon_H35f zenon_H12a zenon_He2 zenon_Ha9 zenon_H12c zenon_H105 zenon_H2f zenon_Heb zenon_H7a zenon_H2a zenon_H20 zenon_He8 zenon_H82 zenon_Hfe zenon_Hf3 zenon_H101 zenon_H10d zenon_H1f6 zenon_H1ea zenon_H1d5 zenon_H1f5 zenon_H5d zenon_H14b. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.58 apply (zenon_L27_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.58 apply (zenon_L336_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.58 apply (zenon_L389_); trivial. % 10.40/10.58 apply (zenon_L996_); trivial. % 10.40/10.58 (* end of lemma zenon_L1079_ *) % 10.40/10.58 assert (zenon_L1080_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.40/10.58 do 0 intro. intros zenon_H21c zenon_He8 zenon_H20 zenon_H2a zenon_H7a zenon_Heb zenon_H2f zenon_H105. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H21c). zenon_intro zenon_H128. zenon_intro zenon_H21d. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H166. zenon_intro zenon_H174. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H109. zenon_intro zenon_H79. % 10.40/10.58 apply (zenon_L807_); trivial. % 10.40/10.58 (* end of lemma zenon_L1080_ *) % 10.40/10.58 assert (zenon_L1081_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> False). % 10.40/10.58 do 0 intro. intros zenon_H223 zenon_H187 zenon_H27. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H79. zenon_intro zenon_H224. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H109. zenon_intro zenon_Hc8. % 10.40/10.58 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H18c. zenon_intro zenon_H188. % 10.40/10.58 apply (zenon_L119_); trivial. % 10.40/10.58 (* end of lemma zenon_L1081_ *) % 10.40/10.58 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H374. zenon_intro zenon_H373. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H373). zenon_intro zenon_H33b. zenon_intro zenon_H375. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H375). zenon_intro zenon_H2f4. zenon_intro zenon_H376. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H376). zenon_intro zenon_H1ce. zenon_intro zenon_H377. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H377). zenon_intro zenon_H379. zenon_intro zenon_H378. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H378). zenon_intro zenon_H37b. zenon_intro zenon_H37a. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H37a). zenon_intro zenon_H1f2. zenon_intro zenon_H37c. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H37c). zenon_intro zenon_H10d. zenon_intro zenon_H37d. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H37d). zenon_intro zenon_H37f. zenon_intro zenon_H37e. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H37e). zenon_intro zenon_H2c7. zenon_intro zenon_H380. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H380). zenon_intro zenon_H382. zenon_intro zenon_H381. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H381). zenon_intro zenon_H12c. zenon_intro zenon_H383. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H383). zenon_intro zenon_H1db. zenon_intro zenon_H384. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H384). zenon_intro zenon_H14c. zenon_intro zenon_H385. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H385). zenon_intro zenon_H1f6. zenon_intro zenon_H386. % 10.40/10.58 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H156. zenon_intro zenon_H387. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H387). zenon_intro zenon_H1dc. zenon_intro zenon_H388. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H388). zenon_intro zenon_H2fe. zenon_intro zenon_H389. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H389). zenon_intro zenon_H328. zenon_intro zenon_H38a. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H38a). zenon_intro zenon_H155. zenon_intro zenon_H38b. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H38b). zenon_intro zenon_H1d1. zenon_intro zenon_H38c. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H38c). zenon_intro zenon_He8. zenon_intro zenon_H38d. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H38d). zenon_intro zenon_H130. zenon_intro zenon_H38e. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H38e). zenon_intro zenon_H13d. zenon_intro zenon_H38f. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H38f). zenon_intro zenon_H2ae. zenon_intro zenon_H390. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H390). zenon_intro zenon_H301. zenon_intro zenon_H391. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H391). zenon_intro zenon_H362. zenon_intro zenon_H392. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H392). zenon_intro zenon_H2a8. zenon_intro zenon_H393. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H393). zenon_intro zenon_H2ca. zenon_intro zenon_H394. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H394). zenon_intro zenon_H22e. zenon_intro zenon_H395. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H395). zenon_intro zenon_H2ee. zenon_intro zenon_H396. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H396). zenon_intro zenon_Hae. zenon_intro zenon_H397. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H397). zenon_intro zenon_H399. zenon_intro zenon_H398. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H398). zenon_intro zenon_H2b4. zenon_intro zenon_H39a. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H39a). zenon_intro zenon_H338. zenon_intro zenon_H39b. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H39b). zenon_intro zenon_H1cb. zenon_intro zenon_H39c. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H39c). zenon_intro zenon_H22a. zenon_intro zenon_H39d. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H39d). zenon_intro zenon_H12f. zenon_intro zenon_H39e. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H39e). zenon_intro zenon_H2f7. zenon_intro zenon_H39f. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H39f). zenon_intro zenon_H272. zenon_intro zenon_H3a0. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3a0). zenon_intro zenon_H35f. zenon_intro zenon_H3a1. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3a1). zenon_intro zenon_H2fa. zenon_intro zenon_H3a2. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3a2). zenon_intro zenon_H124. zenon_intro zenon_H3a3. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3a3). zenon_intro zenon_H192. zenon_intro zenon_H3a4. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3a4). zenon_intro zenon_H2f1. zenon_intro zenon_H3a5. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3a5). zenon_intro zenon_H83. zenon_intro zenon_H118. % 10.40/10.58 apply (zenon_and_s _ _ ax3). zenon_intro zenon_Hbe. zenon_intro zenon_H3a6. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3a6). zenon_intro zenon_H2dd. zenon_intro zenon_H3a7. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3a7). zenon_intro zenon_H1d4. zenon_intro zenon_H3a8. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3a8). zenon_intro zenon_H9c. zenon_intro zenon_H3a9. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3a9). zenon_intro zenon_H74. zenon_intro zenon_H3aa. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3aa). zenon_intro zenon_H11f. zenon_intro zenon_H3ab. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3ab). zenon_intro zenon_H5f. zenon_intro zenon_H3ac. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3ac). zenon_intro zenon_Ha1. zenon_intro zenon_H3ad. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3ad). zenon_intro zenon_H7a. zenon_intro zenon_H3ae. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3ae). zenon_intro zenon_Hd1. zenon_intro zenon_H3af. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3af). zenon_intro zenon_H93. zenon_intro zenon_H3b0. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3b0). zenon_intro zenon_H2c4. zenon_intro zenon_H3b1. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3b1). zenon_intro zenon_H13a. zenon_intro zenon_H3b2. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3b2). zenon_intro zenon_Heb. zenon_intro zenon_H3b3. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3b3). zenon_intro zenon_H96. zenon_intro zenon_H3b4. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3b4). zenon_intro zenon_H1b9. zenon_intro zenon_H3b5. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3b5). zenon_intro zenon_H1ec. zenon_intro zenon_H3b6. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3b6). zenon_intro zenon_H7e. zenon_intro zenon_H3b7. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3b7). zenon_intro zenon_H105. zenon_intro zenon_H3b8. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3b8). zenon_intro zenon_H12a. zenon_intro zenon_H3b9. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3b9). zenon_intro zenon_Hb8. zenon_intro zenon_H3ba. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3ba). zenon_intro zenon_H101. zenon_intro zenon_H3bb. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3bb). zenon_intro zenon_Hfe. zenon_intro zenon_H3bc. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3bc). zenon_intro zenon_Ha9. zenon_intro zenon_H3bd. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3bd). zenon_intro zenon_H64. zenon_intro zenon_H3be. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3be). zenon_intro zenon_Hef. zenon_intro zenon_H3bf. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3bf). zenon_intro zenon_H1c9. zenon_intro zenon_H3c0. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3c0). zenon_intro zenon_H335. zenon_intro zenon_H3c1. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3c1). zenon_intro zenon_H3c3. zenon_intro zenon_H3c2. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3c2). zenon_intro zenon_H3c5. zenon_intro zenon_H3c4. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3c4). zenon_intro zenon_Hf1. zenon_intro zenon_H3c6. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3c6). zenon_intro zenon_H35c. zenon_intro zenon_H3c7. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3c7). zenon_intro zenon_H3c9. zenon_intro zenon_H3c8. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H187. zenon_intro zenon_H3ca. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H110. zenon_intro zenon_H3cb. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3cb). zenon_intro zenon_H3cd. zenon_intro zenon_H3cc. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3cc). zenon_intro zenon_H2b1. zenon_intro zenon_H3ce. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3ce). zenon_intro zenon_H1d7. zenon_intro zenon_H3cf. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3cf). zenon_intro zenon_H113. zenon_intro zenon_H3d0. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3d0). zenon_intro zenon_H2ac. zenon_intro zenon_H3d1. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3d1). zenon_intro zenon_H3d3. zenon_intro zenon_H3d2. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3d2). zenon_intro zenon_H127. zenon_intro zenon_H3d4. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3d4). zenon_intro zenon_H1d9. zenon_intro zenon_H3d5. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3d5). zenon_intro zenon_H1f5. zenon_intro zenon_H3d6. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3d6). zenon_intro zenon_H16c. zenon_intro zenon_H3d7. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3d7). zenon_intro zenon_H14b. zenon_intro zenon_H3d8. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3d8). zenon_intro zenon_H141. zenon_intro zenon_H1ea. % 10.40/10.58 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H1e. zenon_intro zenon_H3d9. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3d9). zenon_intro zenon_H23. zenon_intro zenon_H3da. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3da). zenon_intro zenon_H2a. zenon_intro zenon_H3db. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3db). zenon_intro zenon_H25. zenon_intro zenon_H3dc. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3dc). zenon_intro zenon_H2c. zenon_intro zenon_H30. % 10.40/10.58 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H3de. zenon_intro zenon_H3dd. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H304. zenon_intro zenon_H3df. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3df). zenon_intro zenon_H22d. zenon_intro zenon_H3e0. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3e0). zenon_intro zenon_H154. zenon_intro zenon_H3e1. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H3e1). zenon_intro zenon_H157. zenon_intro zenon_H22f. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H3de); [ zenon_intro zenon_H20 | zenon_intro zenon_H3e2 ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H1f | zenon_intro zenon_H305 ]. % 10.40/10.58 apply (zenon_L2_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H27 | zenon_intro zenon_H306 ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H24 | zenon_intro zenon_H230 ]. % 10.40/10.58 apply (zenon_L4_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H26 | zenon_intro zenon_H231 ]. % 10.40/10.58 apply (zenon_L5_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H2e | zenon_intro zenon_H82 ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.40/10.58 apply (zenon_L7_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.40/10.58 apply (zenon_L8_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.40/10.58 apply (zenon_L9_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.40/10.58 apply (zenon_L11_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.40/10.58 apply (zenon_L13_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.40/10.58 apply (zenon_L15_); trivial. % 10.40/10.58 apply (zenon_L17_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H2b | zenon_intro zenon_H158 ]. % 10.40/10.58 apply (zenon_L7_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H2d | zenon_intro zenon_H159 ]. % 10.40/10.58 apply (zenon_L8_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H35 | zenon_intro zenon_H15a ]. % 10.40/10.58 apply (zenon_L11_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H41 | zenon_intro zenon_H15f ]. % 10.40/10.58 apply (zenon_L13_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H4b | zenon_intro zenon_H58 ]. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 10.40/10.58 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H45. zenon_intro zenon_H50. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.58 apply (zenon_L2_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.58 apply (zenon_L18_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.40/10.58 apply (zenon_L2_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.58 apply (zenon_L4_); trivial. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.58 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.59 apply (zenon_L19_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.59 apply (zenon_L20_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L21_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.59 apply (zenon_L22_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.59 apply (zenon_L27_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.59 apply (zenon_L28_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.59 apply (zenon_L29_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.59 apply (zenon_L770_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.59 apply (zenon_L870_); trivial. % 10.40/10.59 apply (zenon_L860_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L599_); trivial. % 10.40/10.59 apply (zenon_L880_); trivial. % 10.40/10.59 apply (zenon_L343_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.59 apply (zenon_L882_); trivial. % 10.40/10.59 apply (zenon_L344_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.59 apply (zenon_L424_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.59 apply (zenon_L424_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L7_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_L888_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L259_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.59 apply (zenon_L370_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.40/10.59 apply (zenon_L371_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.40/10.59 apply (zenon_L231_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.59 apply (zenon_L29_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.59 apply (zenon_L231_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.59 apply (zenon_L27_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.59 apply (zenon_L8_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.59 apply (zenon_L389_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.40/10.59 apply (zenon_L900_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.40/10.59 apply (zenon_L903_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.40/10.59 apply (zenon_L907_); trivial. % 10.40/10.59 apply (zenon_L125_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.59 apply (zenon_L860_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.59 apply (zenon_L65_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.59 apply (zenon_L389_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.40/10.59 apply (zenon_L783_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.40/10.59 apply (zenon_L903_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.40/10.59 apply (zenon_L341_); trivial. % 10.40/10.59 apply (zenon_L892_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.59 apply (zenon_L908_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.59 apply (zenon_L770_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.59 apply (zenon_L27_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.59 apply (zenon_L8_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.59 apply (zenon_L389_); trivial. % 10.40/10.59 apply (zenon_L899_); trivial. % 10.40/10.59 apply (zenon_L909_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.59 apply (zenon_L161_); trivial. % 10.40/10.59 apply (zenon_L879_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.59 apply (zenon_L684_); trivial. % 10.40/10.59 apply (zenon_L343_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.59 apply (zenon_L152_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L7_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_L888_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L910_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.59 apply (zenon_L370_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.40/10.59 apply (zenon_L153_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.40/10.59 apply (zenon_L231_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.59 apply (zenon_L911_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.59 apply (zenon_L5_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.59 apply (zenon_L27_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.59 apply (zenon_L8_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.59 apply (zenon_L738_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.40/10.59 apply (zenon_L783_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.40/10.59 apply (zenon_L914_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.40/10.59 apply (zenon_L691_); trivial. % 10.40/10.59 apply (zenon_L892_); trivial. % 10.40/10.59 apply (zenon_L390_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.59 apply (zenon_L770_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.59 apply (zenon_L911_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.59 apply (zenon_L809_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.59 apply (zenon_L27_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.59 apply (zenon_L65_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.59 apply (zenon_L738_); trivial. % 10.40/10.59 apply (zenon_L914_); trivial. % 10.40/10.59 apply (zenon_L358_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.59 apply (zenon_L911_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.59 apply (zenon_L877_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.59 apply (zenon_L860_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.59 apply (zenon_L8_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.59 apply (zenon_L738_); trivial. % 10.40/10.59 apply (zenon_L913_); trivial. % 10.40/10.59 apply (zenon_L358_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.59 apply (zenon_L908_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.59 apply (zenon_L231_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.59 apply (zenon_L912_); trivial. % 10.40/10.59 apply (zenon_L909_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.59 apply (zenon_L161_); trivial. % 10.40/10.59 apply (zenon_L879_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.59 apply (zenon_L916_); trivial. % 10.40/10.59 apply (zenon_L343_); trivial. % 10.40/10.59 apply (zenon_L344_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.59 apply (zenon_L424_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L7_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_L772_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L259_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.59 apply (zenon_L370_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.59 apply (zenon_L918_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.59 apply (zenon_L161_); trivial. % 10.40/10.59 apply (zenon_L771_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.59 apply (zenon_L152_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L21_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_L772_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L910_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.59 apply (zenon_L21_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.59 apply (zenon_L919_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.59 apply (zenon_L770_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.59 apply (zenon_L920_); trivial. % 10.40/10.59 apply (zenon_L921_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.59 apply (zenon_L161_); trivial. % 10.40/10.59 apply (zenon_L771_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.59 apply (zenon_L916_); trivial. % 10.40/10.59 apply (zenon_L613_); trivial. % 10.40/10.59 apply (zenon_L344_); trivial. % 10.40/10.59 apply (zenon_L925_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.40/10.59 apply (zenon_L795_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.40/10.59 apply (zenon_L926_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.40/10.59 apply (zenon_and_s _ _ zenon_Hbb). zenon_intro zenon_H20. zenon_intro zenon_Hbc. % 10.40/10.59 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_H20. zenon_intro zenon_Hbd. % 10.40/10.59 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H90. zenon_intro zenon_Hb7. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.59 apply (zenon_L244_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.59 apply (zenon_L18_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.40/10.59 apply (zenon_L244_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.59 apply (zenon_L503_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.59 apply (zenon_L928_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.59 apply (zenon_L882_); trivial. % 10.40/10.59 apply (zenon_L344_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.59 apply (zenon_L4_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.59 apply (zenon_L928_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.59 apply (zenon_L152_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L7_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_L927_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L910_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.59 apply (zenon_L370_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.59 apply (zenon_L894_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.59 apply (zenon_L365_); trivial. % 10.40/10.59 apply (zenon_L879_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.59 apply (zenon_L916_); trivial. % 10.40/10.59 apply (zenon_L35_); trivial. % 10.40/10.59 apply (zenon_L344_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.59 apply (zenon_L4_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L7_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_L772_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L599_); trivial. % 10.40/10.59 apply (zenon_L891_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.59 apply (zenon_L152_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L7_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_L772_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L910_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.59 apply (zenon_L370_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.59 apply (zenon_L919_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.59 apply (zenon_L692_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.59 apply (zenon_L920_); trivial. % 10.40/10.59 apply (zenon_L921_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.59 apply (zenon_L161_); trivial. % 10.40/10.59 apply (zenon_L879_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.59 apply (zenon_L916_); trivial. % 10.40/10.59 apply (zenon_L613_); trivial. % 10.40/10.59 apply (zenon_L344_); trivial. % 10.40/10.59 apply (zenon_L925_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.40/10.59 apply (zenon_L246_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.40/10.59 apply (zenon_L929_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.40/10.59 apply (zenon_L364_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.40/10.59 apply (zenon_L930_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.40/10.59 apply (zenon_L55_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.40/10.59 apply (zenon_L372_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.40/10.59 apply (zenon_L254_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.40/10.59 apply (zenon_L198_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.40/10.59 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hb7. zenon_intro zenon_H170. % 10.40/10.59 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_H90. zenon_intro zenon_H171. % 10.40/10.59 apply (zenon_and_s _ _ zenon_H171). zenon_intro zenon_He2. zenon_intro zenon_H72. % 10.40/10.59 apply (zenon_L879_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.40/10.59 apply (zenon_L931_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.40/10.59 apply (zenon_L596_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.40/10.59 apply (zenon_L263_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.40/10.59 apply (zenon_L932_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.40/10.59 apply (zenon_L264_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.40/10.59 apply (zenon_L597_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.40/10.59 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H68. zenon_intro zenon_H182. % 10.40/10.59 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_H5e. zenon_intro zenon_Hbd. % 10.40/10.59 apply (zenon_L18_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.40/10.59 apply (zenon_L117_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.59 apply (zenon_L2_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.59 apply (zenon_L18_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.40/10.59 apply (zenon_L2_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.59 apply (zenon_L4_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.59 apply (zenon_L19_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.59 apply (zenon_L20_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L7_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_L933_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L259_); trivial. % 10.40/10.59 apply (zenon_L880_); trivial. % 10.40/10.59 apply (zenon_L343_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.59 apply (zenon_L882_); trivial. % 10.40/10.59 apply (zenon_L344_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.59 apply (zenon_L4_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L7_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_L933_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L599_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.59 apply (zenon_L370_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.59 apply (zenon_L29_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.59 apply (zenon_L770_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.59 apply (zenon_L27_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.59 apply (zenon_L65_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.59 apply (zenon_L389_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.40/10.59 apply (zenon_L684_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H360 ]. % 10.40/10.59 apply (zenon_L890_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Hfd | zenon_intro zenon_H361 ]. % 10.40/10.59 apply (zenon_L934_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 10.40/10.59 apply (zenon_L892_); trivial. % 10.40/10.59 apply (zenon_L108_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.40/10.59 apply (zenon_L936_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.40/10.59 apply (zenon_L907_); trivial. % 10.40/10.59 apply (zenon_L500_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.40/10.59 apply (zenon_L9_); trivial. % 10.40/10.59 apply (zenon_L199_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H86 | zenon_intro zenon_H1cc ]. % 10.40/10.59 apply (zenon_L684_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cd ]. % 10.40/10.59 apply (zenon_L936_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H2e | zenon_intro zenon_H128 ]. % 10.40/10.59 apply (zenon_L14_); trivial. % 10.40/10.59 apply (zenon_L255_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.59 apply (zenon_L365_); trivial. % 10.40/10.59 apply (zenon_L879_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L7_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.59 apply (zenon_L7_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.59 apply (zenon_L27_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.59 apply (zenon_L161_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.59 apply (zenon_L29_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.59 apply (zenon_L118_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.40/10.59 apply (zenon_L27_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.40/10.59 apply (zenon_L59_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.40/10.59 apply (zenon_L174_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.40/10.59 apply (zenon_L783_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.40/10.59 apply (zenon_L869_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.40/10.59 apply (zenon_L657_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.40/10.59 apply (zenon_L937_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.40/10.59 apply (zenon_L269_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.40/10.59 apply (zenon_L883_); trivial. % 10.40/10.59 apply (zenon_L560_); trivial. % 10.40/10.59 apply (zenon_L390_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.59 apply (zenon_L268_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.59 apply (zenon_L870_); trivial. % 10.40/10.59 apply (zenon_L860_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L910_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.59 apply (zenon_L370_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9d | zenon_intro zenon_H13e ]. % 10.40/10.59 apply (zenon_L371_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H8d | zenon_intro zenon_H13f ]. % 10.40/10.59 apply (zenon_L268_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H13b | zenon_intro zenon_Hfd ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.59 apply (zenon_L911_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.59 apply (zenon_L809_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.59 apply (zenon_L27_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.59 apply (zenon_L336_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.59 apply (zenon_L738_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.40/10.59 apply (zenon_L783_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.40/10.59 apply (zenon_L940_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.40/10.59 apply (zenon_L341_); trivial. % 10.40/10.59 apply (zenon_L892_); trivial. % 10.40/10.59 apply (zenon_L390_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.59 apply (zenon_L770_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.59 apply (zenon_L911_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.59 apply (zenon_L871_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.59 apply (zenon_L27_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.59 apply (zenon_L65_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.59 apply (zenon_L738_); trivial. % 10.40/10.59 apply (zenon_L940_); trivial. % 10.40/10.59 apply (zenon_L358_); trivial. % 10.40/10.59 apply (zenon_L938_); trivial. % 10.40/10.59 apply (zenon_L939_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.59 apply (zenon_L365_); trivial. % 10.40/10.59 apply (zenon_L879_); trivial. % 10.40/10.59 apply (zenon_L344_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L7_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_L772_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L599_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H70 | zenon_intro zenon_H2ef ]. % 10.40/10.59 apply (zenon_L772_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ef); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f0 ]. % 10.40/10.59 apply (zenon_L336_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H121 | zenon_intro zenon_H79 ]. % 10.40/10.59 apply (zenon_L389_); trivial. % 10.40/10.59 apply (zenon_L898_); trivial. % 10.40/10.59 apply (zenon_L925_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.40/10.59 apply (zenon_L121_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.40/10.59 apply (zenon_L271_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.40/10.59 apply (zenon_L694_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.40/10.59 apply (zenon_L374_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.40/10.59 apply (zenon_L129_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.40/10.59 apply (zenon_L375_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.40/10.59 apply (zenon_L655_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.40/10.59 apply (zenon_L133_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.40/10.59 apply (zenon_L134_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.40/10.59 apply (zenon_L276_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.40/10.59 apply (zenon_L941_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.40/10.59 apply (zenon_L942_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.40/10.59 apply (zenon_L138_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.40/10.59 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H86. zenon_intro zenon_H1ae. % 10.40/10.59 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_Hd0. zenon_intro zenon_Hbd. % 10.40/10.59 apply (zenon_L916_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.40/10.59 apply (zenon_L629_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.40/10.59 apply (zenon_L945_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.40/10.59 apply (zenon_L377_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.40/10.59 apply (zenon_L632_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.40/10.59 apply (zenon_L284_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.40/10.59 apply (zenon_L146_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.40/10.59 apply (zenon_L147_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.40/10.59 apply (zenon_L201_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.40/10.59 apply (zenon_L202_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.40/10.59 apply (zenon_L203_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.40/10.59 apply (zenon_L167_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.40/10.59 apply (zenon_L286_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.40/10.59 apply (zenon_L946_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.40/10.59 apply (zenon_L858_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.40/10.59 apply (zenon_L204_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.40/10.59 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H72. zenon_intro zenon_H1fc. % 10.40/10.59 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_He2. zenon_intro zenon_Hbd. % 10.40/10.59 apply (zenon_L879_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.40/10.59 apply (zenon_L808_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.40/10.59 apply (zenon_L947_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.40/10.59 apply (zenon_L206_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.40/10.59 apply (zenon_L183_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.40/10.59 apply (zenon_L948_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.40/10.59 apply (zenon_L196_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.40/10.59 apply (zenon_L186_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.40/10.59 apply (zenon_L187_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.40/10.59 apply (zenon_L296_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.40/10.59 apply (zenon_L298_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.40/10.59 apply (zenon_L300_); trivial. % 10.40/10.59 apply (zenon_L301_); trivial. % 10.40/10.59 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.40/10.59 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 10.40/10.59 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H51. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H6d | zenon_intro zenon_H232 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.59 apply (zenon_L2_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.59 apply (zenon_L18_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.40/10.59 apply (zenon_L2_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.40/10.59 apply (zenon_L993_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.59 apply (zenon_L4_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.59 apply (zenon_L950_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.59 apply (zenon_L152_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L21_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.59 apply (zenon_L22_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.59 apply (zenon_L27_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.59 apply (zenon_L365_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.59 apply (zenon_L950_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.59 apply (zenon_L5_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.40/10.59 apply (zenon_L1000_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.40/10.59 apply (zenon_L8_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.40/10.59 apply (zenon_L174_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.40/10.59 apply (zenon_L783_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.40/10.59 apply (zenon_L1008_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.40/10.59 apply (zenon_L501_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.40/10.59 apply (zenon_L381_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.40/10.59 apply (zenon_L382_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.40/10.59 apply (zenon_L1017_); trivial. % 10.40/10.59 apply (zenon_L125_); trivial. % 10.40/10.59 apply (zenon_L390_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.59 apply (zenon_L770_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.59 apply (zenon_L992_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.59 apply (zenon_L163_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.40/10.59 apply (zenon_L1011_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.40/10.59 apply (zenon_L59_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.40/10.59 apply (zenon_L174_); trivial. % 10.40/10.59 apply (zenon_L1008_); trivial. % 10.40/10.59 apply (zenon_L358_); trivial. % 10.40/10.59 apply (zenon_L1019_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L910_); trivial. % 10.40/10.59 apply (zenon_L1020_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.59 apply (zenon_L684_); trivial. % 10.40/10.59 apply (zenon_L343_); trivial. % 10.40/10.59 apply (zenon_L344_); trivial. % 10.40/10.59 apply (zenon_L1015_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.40/10.59 apply (zenon_L154_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.40/10.59 apply (zenon_L1069_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.59 apply (zenon_L4_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.59 apply (zenon_L950_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.59 apply (zenon_L152_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L21_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.59 apply (zenon_L22_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.59 apply (zenon_L27_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.59 apply (zenon_L365_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.40/10.59 apply (zenon_L23_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.40/10.59 apply (zenon_L8_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.40/10.59 apply (zenon_L174_); trivial. % 10.40/10.59 apply (zenon_L1070_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L910_); trivial. % 10.40/10.59 apply (zenon_L1072_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.59 apply (zenon_L916_); trivial. % 10.40/10.59 apply (zenon_L343_); trivial. % 10.40/10.59 apply (zenon_L344_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.59 apply (zenon_L424_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.59 apply (zenon_L1009_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.59 apply (zenon_L1074_); trivial. % 10.40/10.59 apply (zenon_L66_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H233 ]. % 10.40/10.59 apply (zenon_L795_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H234 ]. % 10.40/10.59 apply (zenon_L926_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_Hbb | zenon_intro zenon_H235 ]. % 10.40/10.59 apply (zenon_L502_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H236 ]. % 10.40/10.59 apply (zenon_L246_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H237 ]. % 10.40/10.59 apply (zenon_L929_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H238 ]. % 10.40/10.59 apply (zenon_L646_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H239 ]. % 10.40/10.59 apply (zenon_L207_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hcd | zenon_intro zenon_H23a ]. % 10.40/10.59 apply (zenon_L55_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H23b ]. % 10.40/10.59 apply (zenon_L989_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H163 | zenon_intro zenon_H23c ]. % 10.40/10.59 apply (zenon_L254_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H169 | zenon_intro zenon_H23d ]. % 10.40/10.59 apply (zenon_L209_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H16f | zenon_intro zenon_H23e ]. % 10.40/10.59 apply (zenon_L700_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H172 | zenon_intro zenon_H23f ]. % 10.40/10.59 apply (zenon_L931_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H175 | zenon_intro zenon_H240 ]. % 10.40/10.59 apply (zenon_L701_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H178 | zenon_intro zenon_H241 ]. % 10.40/10.59 apply (zenon_L263_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H17b | zenon_intro zenon_H242 ]. % 10.40/10.59 apply (zenon_L932_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H17d | zenon_intro zenon_H243 ]. % 10.40/10.59 apply (zenon_L264_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H17f | zenon_intro zenon_H244 ]. % 10.40/10.59 apply (zenon_L961_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H181 | zenon_intro zenon_H245 ]. % 10.40/10.59 apply (zenon_L553_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H183 | zenon_intro zenon_H246 ]. % 10.40/10.59 apply (zenon_L117_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H185 | zenon_intro zenon_H247 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H1f | zenon_intro zenon_H2ff ]. % 10.40/10.59 apply (zenon_L2_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H5e | zenon_intro zenon_H300 ]. % 10.40/10.59 apply (zenon_L18_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2d4 | zenon_intro zenon_Hf3 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.40/10.59 apply (zenon_L2_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.40/10.59 apply (zenon_L993_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.59 apply (zenon_L4_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.59 apply (zenon_L950_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.59 apply (zenon_L152_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L7_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.59 apply (zenon_L7_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.59 apply (zenon_L27_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.59 apply (zenon_L161_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H89 | zenon_intro zenon_H2af ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.59 apply (zenon_L950_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.59 apply (zenon_L5_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.40/10.59 apply (zenon_L1000_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.40/10.59 apply (zenon_L336_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.40/10.59 apply (zenon_L174_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9e | zenon_intro zenon_Haf ]. % 10.40/10.59 apply (zenon_L783_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hb0 ]. % 10.40/10.59 apply (zenon_L1078_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha8 ]. % 10.40/10.59 apply (zenon_L501_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H90 | zenon_intro zenon_H273 ]. % 10.40/10.59 apply (zenon_L381_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H94 | zenon_intro zenon_H274 ]. % 10.40/10.59 apply (zenon_L382_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha7 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2fb ]. % 10.40/10.59 apply (zenon_L1076_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H143 | zenon_intro zenon_H2fc ]. % 10.40/10.59 apply (zenon_L93_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H1ed | zenon_intro zenon_H11b ]. % 10.40/10.59 apply (zenon_L1016_); trivial. % 10.40/10.59 apply (zenon_L560_); trivial. % 10.40/10.59 apply (zenon_L98_); trivial. % 10.40/10.59 apply (zenon_L390_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H8d | zenon_intro zenon_H2b0 ]. % 10.40/10.59 apply (zenon_L231_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H94 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H65 | zenon_intro zenon_H2cb ]. % 10.40/10.59 apply (zenon_L911_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H26 | zenon_intro zenon_H2cc ]. % 10.40/10.59 apply (zenon_L163_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H149 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H73 | zenon_intro zenon_H270 ]. % 10.40/10.59 apply (zenon_L1011_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H2d | zenon_intro zenon_H271 ]. % 10.40/10.59 apply (zenon_L59_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H109 ]. % 10.40/10.59 apply (zenon_L174_); trivial. % 10.40/10.59 apply (zenon_L1078_); trivial. % 10.40/10.59 apply (zenon_L358_); trivial. % 10.40/10.59 apply (zenon_L1019_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L259_); trivial. % 10.40/10.59 apply (zenon_L1020_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.59 apply (zenon_L916_); trivial. % 10.40/10.59 apply (zenon_L343_); trivial. % 10.40/10.59 apply (zenon_L344_); trivial. % 10.40/10.59 apply (zenon_L1077_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H1f | zenon_intro zenon_H329 ]. % 10.40/10.59 apply (zenon_L154_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H68 | zenon_intro zenon_H32a ]. % 10.40/10.59 apply (zenon_L1069_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H1d5 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H24 | zenon_intro zenon_H161 ]. % 10.40/10.59 apply (zenon_L4_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H65 | zenon_intro zenon_H162 ]. % 10.40/10.59 apply (zenon_L950_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf4 ]. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H24 | zenon_intro zenon_H1d2 ]. % 10.40/10.59 apply (zenon_L152_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H69 | zenon_intro zenon_H1d3 ]. % 10.40/10.59 apply (zenon_L1075_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ]. % 10.40/10.59 apply (zenon_L916_); trivial. % 10.40/10.59 apply (zenon_L343_); trivial. % 10.40/10.59 apply (zenon_L344_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H2b | zenon_intro zenon_He9 ]. % 10.40/10.59 apply (zenon_L7_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H70 | zenon_intro zenon_Hea ]. % 10.40/10.59 apply (zenon_L772_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hde | zenon_intro zenon_He2 ]. % 10.40/10.59 apply (zenon_L259_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H2b | zenon_intro zenon_H131 ]. % 10.40/10.59 apply (zenon_L370_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H73 | zenon_intro zenon_H132 ]. % 10.40/10.59 apply (zenon_L1079_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H87 | zenon_intro zenon_H72 ]. % 10.40/10.59 apply (zenon_L161_); trivial. % 10.40/10.59 apply (zenon_L771_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H18a | zenon_intro zenon_H248 ]. % 10.40/10.59 apply (zenon_L120_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H18d | zenon_intro zenon_H249 ]. % 10.40/10.59 apply (zenon_L583_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H195 | zenon_intro zenon_H24a ]. % 10.40/10.59 apply (zenon_L626_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H197 | zenon_intro zenon_H24b ]. % 10.40/10.59 apply (zenon_L274_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H199 | zenon_intro zenon_H24c ]. % 10.40/10.59 apply (zenon_L129_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H19b | zenon_intro zenon_H24d ]. % 10.40/10.59 apply (zenon_L211_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H19d | zenon_intro zenon_H24e ]. % 10.40/10.59 apply (zenon_L703_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H24f ]. % 10.40/10.59 apply (zenon_L133_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H250 ]. % 10.40/10.59 apply (zenon_L585_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H251 ]. % 10.40/10.59 apply (zenon_L276_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H252 ]. % 10.40/10.59 apply (zenon_L941_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H253 ]. % 10.40/10.59 apply (zenon_L942_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1ab | zenon_intro zenon_H254 ]. % 10.40/10.59 apply (zenon_L138_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1ad | zenon_intro zenon_H255 ]. % 10.40/10.59 apply (zenon_L578_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1af | zenon_intro zenon_H256 ]. % 10.40/10.59 apply (zenon_L964_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H257 ]. % 10.40/10.59 apply (zenon_L945_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H258 ]. % 10.40/10.59 apply (zenon_L631_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H259 ]. % 10.40/10.59 apply (zenon_L586_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H25a ]. % 10.40/10.59 apply (zenon_L284_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H1bc | zenon_intro zenon_H25b ]. % 10.40/10.59 apply (zenon_L146_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H1be | zenon_intro zenon_H25c ]. % 10.40/10.59 apply (zenon_L147_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H25d ]. % 10.40/10.59 apply (zenon_L213_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H25e ]. % 10.40/10.59 apply (zenon_L704_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H21c | zenon_intro zenon_H25f ]. % 10.40/10.59 apply (zenon_L1080_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H260 ]. % 10.40/10.59 apply (zenon_L167_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H261 ]. % 10.40/10.59 apply (zenon_L286_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H262 ]. % 10.40/10.59 apply (zenon_L946_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H263 ]. % 10.40/10.59 apply (zenon_L858_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H264 ]. % 10.40/10.59 apply (zenon_L966_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1fb | zenon_intro zenon_H265 ]. % 10.40/10.59 apply (zenon_L579_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H1fd | zenon_intro zenon_H266 ]. % 10.40/10.59 apply (zenon_L633_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H1ff | zenon_intro zenon_H267 ]. % 10.40/10.59 apply (zenon_L947_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H223 | zenon_intro zenon_H268 ]. % 10.40/10.59 apply (zenon_L1081_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H201 | zenon_intro zenon_H269 ]. % 10.40/10.59 apply (zenon_L183_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H203 | zenon_intro zenon_H26a ]. % 10.40/10.59 apply (zenon_L990_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H205 | zenon_intro zenon_H26b ]. % 10.40/10.59 apply (zenon_L706_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 10.40/10.59 apply (zenon_L186_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H209 | zenon_intro zenon_H26d ]. % 10.40/10.59 apply (zenon_L187_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H20b | zenon_intro zenon_H26e ]. % 10.40/10.59 apply (zenon_L296_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H20d | zenon_intro zenon_H26f ]. % 10.40/10.59 apply (zenon_L298_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H20f | zenon_intro zenon_H211 ]. % 10.40/10.59 apply (zenon_L300_); trivial. % 10.40/10.59 apply (zenon_L301_); trivial. % 10.40/10.59 apply (zenon_L26_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H306); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H11b ]. % 10.40/10.59 apply (zenon_L1068_); trivial. % 10.40/10.59 apply (zenon_L859_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H3e2); [ zenon_intro zenon_H8d | zenon_intro zenon_H3e3 ]. % 10.40/10.59 apply (zenon_L770_); trivial. % 10.40/10.59 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha7 ]. % 10.40/10.59 apply (zenon_L691_); trivial. % 10.40/10.59 apply (zenon_L500_); trivial. % 10.40/10.59 Qed. % 10.40/10.59 % SZS output end Proof % 10.40/10.59 (* END-PROOF *) % 10.40/10.59 nodes searched: 241375 % 10.40/10.59 max branch formulas: 334 % 10.40/10.59 proof nodes created: 9752 % 10.40/10.59 formulas created: 107777 % 10.40/10.59 %------------------------------------------------------------------------------