%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG068+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n021.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Thu Jul 14 18:29:08 EDT 2022 % Result : Theorem 40.87s 41.08s % Output : Proof 41.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : ALG068+1 : TPTP v8.1.0. Released v2.7.0. % 0.10/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n021.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Wed Jun 8 21:09:52 EDT 2022 % 0.12/0.33 % CPUTime : % 40.87/41.08 (* PROOF-FOUND *) % 40.87/41.08 % SZS status Theorem % 40.87/41.08 (* BEGIN-PROOF *) % 40.87/41.08 % SZS output start Proof % 40.87/41.08 Theorem co1 : (~(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0)))/\(((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0)))/\(((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0)))/\(((~((op (e0) (e0)) = (e4)))\/((op (e0) (e4)) = (e0)))/\(((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1)))/\(((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1)))/\(((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1)))/\(((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1)))/\(((~((op (e1) (e1)) = (e4)))\/((op (e1) (e4)) = (e1)))/\(((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2)))/\(((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\(((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2)))/\(((~((op (e2) (e2)) = (e4)))\/((op (e2) (e4)) = (e2)))/\(((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3)))/\(((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3)))/\(((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3)))/\(((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3)))/\(((~((op (e3) (e3)) = (e4)))\/((op (e3) (e4)) = (e3)))/\(((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4)))/\(((~((op (e4) (e4)) = (e1)))\/((op (e4) (e1)) = (e4)))/\(((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4)))/\(((~((op (e4) (e4)) = (e3)))\/((op (e4) (e3)) = (e4)))/\(((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4)))/\(((~((op (e0) (e0)) = (op (e0) (e0))))/\(((op (op (e0) (e0)) (e0)) = (e0))/\(~((op (op (e0) (e0)) (e0)) = (e0)))))\/(((~((op (e1) (e0)) = (op (e0) (e1))))/\(((op (op (e0) (e1)) (e1)) = (e0))/\(~((op (op (e0) (e1)) (e0)) = (e1)))))\/(((~((op (e2) (e0)) = (op (e0) (e2))))/\(((op (op (e0) (e2)) (e2)) = (e0))/\(~((op (op (e0) (e2)) (e0)) = (e2)))))\/(((~((op (e3) (e0)) = (op (e0) (e3))))/\(((op (op (e0) (e3)) (e3)) = (e0))/\(~((op (op (e0) (e3)) (e0)) = (e3)))))\/(((~((op (e4) (e0)) = (op (e0) (e4))))/\(((op (op (e0) (e4)) (e4)) = (e0))/\(~((op (op (e0) (e4)) (e0)) = (e4)))))\/(((~((op (e0) (e1)) = (op (e1) (e0))))/\(((op (op (e1) (e0)) (e0)) = (e1))/\(~((op (op (e1) (e0)) (e1)) = (e0)))))\/(((~((op (e1) (e1)) = (op (e1) (e1))))/\(((op (op (e1) (e1)) (e1)) = (e1))/\(~((op (op (e1) (e1)) (e1)) = (e1)))))\/(((~((op (e2) (e1)) = (op (e1) (e2))))/\(((op (op (e1) (e2)) (e2)) = (e1))/\(~((op (op (e1) (e2)) (e1)) = (e2)))))\/(((~((op (e3) (e1)) = (op (e1) (e3))))/\(((op (op (e1) (e3)) (e3)) = (e1))/\(~((op (op (e1) (e3)) (e1)) = (e3)))))\/(((~((op (e4) (e1)) = (op (e1) (e4))))/\(((op (op (e1) (e4)) (e4)) = (e1))/\(~((op (op (e1) (e4)) (e1)) = (e4)))))\/(((~((op (e0) (e2)) = (op (e2) (e0))))/\(((op (op (e2) (e0)) (e0)) = (e2))/\(~((op (op (e2) (e0)) (e2)) = (e0)))))\/(((~((op (e1) (e2)) = (op (e2) (e1))))/\(((op (op (e2) (e1)) (e1)) = (e2))/\(~((op (op (e2) (e1)) (e2)) = (e1)))))\/(((~((op (e2) (e2)) = (op (e2) (e2))))/\(((op (op (e2) (e2)) (e2)) = (e2))/\(~((op (op (e2) (e2)) (e2)) = (e2)))))\/(((~((op (e3) (e2)) = (op (e2) (e3))))/\(((op (op (e2) (e3)) (e3)) = (e2))/\(~((op (op (e2) (e3)) (e2)) = (e3)))))\/(((~((op (e4) (e2)) = (op (e2) (e4))))/\(((op (op (e2) (e4)) (e4)) = (e2))/\(~((op (op (e2) (e4)) (e2)) = (e4)))))\/(((~((op (e0) (e3)) = (op (e3) (e0))))/\(((op (op (e3) (e0)) (e0)) = (e3))/\(~((op (op (e3) (e0)) (e3)) = (e0)))))\/(((~((op (e1) (e3)) = (op (e3) (e1))))/\(((op (op (e3) (e1)) (e1)) = (e3))/\(~((op (op (e3) (e1)) (e3)) = (e1)))))\/(((~((op (e2) (e3)) = (op (e3) (e2))))/\(((op (op (e3) (e2)) (e2)) = (e3))/\(~((op (op (e3) (e2)) (e3)) = (e2)))))\/(((~((op (e3) (e3)) = (op (e3) (e3))))/\(((op (op (e3) (e3)) (e3)) = (e3))/\(~((op (op (e3) (e3)) (e3)) = (e3)))))\/(((~((op (e4) (e3)) = (op (e3) (e4))))/\(((op (op (e3) (e4)) (e4)) = (e3))/\(~((op (op (e3) (e4)) (e3)) = (e4)))))\/(((~((op (e0) (e4)) = (op (e4) (e0))))/\(((op (op (e4) (e0)) (e0)) = (e4))/\(~((op (op (e4) (e0)) (e4)) = (e0)))))\/(((~((op (e1) (e4)) = (op (e4) (e1))))/\(((op (op (e4) (e1)) (e1)) = (e4))/\(~((op (op (e4) (e1)) (e4)) = (e1)))))\/(((~((op (e2) (e4)) = (op (e4) (e2))))/\(((op (op (e4) (e2)) (e2)) = (e4))/\(~((op (op (e4) (e2)) (e4)) = (e2)))))\/(((~((op (e3) (e4)) = (op (e4) (e3))))/\(((op (op (e4) (e3)) (e3)) = (e4))/\(~((op (op (e4) (e3)) (e4)) = (e3)))))\/((~((op (e4) (e4)) = (op (e4) (e4))))/\(((op (op (e4) (e4)) (e4)) = (e4))/\(~((op (op (e4) (e4)) (e4)) = (e4))))))))))))))))))))))))))))))))))))))))))))))))))))))). % 40.87/41.08 Proof. % 40.87/41.08 assert (zenon_L1_ : (~((e2) = (e2))) -> False). % 40.87/41.08 do 0 intro. intros zenon_H7. % 40.87/41.08 apply zenon_H7. apply refl_equal. % 40.87/41.08 (* end of lemma zenon_L1_ *) % 40.87/41.08 assert (zenon_L2_ : (~((op (e0) (e2)) = (op (unit) (e2)))) -> ((unit) = (e0)) -> False). % 40.87/41.08 do 0 intro. intros zenon_H8 zenon_H9. % 40.87/41.08 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 40.87/41.08 cut (((e0) = (unit))); [idtac | apply NNPP; zenon_intro zenon_Ha]. % 40.87/41.08 congruence. % 40.87/41.08 apply zenon_Ha. apply sym_equal. exact zenon_H9. % 40.87/41.08 apply zenon_H7. apply refl_equal. % 40.87/41.08 (* end of lemma zenon_L2_ *) % 40.87/41.08 assert (zenon_L3_ : (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((unit) = (e0)) -> ((op (e0) (e3)) = (e2)) -> False). % 40.87/41.08 do 0 intro. intros zenon_Hb zenon_Hc zenon_H9 zenon_Hd. % 40.87/41.08 cut (((op (unit) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e0) (e3)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_Hb. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_Hc. % 40.87/41.08 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He]. % 40.87/41.08 cut (((op (unit) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 40.87/41.08 congruence. % 40.87/41.08 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H10 | zenon_intro zenon_H11 ]. % 40.87/41.08 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (unit) (e2)) = (op (e0) (e2)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_Hf. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H10. % 40.87/41.08 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 40.87/41.08 cut (((op (e0) (e2)) = (op (unit) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H8]. % 40.87/41.08 congruence. % 40.87/41.08 apply (zenon_L2_); trivial. % 40.87/41.08 apply zenon_H11. apply refl_equal. % 40.87/41.08 apply zenon_H11. apply refl_equal. % 40.87/41.08 apply zenon_He. apply sym_equal. exact zenon_Hd. % 40.87/41.08 (* end of lemma zenon_L3_ *) % 40.87/41.08 assert (zenon_L4_ : (~((e1) = (e1))) -> False). % 40.87/41.08 do 0 intro. intros zenon_H12. % 40.87/41.08 apply zenon_H12. apply refl_equal. % 40.87/41.08 (* end of lemma zenon_L4_ *) % 40.87/41.08 assert (zenon_L5_ : (~((op (e1) (e1)) = (op (unit) (e1)))) -> ((unit) = (e1)) -> False). % 40.87/41.08 do 0 intro. intros zenon_H13 zenon_H14. % 40.87/41.08 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 40.87/41.08 cut (((e1) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 40.87/41.08 congruence. % 40.87/41.08 apply zenon_H15. apply sym_equal. exact zenon_H14. % 40.87/41.08 apply zenon_H12. apply refl_equal. % 40.87/41.08 (* end of lemma zenon_L5_ *) % 40.87/41.08 assert (zenon_L6_ : ((op (unit) (e1)) = (e1)) -> ((unit) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 40.87/41.08 do 0 intro. intros zenon_H16 zenon_H14 zenon_H17 zenon_H18. % 40.87/41.08 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H19 | zenon_intro zenon_H1a ]. % 40.87/41.08 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (e0)) = (op (e1) (e1)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H18. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H19. % 40.87/41.08 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 40.87/41.08 cut (((op (e1) (e1)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 40.87/41.08 congruence. % 40.87/41.08 cut (((op (unit) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e0)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H1b. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H16. % 40.87/41.08 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 40.87/41.08 cut (((op (unit) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 40.87/41.08 congruence. % 40.87/41.08 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H19 | zenon_intro zenon_H1a ]. % 40.87/41.08 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (unit) (e1)) = (op (e1) (e1)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H1d. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H19. % 40.87/41.08 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 40.87/41.08 cut (((op (e1) (e1)) = (op (unit) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13]. % 40.87/41.08 congruence. % 40.87/41.08 apply (zenon_L5_); trivial. % 40.87/41.08 apply zenon_H1a. apply refl_equal. % 40.87/41.08 apply zenon_H1a. apply refl_equal. % 40.87/41.08 apply zenon_H1c. apply sym_equal. exact zenon_H17. % 40.87/41.08 apply zenon_H1a. apply refl_equal. % 40.87/41.08 apply zenon_H1a. apply refl_equal. % 40.87/41.08 (* end of lemma zenon_L6_ *) % 40.87/41.08 assert (zenon_L7_ : (~((e3) = (e3))) -> False). % 40.87/41.08 do 0 intro. intros zenon_H1e. % 40.87/41.08 apply zenon_H1e. apply refl_equal. % 40.87/41.08 (* end of lemma zenon_L7_ *) % 40.87/41.08 assert (zenon_L8_ : (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((unit) = (e2)) -> ((e3) = (op (e2) (e4))) -> False). % 40.87/41.08 do 0 intro. intros zenon_H1f zenon_H20 zenon_H21 zenon_H22. % 40.87/41.08 cut (((op (unit) (e3)) = (e3)) = ((op (e2) (e3)) = (op (e2) (e4)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H1f. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H20. % 40.87/41.08 cut (((e3) = (op (e2) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 40.87/41.08 cut (((op (unit) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 40.87/41.08 congruence. % 40.87/41.08 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 40.87/41.08 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (unit) (e3)) = (op (e2) (e3)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H24. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H25. % 40.87/41.08 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 40.87/41.08 cut (((op (e2) (e3)) = (op (unit) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 40.87/41.08 congruence. % 40.87/41.08 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 40.87/41.08 cut (((e2) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 40.87/41.08 congruence. % 40.87/41.08 apply zenon_H28. apply sym_equal. exact zenon_H21. % 40.87/41.08 apply zenon_H1e. apply refl_equal. % 40.87/41.08 apply zenon_H26. apply refl_equal. % 40.87/41.08 apply zenon_H26. apply refl_equal. % 40.87/41.08 exact (zenon_H23 zenon_H22). % 40.87/41.08 (* end of lemma zenon_L8_ *) % 40.87/41.08 assert (zenon_L9_ : (~((op (e1) (e3)) = (op (e1) (unit)))) -> ((unit) = (e3)) -> False). % 40.87/41.08 do 0 intro. intros zenon_H29 zenon_H2a. % 40.87/41.08 cut (((e3) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 40.87/41.08 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 40.87/41.08 congruence. % 40.87/41.08 apply zenon_H12. apply refl_equal. % 40.87/41.08 apply zenon_H2b. apply sym_equal. exact zenon_H2a. % 40.87/41.08 (* end of lemma zenon_L9_ *) % 40.87/41.08 assert (zenon_L10_ : ((op (e1) (unit)) = (e1)) -> ((unit) = (e3)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 40.87/41.08 do 0 intro. intros zenon_H2c zenon_H2a zenon_H17 zenon_H2d. % 40.87/41.08 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 40.87/41.08 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e0)) = (op (e1) (e3)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H2d. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H2e. % 40.87/41.08 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 40.87/41.08 cut (((op (e1) (e3)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 40.87/41.08 congruence. % 40.87/41.08 cut (((op (e1) (unit)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e0)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H30. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H2c. % 40.87/41.08 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 40.87/41.08 cut (((op (e1) (unit)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 40.87/41.08 congruence. % 40.87/41.08 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 40.87/41.08 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (unit)) = (op (e1) (e3)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H31. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H2e. % 40.87/41.08 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 40.87/41.08 cut (((op (e1) (e3)) = (op (e1) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 40.87/41.08 congruence. % 40.87/41.08 apply (zenon_L9_); trivial. % 40.87/41.08 apply zenon_H2f. apply refl_equal. % 40.87/41.08 apply zenon_H2f. apply refl_equal. % 40.87/41.08 apply zenon_H1c. apply sym_equal. exact zenon_H17. % 40.87/41.08 apply zenon_H2f. apply refl_equal. % 40.87/41.08 apply zenon_H2f. apply refl_equal. % 40.87/41.08 (* end of lemma zenon_L10_ *) % 40.87/41.08 assert (zenon_L11_ : (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((unit) = (e4)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.08 do 0 intro. intros zenon_H32 zenon_H16 zenon_H33 zenon_H34. % 40.87/41.08 cut (((op (unit) (e1)) = (e1)) = ((op (e4) (e1)) = (op (e4) (e2)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H32. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H16. % 40.87/41.08 cut (((e1) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 40.87/41.08 cut (((op (unit) (e1)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H36]. % 40.87/41.08 congruence. % 40.87/41.08 elim (classic ((op (e4) (e1)) = (op (e4) (e1)))); [ zenon_intro zenon_H37 | zenon_intro zenon_H38 ]. % 40.87/41.08 cut (((op (e4) (e1)) = (op (e4) (e1))) = ((op (unit) (e1)) = (op (e4) (e1)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H36. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H37. % 40.87/41.08 cut (((op (e4) (e1)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 40.87/41.08 cut (((op (e4) (e1)) = (op (unit) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 40.87/41.08 congruence. % 40.87/41.08 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 40.87/41.08 cut (((e4) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 40.87/41.08 congruence. % 40.87/41.08 apply zenon_H3a. apply sym_equal. exact zenon_H33. % 40.87/41.08 apply zenon_H12. apply refl_equal. % 40.87/41.08 apply zenon_H38. apply refl_equal. % 40.87/41.08 apply zenon_H38. apply refl_equal. % 40.87/41.08 exact (zenon_H35 zenon_H34). % 40.87/41.08 (* end of lemma zenon_L11_ *) % 40.87/41.08 assert (zenon_L12_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.08 do 0 intro. intros zenon_H3b zenon_Hd zenon_Hc zenon_Hb zenon_H18 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H32 zenon_H16 zenon_H34. % 40.87/41.08 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.08 apply (zenon_L3_); trivial. % 40.87/41.08 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.08 apply (zenon_L6_); trivial. % 40.87/41.08 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.08 apply (zenon_L8_); trivial. % 40.87/41.08 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.08 apply (zenon_L10_); trivial. % 40.87/41.08 apply (zenon_L11_); trivial. % 40.87/41.08 (* end of lemma zenon_L12_ *) % 40.87/41.08 assert (zenon_L13_ : (~((e0) = (e0))) -> False). % 40.87/41.08 do 0 intro. intros zenon_H3f. % 40.87/41.08 apply zenon_H3f. apply refl_equal. % 40.87/41.08 (* end of lemma zenon_L13_ *) % 40.87/41.08 assert (zenon_L14_ : (~((op (e0) (e0)) = (op (unit) (e0)))) -> ((unit) = (e0)) -> False). % 40.87/41.08 do 0 intro. intros zenon_H40 zenon_H9. % 40.87/41.08 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 40.87/41.08 cut (((e0) = (unit))); [idtac | apply NNPP; zenon_intro zenon_Ha]. % 40.87/41.08 congruence. % 40.87/41.08 apply zenon_Ha. apply sym_equal. exact zenon_H9. % 40.87/41.08 apply zenon_H3f. apply refl_equal. % 40.87/41.08 (* end of lemma zenon_L14_ *) % 40.87/41.08 assert (zenon_L15_ : (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((unit) = (e0)) -> ((op (e0) (e1)) = (e0)) -> False). % 40.87/41.08 do 0 intro. intros zenon_H41 zenon_H42 zenon_H9 zenon_H43. % 40.87/41.08 cut (((op (unit) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e0) (e1)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H41. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H42. % 40.87/41.08 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 40.87/41.08 cut (((op (unit) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 40.87/41.08 congruence. % 40.87/41.08 elim (classic ((op (e0) (e0)) = (op (e0) (e0)))); [ zenon_intro zenon_H46 | zenon_intro zenon_H47 ]. % 40.87/41.08 cut (((op (e0) (e0)) = (op (e0) (e0))) = ((op (unit) (e0)) = (op (e0) (e0)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H45. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H46. % 40.87/41.08 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 40.87/41.08 cut (((op (e0) (e0)) = (op (unit) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 40.87/41.08 congruence. % 40.87/41.08 apply (zenon_L14_); trivial. % 40.87/41.08 apply zenon_H47. apply refl_equal. % 40.87/41.08 apply zenon_H47. apply refl_equal. % 40.87/41.08 apply zenon_H44. apply sym_equal. exact zenon_H43. % 40.87/41.08 (* end of lemma zenon_L15_ *) % 40.87/41.08 assert (zenon_L16_ : (~((op (e1) (e2)) = (op (unit) (e2)))) -> ((unit) = (e1)) -> False). % 40.87/41.08 do 0 intro. intros zenon_H48 zenon_H14. % 40.87/41.08 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 40.87/41.08 cut (((e1) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 40.87/41.08 congruence. % 40.87/41.08 apply zenon_H15. apply sym_equal. exact zenon_H14. % 40.87/41.08 apply zenon_H7. apply refl_equal. % 40.87/41.08 (* end of lemma zenon_L16_ *) % 40.87/41.08 assert (zenon_L17_ : (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((unit) = (e1)) -> ((op (e1) (e3)) = (e2)) -> False). % 40.87/41.08 do 0 intro. intros zenon_H49 zenon_Hc zenon_H14 zenon_H4a. % 40.87/41.08 cut (((op (unit) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e1) (e3)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H49. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_Hc. % 40.87/41.08 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 40.87/41.08 cut (((op (unit) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 40.87/41.08 congruence. % 40.87/41.08 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 40.87/41.08 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (unit) (e2)) = (op (e1) (e2)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H4c. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H4d. % 40.87/41.08 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 40.87/41.08 cut (((op (e1) (e2)) = (op (unit) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 40.87/41.08 congruence. % 40.87/41.08 apply (zenon_L16_); trivial. % 40.87/41.08 apply zenon_H4e. apply refl_equal. % 40.87/41.08 apply zenon_H4e. apply refl_equal. % 40.87/41.08 apply zenon_H4b. apply sym_equal. exact zenon_H4a. % 40.87/41.08 (* end of lemma zenon_L17_ *) % 40.87/41.08 assert (zenon_L18_ : (~((op (e0) (e3)) = (op (e0) (unit)))) -> ((unit) = (e3)) -> False). % 40.87/41.08 do 0 intro. intros zenon_H4f zenon_H2a. % 40.87/41.08 cut (((e3) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 40.87/41.08 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 40.87/41.08 congruence. % 40.87/41.08 apply zenon_H3f. apply refl_equal. % 40.87/41.08 apply zenon_H2b. apply sym_equal. exact zenon_H2a. % 40.87/41.08 (* end of lemma zenon_L18_ *) % 40.87/41.08 assert (zenon_L19_ : ((op (e0) (unit)) = (e0)) -> ((unit) = (e3)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 40.87/41.08 do 0 intro. intros zenon_H50 zenon_H2a zenon_H43 zenon_H51. % 40.87/41.08 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 40.87/41.08 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e1)) = (op (e0) (e3)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H51. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H52. % 40.87/41.08 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 40.87/41.08 cut (((op (e0) (e3)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 40.87/41.08 congruence. % 40.87/41.08 cut (((op (e0) (unit)) = (e0)) = ((op (e0) (e3)) = (op (e0) (e1)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H54. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H50. % 40.87/41.08 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 40.87/41.08 cut (((op (e0) (unit)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 40.87/41.08 congruence. % 40.87/41.08 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 40.87/41.08 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (unit)) = (op (e0) (e3)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H55. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H52. % 40.87/41.08 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 40.87/41.08 cut (((op (e0) (e3)) = (op (e0) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 40.87/41.08 congruence. % 40.87/41.08 apply (zenon_L18_); trivial. % 40.87/41.08 apply zenon_H53. apply refl_equal. % 40.87/41.08 apply zenon_H53. apply refl_equal. % 40.87/41.08 apply zenon_H44. apply sym_equal. exact zenon_H43. % 40.87/41.08 apply zenon_H53. apply refl_equal. % 40.87/41.08 apply zenon_H53. apply refl_equal. % 40.87/41.08 (* end of lemma zenon_L19_ *) % 40.87/41.08 assert (zenon_L20_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.08 do 0 intro. intros zenon_H3b zenon_H42 zenon_H41 zenon_H4a zenon_Hc zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_H51 zenon_H43 zenon_H50 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.08 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.08 apply (zenon_L15_); trivial. % 40.87/41.08 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.08 apply (zenon_L17_); trivial. % 40.87/41.08 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.08 apply (zenon_L8_); trivial. % 40.87/41.08 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.08 apply (zenon_L19_); trivial. % 40.87/41.08 apply (zenon_L11_); trivial. % 40.87/41.08 (* end of lemma zenon_L20_ *) % 40.87/41.08 assert (zenon_L21_ : (~((op (e2) (e0)) = (op (e2) (unit)))) -> ((unit) = (e0)) -> False). % 40.87/41.08 do 0 intro. intros zenon_H56 zenon_H9. % 40.87/41.08 cut (((e0) = (unit))); [idtac | apply NNPP; zenon_intro zenon_Ha]. % 40.87/41.08 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 40.87/41.08 congruence. % 40.87/41.08 apply zenon_H7. apply refl_equal. % 40.87/41.08 apply zenon_Ha. apply sym_equal. exact zenon_H9. % 40.87/41.08 (* end of lemma zenon_L21_ *) % 40.87/41.08 assert (zenon_L22_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> ((unit) = (e0)) -> ((op (e2) (e3)) = (e2)) -> False). % 40.87/41.08 do 0 intro. intros zenon_H57 zenon_H58 zenon_H9 zenon_H59. % 40.87/41.08 cut (((op (e2) (unit)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e3)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H57. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H58. % 40.87/41.08 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 40.87/41.08 cut (((op (e2) (unit)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 40.87/41.08 congruence. % 40.87/41.08 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 40.87/41.08 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e2) (unit)) = (op (e2) (e0)))). % 40.87/41.08 intro zenon_D_pnotp. % 40.87/41.08 apply zenon_H5b. % 40.87/41.08 rewrite <- zenon_D_pnotp. % 40.87/41.08 exact zenon_H5c. % 40.87/41.08 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 40.87/41.08 cut (((op (e2) (e0)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 40.87/41.08 congruence. % 40.87/41.08 apply (zenon_L21_); trivial. % 40.87/41.08 apply zenon_H5d. apply refl_equal. % 40.87/41.08 apply zenon_H5d. apply refl_equal. % 40.87/41.08 apply zenon_H5a. apply sym_equal. exact zenon_H59. % 40.87/41.08 (* end of lemma zenon_L22_ *) % 40.87/41.08 assert (zenon_L23_ : (~((op (e3) (e1)) = (op (e3) (unit)))) -> ((unit) = (e1)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H5e zenon_H14. % 40.87/41.09 cut (((e1) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 40.87/41.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 40.87/41.09 congruence. % 40.87/41.09 apply zenon_H1e. apply refl_equal. % 40.87/41.09 apply zenon_H15. apply sym_equal. exact zenon_H14. % 40.87/41.09 (* end of lemma zenon_L23_ *) % 40.87/41.09 assert (zenon_L24_ : ((op (e3) (unit)) = (e3)) -> ((unit) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H5f zenon_H14 zenon_H60 zenon_H61. % 40.87/41.09 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 40.87/41.09 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (e0)) = (op (e3) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H61. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H62. % 40.87/41.09 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 40.87/41.09 cut (((op (e3) (e1)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 40.87/41.09 congruence. % 40.87/41.09 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H64. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H5f. % 40.87/41.09 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 40.87/41.09 cut (((op (e3) (unit)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 40.87/41.09 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (unit)) = (op (e3) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H66. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H62. % 40.87/41.09 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 40.87/41.09 cut (((op (e3) (e1)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L23_); trivial. % 40.87/41.09 apply zenon_H63. apply refl_equal. % 40.87/41.09 apply zenon_H63. apply refl_equal. % 40.87/41.09 apply zenon_H65. apply sym_equal. exact zenon_H60. % 40.87/41.09 apply zenon_H63. apply refl_equal. % 40.87/41.09 apply zenon_H63. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L24_ *) % 40.87/41.09 assert (zenon_L25_ : (~((op (e3) (e3)) = (op (unit) (e3)))) -> ((unit) = (e3)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H67 zenon_H2a. % 40.87/41.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 40.87/41.09 cut (((e3) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 40.87/41.09 congruence. % 40.87/41.09 apply zenon_H2b. apply sym_equal. exact zenon_H2a. % 40.87/41.09 apply zenon_H1e. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L25_ *) % 40.87/41.09 assert (zenon_L26_ : ((op (unit) (e3)) = (e3)) -> ((unit) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H20 zenon_H2a zenon_H60 zenon_H68. % 40.87/41.09 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H68. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H69. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 40.87/41.09 congruence. % 40.87/41.09 cut (((op (unit) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H6b. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H20. % 40.87/41.09 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 40.87/41.09 cut (((op (unit) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (unit) (e3)) = (op (e3) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H6c. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H69. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 40.87/41.09 cut (((op (e3) (e3)) = (op (unit) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L25_); trivial. % 40.87/41.09 apply zenon_H6a. apply refl_equal. % 40.87/41.09 apply zenon_H6a. apply refl_equal. % 40.87/41.09 apply zenon_H65. apply sym_equal. exact zenon_H60. % 40.87/41.09 apply zenon_H6a. apply refl_equal. % 40.87/41.09 apply zenon_H6a. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L26_ *) % 40.87/41.09 assert (zenon_L27_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_H59 zenon_H58 zenon_H57 zenon_H61 zenon_H5f zenon_H22 zenon_H1f zenon_H68 zenon_H60 zenon_H20 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L22_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L24_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L8_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L26_); trivial. % 40.87/41.09 apply (zenon_L11_); trivial. % 40.87/41.09 (* end of lemma zenon_L27_ *) % 40.87/41.09 assert (zenon_L28_ : (~((op (e2) (e1)) = (op (e2) (unit)))) -> ((unit) = (e1)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H6d zenon_H14. % 40.87/41.09 cut (((e1) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 40.87/41.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 40.87/41.09 congruence. % 40.87/41.09 apply zenon_H7. apply refl_equal. % 40.87/41.09 apply zenon_H15. apply sym_equal. exact zenon_H14. % 40.87/41.09 (* end of lemma zenon_L28_ *) % 40.87/41.09 assert (zenon_L29_ : (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> ((unit) = (e1)) -> ((op (e2) (e3)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H6e zenon_H58 zenon_H14 zenon_H59. % 40.87/41.09 cut (((op (e2) (unit)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H6e. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H58. % 40.87/41.09 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 40.87/41.09 cut (((op (e2) (unit)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H70 | zenon_intro zenon_H71 ]. % 40.87/41.09 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (unit)) = (op (e2) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H6f. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H70. % 40.87/41.09 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 40.87/41.09 cut (((op (e2) (e1)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L28_); trivial. % 40.87/41.09 apply zenon_H71. apply refl_equal. % 40.87/41.09 apply zenon_H71. apply refl_equal. % 40.87/41.09 apply zenon_H5a. apply sym_equal. exact zenon_H59. % 40.87/41.09 (* end of lemma zenon_L29_ *) % 40.87/41.09 assert (zenon_L30_ : ((op (unit) (e3)) = (e3)) -> ((unit) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H20 zenon_H2a zenon_H72 zenon_H73. % 40.87/41.09 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H73. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H69. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 40.87/41.09 congruence. % 40.87/41.09 cut (((op (unit) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H74. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H20. % 40.87/41.09 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 40.87/41.09 cut (((op (unit) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (unit) (e3)) = (op (e3) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H6c. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H69. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 40.87/41.09 cut (((op (e3) (e3)) = (op (unit) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L25_); trivial. % 40.87/41.09 apply zenon_H6a. apply refl_equal. % 40.87/41.09 apply zenon_H6a. apply refl_equal. % 40.87/41.09 apply zenon_H75. apply sym_equal. exact zenon_H72. % 40.87/41.09 apply zenon_H6a. apply refl_equal. % 40.87/41.09 apply zenon_H6a. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L30_ *) % 40.87/41.09 assert (zenon_L31_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_H57 zenon_H59 zenon_H58 zenon_H6e zenon_H22 zenon_H1f zenon_H73 zenon_H72 zenon_H20 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L22_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L29_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L8_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L30_); trivial. % 40.87/41.09 apply (zenon_L11_); trivial. % 40.87/41.09 (* end of lemma zenon_L31_ *) % 40.87/41.09 assert (zenon_L32_ : ((op (unit) (e3)) = (e3)) -> ((unit) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H20 zenon_H2a zenon_H76 zenon_H77. % 40.87/41.09 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H77. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H69. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 40.87/41.09 congruence. % 40.87/41.09 cut (((op (unit) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H78. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H20. % 40.87/41.09 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 40.87/41.09 cut (((op (unit) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (unit) (e3)) = (op (e3) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H6c. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H69. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 40.87/41.09 cut (((op (e3) (e3)) = (op (unit) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L25_); trivial. % 40.87/41.09 apply zenon_H6a. apply refl_equal. % 40.87/41.09 apply zenon_H6a. apply refl_equal. % 40.87/41.09 apply zenon_H79. apply sym_equal. exact zenon_H76. % 40.87/41.09 apply zenon_H6a. apply refl_equal. % 40.87/41.09 apply zenon_H6a. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L32_ *) % 40.87/41.09 assert (zenon_L33_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_H57 zenon_H59 zenon_H58 zenon_H6e zenon_H22 zenon_H1f zenon_H77 zenon_H76 zenon_H20 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L22_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L29_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L8_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L32_); trivial. % 40.87/41.09 apply (zenon_L11_); trivial. % 40.87/41.09 (* end of lemma zenon_L33_ *) % 40.87/41.09 assert (zenon_L34_ : (~((op (e3) (e0)) = (op (e3) (unit)))) -> ((unit) = (e0)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H7a zenon_H9. % 40.87/41.09 cut (((e0) = (unit))); [idtac | apply NNPP; zenon_intro zenon_Ha]. % 40.87/41.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 40.87/41.09 congruence. % 40.87/41.09 apply zenon_H1e. apply refl_equal. % 40.87/41.09 apply zenon_Ha. apply sym_equal. exact zenon_H9. % 40.87/41.09 (* end of lemma zenon_L34_ *) % 40.87/41.09 assert (zenon_L35_ : (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> ((unit) = (e0)) -> ((op (e3) (e4)) = (e3)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H7b zenon_H5f zenon_H9 zenon_H7c. % 40.87/41.09 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e4)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H7b. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H5f. % 40.87/41.09 cut (((e3) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 40.87/41.09 cut (((op (e3) (unit)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H7f | zenon_intro zenon_H80 ]. % 40.87/41.09 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e3) (unit)) = (op (e3) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H7e. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H7f. % 40.87/41.09 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 40.87/41.09 cut (((op (e3) (e0)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L34_); trivial. % 40.87/41.09 apply zenon_H80. apply refl_equal. % 40.87/41.09 apply zenon_H80. apply refl_equal. % 40.87/41.09 apply zenon_H7d. apply sym_equal. exact zenon_H7c. % 40.87/41.09 (* end of lemma zenon_L35_ *) % 40.87/41.09 assert (zenon_L36_ : (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> ((unit) = (e1)) -> ((op (e3) (e4)) = (e3)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H81 zenon_H5f zenon_H14 zenon_H7c. % 40.87/41.09 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e4)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H81. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H5f. % 40.87/41.09 cut (((e3) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 40.87/41.09 cut (((op (e3) (unit)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 40.87/41.09 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (unit)) = (op (e3) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H66. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H62. % 40.87/41.09 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 40.87/41.09 cut (((op (e3) (e1)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L23_); trivial. % 40.87/41.09 apply zenon_H63. apply refl_equal. % 40.87/41.09 apply zenon_H63. apply refl_equal. % 40.87/41.09 apply zenon_H7d. apply sym_equal. exact zenon_H7c. % 40.87/41.09 (* end of lemma zenon_L36_ *) % 40.87/41.09 assert (zenon_L37_ : (~((op (e3) (e2)) = (op (e3) (unit)))) -> ((unit) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H82 zenon_H21. % 40.87/41.09 cut (((e2) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 40.87/41.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 40.87/41.09 congruence. % 40.87/41.09 apply zenon_H1e. apply refl_equal. % 40.87/41.09 apply zenon_H28. apply sym_equal. exact zenon_H21. % 40.87/41.09 (* end of lemma zenon_L37_ *) % 40.87/41.09 assert (zenon_L38_ : (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> ((unit) = (e2)) -> ((op (e3) (e4)) = (e3)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H83 zenon_H5f zenon_H21 zenon_H7c. % 40.87/41.09 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e4)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H83. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H5f. % 40.87/41.09 cut (((e3) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 40.87/41.09 cut (((op (e3) (unit)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (unit)) = (op (e3) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H84. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H85. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L37_); trivial. % 40.87/41.09 apply zenon_H86. apply refl_equal. % 40.87/41.09 apply zenon_H86. apply refl_equal. % 40.87/41.09 apply zenon_H7d. apply sym_equal. exact zenon_H7c. % 40.87/41.09 (* end of lemma zenon_L38_ *) % 40.87/41.09 assert (zenon_L39_ : (~((op (e3) (e3)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((unit) = (e3)) -> ((op (e3) (e4)) = (e3)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H87 zenon_H20 zenon_H2a zenon_H7c. % 40.87/41.09 cut (((op (unit) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e4)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H87. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H20. % 40.87/41.09 cut (((e3) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 40.87/41.09 cut (((op (unit) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (unit) (e3)) = (op (e3) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H6c. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H69. % 40.87/41.09 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 40.87/41.09 cut (((op (e3) (e3)) = (op (unit) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L25_); trivial. % 40.87/41.09 apply zenon_H6a. apply refl_equal. % 40.87/41.09 apply zenon_H6a. apply refl_equal. % 40.87/41.09 apply zenon_H7d. apply sym_equal. exact zenon_H7c. % 40.87/41.09 (* end of lemma zenon_L39_ *) % 40.87/41.09 assert (zenon_L40_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_H7b zenon_H81 zenon_H5f zenon_H83 zenon_H7c zenon_H20 zenon_H87 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L35_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L36_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L38_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L39_); trivial. % 40.87/41.09 apply (zenon_L11_); trivial. % 40.87/41.09 (* end of lemma zenon_L40_ *) % 40.87/41.09 assert (zenon_L41_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H88 zenon_H68 zenon_H61 zenon_H73 zenon_H77 zenon_H1f zenon_H22 zenon_H6e zenon_H58 zenon_H59 zenon_H57 zenon_H89 zenon_H3b zenon_H7b zenon_H81 zenon_H5f zenon_H83 zenon_H20 zenon_H87 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H60 | zenon_intro zenon_H8a ]. % 40.87/41.09 apply (zenon_L27_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H72 | zenon_intro zenon_H8b ]. % 40.87/41.09 apply (zenon_L31_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H8b); [ zenon_intro zenon_H76 | zenon_intro zenon_H8c ]. % 40.87/41.09 apply (zenon_L33_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H8d | zenon_intro zenon_H7c ]. % 40.87/41.09 exact (zenon_H89 zenon_H8d). % 40.87/41.09 apply (zenon_L40_); trivial. % 40.87/41.09 (* end of lemma zenon_L41_ *) % 40.87/41.09 assert (zenon_L42_ : ((op (e3) (unit)) = (e3)) -> ((unit) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H5f zenon_H21 zenon_H60 zenon_H8e. % 40.87/41.09 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e0)) = (op (e3) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H8e. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H85. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 40.87/41.09 congruence. % 40.87/41.09 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H8f. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H5f. % 40.87/41.09 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 40.87/41.09 cut (((op (e3) (unit)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (unit)) = (op (e3) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H84. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H85. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L37_); trivial. % 40.87/41.09 apply zenon_H86. apply refl_equal. % 40.87/41.09 apply zenon_H86. apply refl_equal. % 40.87/41.09 apply zenon_H65. apply sym_equal. exact zenon_H60. % 40.87/41.09 apply zenon_H86. apply refl_equal. % 40.87/41.09 apply zenon_H86. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L42_ *) % 40.87/41.09 assert (zenon_L43_ : (~((op (e4) (e2)) = (op (unit) (e2)))) -> ((unit) = (e4)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H90 zenon_H33. % 40.87/41.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 40.87/41.09 cut (((e4) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 40.87/41.09 congruence. % 40.87/41.09 apply zenon_H3a. apply sym_equal. exact zenon_H33. % 40.87/41.09 apply zenon_H7. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L43_ *) % 40.87/41.09 assert (zenon_L44_ : (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((unit) = (e4)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H91 zenon_Hc zenon_H33 zenon_H92. % 40.87/41.09 cut (((op (unit) (e2)) = (e2)) = ((op (e4) (e2)) = (op (e4) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H91. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Hc. % 40.87/41.09 cut (((e2) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H93]. % 40.87/41.09 cut (((op (unit) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e2)) = (op (e4) (e2)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e2))) = ((op (unit) (e2)) = (op (e4) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H94. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H95. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 40.87/41.09 cut (((op (e4) (e2)) = (op (unit) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L43_); trivial. % 40.87/41.09 apply zenon_H96. apply refl_equal. % 40.87/41.09 apply zenon_H96. apply refl_equal. % 40.87/41.09 apply zenon_H93. apply sym_equal. exact zenon_H92. % 40.87/41.09 (* end of lemma zenon_L44_ *) % 40.87/41.09 assert (zenon_L45_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_H43 zenon_H42 zenon_H41 zenon_H18 zenon_H16 zenon_H8e zenon_H60 zenon_H5f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc zenon_H92. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L15_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L6_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L42_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L10_); trivial. % 40.87/41.09 apply (zenon_L44_); trivial. % 40.87/41.09 (* end of lemma zenon_L45_ *) % 40.87/41.09 assert (zenon_L46_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> ((unit) = (e0)) -> ((op (e3) (e1)) = (e3)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H61 zenon_H5f zenon_H9 zenon_H72. % 40.87/41.09 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H61. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H5f. % 40.87/41.09 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 40.87/41.09 cut (((op (e3) (unit)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H7f | zenon_intro zenon_H80 ]. % 40.87/41.09 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e3) (unit)) = (op (e3) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H7e. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H7f. % 40.87/41.09 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 40.87/41.09 cut (((op (e3) (e0)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L34_); trivial. % 40.87/41.09 apply zenon_H80. apply refl_equal. % 40.87/41.09 apply zenon_H80. apply refl_equal. % 40.87/41.09 apply zenon_H75. apply sym_equal. exact zenon_H72. % 40.87/41.09 (* end of lemma zenon_L46_ *) % 40.87/41.09 assert (zenon_L47_ : (~((e4) = (e4))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H97. % 40.87/41.09 apply zenon_H97. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L47_ *) % 40.87/41.09 assert (zenon_L48_ : (~((op (e4) (e1)) = (op (e4) (unit)))) -> ((unit) = (e1)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H98 zenon_H14. % 40.87/41.09 cut (((e1) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 40.87/41.09 cut (((e4) = (e4))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 40.87/41.09 congruence. % 40.87/41.09 apply zenon_H97. apply refl_equal. % 40.87/41.09 apply zenon_H15. apply sym_equal. exact zenon_H14. % 40.87/41.09 (* end of lemma zenon_L48_ *) % 40.87/41.09 assert (zenon_L49_ : ((op (e4) (unit)) = (e4)) -> ((unit) = (e1)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H99 zenon_H14 zenon_H9a zenon_H9b. % 40.87/41.09 elim (classic ((op (e4) (e1)) = (op (e4) (e1)))); [ zenon_intro zenon_H37 | zenon_intro zenon_H38 ]. % 40.87/41.09 cut (((op (e4) (e1)) = (op (e4) (e1))) = ((op (e4) (e0)) = (op (e4) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H9b. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H37. % 40.87/41.09 cut (((op (e4) (e1)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 40.87/41.09 cut (((op (e4) (e1)) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 40.87/41.09 congruence. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e1)) = (op (e4) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H9c. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e1)) = (op (e4) (e1)))); [ zenon_intro zenon_H37 | zenon_intro zenon_H38 ]. % 40.87/41.09 cut (((op (e4) (e1)) = (op (e4) (e1))) = ((op (e4) (unit)) = (op (e4) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H9e. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H37. % 40.87/41.09 cut (((op (e4) (e1)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 40.87/41.09 cut (((op (e4) (e1)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L48_); trivial. % 40.87/41.09 apply zenon_H38. apply refl_equal. % 40.87/41.09 apply zenon_H38. apply refl_equal. % 40.87/41.09 apply zenon_H9d. apply sym_equal. exact zenon_H9a. % 40.87/41.09 apply zenon_H38. apply refl_equal. % 40.87/41.09 apply zenon_H38. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L49_ *) % 40.87/41.09 assert (zenon_L50_ : ((op (e3) (unit)) = (e3)) -> ((unit) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H5f zenon_H21 zenon_H72 zenon_H9f. % 40.87/41.09 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e1)) = (op (e3) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H9f. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H85. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 40.87/41.09 congruence. % 40.87/41.09 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Ha0. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H5f. % 40.87/41.09 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 40.87/41.09 cut (((op (e3) (unit)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (unit)) = (op (e3) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H84. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H85. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L37_); trivial. % 40.87/41.09 apply zenon_H86. apply refl_equal. % 40.87/41.09 apply zenon_H86. apply refl_equal. % 40.87/41.09 apply zenon_H75. apply sym_equal. exact zenon_H72. % 40.87/41.09 apply zenon_H86. apply refl_equal. % 40.87/41.09 apply zenon_H86. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L50_ *) % 40.87/41.09 assert (zenon_L51_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_H61 zenon_H9b zenon_H9a zenon_H99 zenon_H9f zenon_H5f zenon_H73 zenon_H72 zenon_H20 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L46_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L49_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L50_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L30_); trivial. % 40.87/41.09 apply (zenon_L11_); trivial. % 40.87/41.09 (* end of lemma zenon_L51_ *) % 40.87/41.09 assert (zenon_L52_ : (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((unit) = (e0)) -> ((op (e0) (e4)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_Ha1 zenon_Hc zenon_H9 zenon_Ha2. % 40.87/41.09 cut (((op (unit) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e0) (e4)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Ha1. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Hc. % 40.87/41.09 cut (((e2) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 40.87/41.09 cut (((op (unit) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H10 | zenon_intro zenon_H11 ]. % 40.87/41.09 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (unit) (e2)) = (op (e0) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hf. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H10. % 40.87/41.09 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 40.87/41.09 cut (((op (e0) (e2)) = (op (unit) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H8]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L2_); trivial. % 40.87/41.09 apply zenon_H11. apply refl_equal. % 40.87/41.09 apply zenon_H11. apply refl_equal. % 40.87/41.09 apply zenon_Ha3. apply sym_equal. exact zenon_Ha2. % 40.87/41.09 (* end of lemma zenon_L52_ *) % 40.87/41.09 assert (zenon_L53_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e4)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_Ha2 zenon_Ha1 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc zenon_H92. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L52_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L6_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L8_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L10_); trivial. % 40.87/41.09 apply (zenon_L44_); trivial. % 40.87/41.09 (* end of lemma zenon_L53_ *) % 40.87/41.09 assert (zenon_L54_ : (~((op (e4) (e0)) = (op (e4) (unit)))) -> ((unit) = (e0)) -> False). % 40.87/41.09 do 0 intro. intros zenon_Ha4 zenon_H9. % 40.87/41.09 cut (((e0) = (unit))); [idtac | apply NNPP; zenon_intro zenon_Ha]. % 40.87/41.09 cut (((e4) = (e4))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 40.87/41.09 congruence. % 40.87/41.09 apply zenon_H97. apply refl_equal. % 40.87/41.09 apply zenon_Ha. apply sym_equal. exact zenon_H9. % 40.87/41.09 (* end of lemma zenon_L54_ *) % 40.87/41.09 assert (zenon_L55_ : (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> ((unit) = (e0)) -> ((op (e4) (e1)) = (e4)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H9b zenon_H99 zenon_H9 zenon_Ha5. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e0)) = (op (e4) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H9b. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e0)) = (op (e4) (e0)))); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha9 ]. % 40.87/41.09 cut (((op (e4) (e0)) = (op (e4) (e0))) = ((op (e4) (unit)) = (op (e4) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Ha7. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Ha8. % 40.87/41.09 cut (((op (e4) (e0)) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 40.87/41.09 cut (((op (e4) (e0)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L54_); trivial. % 40.87/41.09 apply zenon_Ha9. apply refl_equal. % 40.87/41.09 apply zenon_Ha9. apply refl_equal. % 40.87/41.09 apply zenon_Ha6. apply sym_equal. exact zenon_Ha5. % 40.87/41.09 (* end of lemma zenon_L55_ *) % 40.87/41.09 assert (zenon_L56_ : (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((unit) = (e1)) -> ((op (e1) (e4)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_Haa zenon_Hc zenon_H14 zenon_Hab. % 40.87/41.09 cut (((op (unit) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e1) (e4)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Haa. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Hc. % 40.87/41.09 cut (((e2) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 40.87/41.09 cut (((op (unit) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 40.87/41.09 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (unit) (e2)) = (op (e1) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H4c. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H4d. % 40.87/41.09 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 40.87/41.09 cut (((op (e1) (e2)) = (op (unit) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L16_); trivial. % 40.87/41.09 apply zenon_H4e. apply refl_equal. % 40.87/41.09 apply zenon_H4e. apply refl_equal. % 40.87/41.09 apply zenon_Hac. apply sym_equal. exact zenon_Hab. % 40.87/41.09 (* end of lemma zenon_L56_ *) % 40.87/41.09 assert (zenon_L57_ : (~((op (e4) (e2)) = (op (e4) (unit)))) -> ((unit) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_Had zenon_H21. % 40.87/41.09 cut (((e2) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 40.87/41.09 cut (((e4) = (e4))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 40.87/41.09 congruence. % 40.87/41.09 apply zenon_H97. apply refl_equal. % 40.87/41.09 apply zenon_H28. apply sym_equal. exact zenon_H21. % 40.87/41.09 (* end of lemma zenon_L57_ *) % 40.87/41.09 assert (zenon_L58_ : ((op (e4) (unit)) = (e4)) -> ((unit) = (e2)) -> ((op (e4) (e1)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H99 zenon_H21 zenon_Ha5 zenon_H32. % 40.87/41.09 elim (classic ((op (e4) (e2)) = (op (e4) (e2)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e2))) = ((op (e4) (e1)) = (op (e4) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H32. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H95. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 40.87/41.09 congruence. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e2)) = (op (e4) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hae. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e2)) = (op (e4) (e2)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e2))) = ((op (e4) (unit)) = (op (e4) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Haf. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H95. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L57_); trivial. % 40.87/41.09 apply zenon_H96. apply refl_equal. % 40.87/41.09 apply zenon_H96. apply refl_equal. % 40.87/41.09 apply zenon_Ha6. apply sym_equal. exact zenon_Ha5. % 40.87/41.09 apply zenon_H96. apply refl_equal. % 40.87/41.09 apply zenon_H96. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L58_ *) % 40.87/41.09 assert (zenon_L59_ : (~((op (e4) (e3)) = (op (e4) (unit)))) -> ((unit) = (e3)) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hb0 zenon_H2a. % 40.87/41.09 cut (((e3) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 40.87/41.09 cut (((e4) = (e4))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 40.87/41.09 congruence. % 40.87/41.09 apply zenon_H97. apply refl_equal. % 40.87/41.09 apply zenon_H2b. apply sym_equal. exact zenon_H2a. % 40.87/41.09 (* end of lemma zenon_L59_ *) % 40.87/41.09 assert (zenon_L60_ : ((op (e4) (unit)) = (e4)) -> ((unit) = (e3)) -> ((op (e4) (e1)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H99 zenon_H2a zenon_Ha5 zenon_Hb1. % 40.87/41.09 elim (classic ((op (e4) (e3)) = (op (e4) (e3)))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ]. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e3))) = ((op (e4) (e1)) = (op (e4) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hb1. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Hb2. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 40.87/41.09 congruence. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e3)) = (op (e4) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hb4. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e3)) = (op (e4) (e3)))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ]. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e3))) = ((op (e4) (unit)) = (op (e4) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hb5. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Hb2. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L59_); trivial. % 40.87/41.09 apply zenon_Hb3. apply refl_equal. % 40.87/41.09 apply zenon_Hb3. apply refl_equal. % 40.87/41.09 apply zenon_Ha6. apply sym_equal. exact zenon_Ha5. % 40.87/41.09 apply zenon_Hb3. apply refl_equal. % 40.87/41.09 apply zenon_Hb3. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L60_ *) % 40.87/41.09 assert (zenon_L61_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_H9b zenon_Hab zenon_Haa zenon_H32 zenon_Hb1 zenon_Ha5 zenon_H99 zenon_H91 zenon_Hc zenon_H92. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L55_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L56_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L58_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L60_); trivial. % 40.87/41.09 apply (zenon_L44_); trivial. % 40.87/41.09 (* end of lemma zenon_L61_ *) % 40.87/41.09 assert (zenon_L62_ : (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((unit) = (e0)) -> ((op (e2) (e4)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hb6 zenon_H58 zenon_H9 zenon_Hb7. % 40.87/41.09 cut (((op (e2) (unit)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e4)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hb6. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H58. % 40.87/41.09 cut (((e2) = (op (e2) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hb8]. % 40.87/41.09 cut (((op (e2) (unit)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 40.87/41.09 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e2) (unit)) = (op (e2) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H5b. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H5c. % 40.87/41.09 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 40.87/41.09 cut (((op (e2) (e0)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L21_); trivial. % 40.87/41.09 apply zenon_H5d. apply refl_equal. % 40.87/41.09 apply zenon_H5d. apply refl_equal. % 40.87/41.09 apply zenon_Hb8. apply sym_equal. exact zenon_Hb7. % 40.87/41.09 (* end of lemma zenon_L62_ *) % 40.87/41.09 assert (zenon_L63_ : (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((unit) = (e1)) -> ((op (e2) (e4)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hb9 zenon_H58 zenon_H14 zenon_Hb7. % 40.87/41.09 cut (((op (e2) (unit)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e4)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hb9. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H58. % 40.87/41.09 cut (((e2) = (op (e2) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hb8]. % 40.87/41.09 cut (((op (e2) (unit)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H70 | zenon_intro zenon_H71 ]. % 40.87/41.09 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (unit)) = (op (e2) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H6f. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H70. % 40.87/41.09 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 40.87/41.09 cut (((op (e2) (e1)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L28_); trivial. % 40.87/41.09 apply zenon_H71. apply refl_equal. % 40.87/41.09 apply zenon_H71. apply refl_equal. % 40.87/41.09 apply zenon_Hb8. apply sym_equal. exact zenon_Hb7. % 40.87/41.09 (* end of lemma zenon_L63_ *) % 40.87/41.09 assert (zenon_L64_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (e4)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_Hb6 zenon_Hb7 zenon_H58 zenon_Hb9 zenon_H9f zenon_H5f zenon_H73 zenon_H72 zenon_H20 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L62_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L63_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L50_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L30_); trivial. % 40.87/41.09 apply (zenon_L11_); trivial. % 40.87/41.09 (* end of lemma zenon_L64_ *) % 40.87/41.09 assert (zenon_L65_ : ((op (e2) (unit)) = (e2)) -> ((unit) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H58 zenon_H14 zenon_Hba zenon_Hbb. % 40.87/41.09 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H70 | zenon_intro zenon_H71 ]. % 40.87/41.09 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (e0)) = (op (e2) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hbb. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H70. % 40.87/41.09 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 40.87/41.09 cut (((op (e2) (e1)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbc]. % 40.87/41.09 congruence. % 40.87/41.09 cut (((op (e2) (unit)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hbc. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H58. % 40.87/41.09 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 40.87/41.09 cut (((op (e2) (unit)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H70 | zenon_intro zenon_H71 ]. % 40.87/41.09 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (unit)) = (op (e2) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H6f. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H70. % 40.87/41.09 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 40.87/41.09 cut (((op (e2) (e1)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L28_); trivial. % 40.87/41.09 apply zenon_H71. apply refl_equal. % 40.87/41.09 apply zenon_H71. apply refl_equal. % 40.87/41.09 apply zenon_Hbd. apply sym_equal. exact zenon_Hba. % 40.87/41.09 apply zenon_H71. apply refl_equal. % 40.87/41.09 apply zenon_H71. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L65_ *) % 40.87/41.09 assert (zenon_L66_ : (~((op (e3) (e2)) = (op (unit) (e2)))) -> ((unit) = (e3)) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hbe zenon_H2a. % 40.87/41.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 40.87/41.09 cut (((e3) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 40.87/41.09 congruence. % 40.87/41.09 apply zenon_H2b. apply sym_equal. exact zenon_H2a. % 40.87/41.09 apply zenon_H7. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L66_ *) % 40.87/41.09 assert (zenon_L67_ : (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((unit) = (e3)) -> ((op (e3) (e4)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H83 zenon_Hc zenon_H2a zenon_Hbf. % 40.87/41.09 cut (((op (unit) (e2)) = (e2)) = ((op (e3) (e2)) = (op (e3) (e4)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H83. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Hc. % 40.87/41.09 cut (((e2) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 40.87/41.09 cut (((op (unit) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (unit) (e2)) = (op (e3) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hc1. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H85. % 40.87/41.09 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 40.87/41.09 cut (((op (e3) (e2)) = (op (unit) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L66_); trivial. % 40.87/41.09 apply zenon_H86. apply refl_equal. % 40.87/41.09 apply zenon_H86. apply refl_equal. % 40.87/41.09 apply zenon_Hc0. apply sym_equal. exact zenon_Hbf. % 40.87/41.09 (* end of lemma zenon_L67_ *) % 40.87/41.09 assert (zenon_L68_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e4) (e1)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (e3) (e4)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_H9b zenon_Hbb zenon_Hba zenon_H58 zenon_H32 zenon_Ha5 zenon_H99 zenon_Hbf zenon_H83 zenon_H91 zenon_Hc zenon_H92. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L55_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L65_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L58_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L67_); trivial. % 40.87/41.09 apply (zenon_L44_); trivial. % 40.87/41.09 (* end of lemma zenon_L68_ *) % 40.87/41.09 assert (zenon_L69_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e3)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e1)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hc2 zenon_H2c zenon_H17 zenon_H2d zenon_H1f zenon_H22 zenon_H18 zenon_Ha1 zenon_Hb1 zenon_Haa zenon_H34 zenon_H16 zenon_H20 zenon_H72 zenon_H73 zenon_H5f zenon_H9f zenon_Hb9 zenon_Hb6 zenon_H92 zenon_Hc zenon_H91 zenon_H83 zenon_H99 zenon_Ha5 zenon_H32 zenon_H58 zenon_Hba zenon_Hbb zenon_H9b zenon_H3b zenon_Hc3. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.87/41.09 apply (zenon_L53_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.87/41.09 apply (zenon_L61_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.87/41.09 apply (zenon_L64_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.87/41.09 apply (zenon_L68_); trivial. % 40.87/41.09 exact (zenon_Hc3 zenon_Hc7). % 40.87/41.09 (* end of lemma zenon_L69_ *) % 40.87/41.09 assert (zenon_L70_ : (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> ((unit) = (e0)) -> ((op (e4) (e2)) = (e4)) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hc8 zenon_H99 zenon_H9 zenon_Hc9. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e0)) = (op (e4) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hc8. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e0)) = (op (e4) (e0)))); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha9 ]. % 40.87/41.09 cut (((op (e4) (e0)) = (op (e4) (e0))) = ((op (e4) (unit)) = (op (e4) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Ha7. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Ha8. % 40.87/41.09 cut (((op (e4) (e0)) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 40.87/41.09 cut (((op (e4) (e0)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L54_); trivial. % 40.87/41.09 apply zenon_Ha9. apply refl_equal. % 40.87/41.09 apply zenon_Ha9. apply refl_equal. % 40.87/41.09 apply zenon_Hca. apply sym_equal. exact zenon_Hc9. % 40.87/41.09 (* end of lemma zenon_L70_ *) % 40.87/41.09 assert (zenon_L71_ : (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> ((unit) = (e1)) -> ((op (e4) (e2)) = (e4)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H32 zenon_H99 zenon_H14 zenon_Hc9. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e1)) = (op (e4) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H32. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e1)) = (op (e4) (e1)))); [ zenon_intro zenon_H37 | zenon_intro zenon_H38 ]. % 40.87/41.09 cut (((op (e4) (e1)) = (op (e4) (e1))) = ((op (e4) (unit)) = (op (e4) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H9e. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H37. % 40.87/41.09 cut (((op (e4) (e1)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 40.87/41.09 cut (((op (e4) (e1)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L48_); trivial. % 40.87/41.09 apply zenon_H38. apply refl_equal. % 40.87/41.09 apply zenon_H38. apply refl_equal. % 40.87/41.09 apply zenon_Hca. apply sym_equal. exact zenon_Hc9. % 40.87/41.09 (* end of lemma zenon_L71_ *) % 40.87/41.09 assert (zenon_L72_ : ((op (e4) (unit)) = (e4)) -> ((unit) = (e3)) -> ((op (e4) (e2)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H99 zenon_H2a zenon_Hc9 zenon_H91. % 40.87/41.09 elim (classic ((op (e4) (e3)) = (op (e4) (e3)))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ]. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e3))) = ((op (e4) (e2)) = (op (e4) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H91. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Hb2. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 40.87/41.09 congruence. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e3)) = (op (e4) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hcb. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e3)) = (op (e4) (e3)))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ]. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e3))) = ((op (e4) (unit)) = (op (e4) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hb5. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Hb2. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L59_); trivial. % 40.87/41.09 apply zenon_Hb3. apply refl_equal. % 40.87/41.09 apply zenon_Hb3. apply refl_equal. % 40.87/41.09 apply zenon_Hca. apply sym_equal. exact zenon_Hc9. % 40.87/41.09 apply zenon_Hb3. apply refl_equal. % 40.87/41.09 apply zenon_Hb3. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L72_ *) % 40.87/41.09 assert (zenon_L73_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e4) (e2)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_Hc8 zenon_H32 zenon_H22 zenon_H20 zenon_H1f zenon_Hc9 zenon_H99 zenon_H91 zenon_Hc zenon_H92. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L70_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L71_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L8_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L72_); trivial. % 40.87/41.09 apply (zenon_L44_); trivial. % 40.87/41.09 (* end of lemma zenon_L73_ *) % 40.87/41.09 assert (zenon_L74_ : (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((unit) = (e0)) -> ((op (e4) (e3)) = (e4)) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hcc zenon_H99 zenon_H9 zenon_Hcd. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e0)) = (op (e4) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hcc. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e0)) = (op (e4) (e0)))); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha9 ]. % 40.87/41.09 cut (((op (e4) (e0)) = (op (e4) (e0))) = ((op (e4) (unit)) = (op (e4) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Ha7. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Ha8. % 40.87/41.09 cut (((op (e4) (e0)) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 40.87/41.09 cut (((op (e4) (e0)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L54_); trivial. % 40.87/41.09 apply zenon_Ha9. apply refl_equal. % 40.87/41.09 apply zenon_Ha9. apply refl_equal. % 40.87/41.09 apply zenon_Hce. apply sym_equal. exact zenon_Hcd. % 40.87/41.09 (* end of lemma zenon_L74_ *) % 40.87/41.09 assert (zenon_L75_ : (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((unit) = (e1)) -> ((op (e4) (e3)) = (e4)) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hb1 zenon_H99 zenon_H14 zenon_Hcd. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e1)) = (op (e4) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hb1. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e1)) = (op (e4) (e1)))); [ zenon_intro zenon_H37 | zenon_intro zenon_H38 ]. % 40.87/41.09 cut (((op (e4) (e1)) = (op (e4) (e1))) = ((op (e4) (unit)) = (op (e4) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H9e. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H37. % 40.87/41.09 cut (((op (e4) (e1)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 40.87/41.09 cut (((op (e4) (e1)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L48_); trivial. % 40.87/41.09 apply zenon_H38. apply refl_equal. % 40.87/41.09 apply zenon_H38. apply refl_equal. % 40.87/41.09 apply zenon_Hce. apply sym_equal. exact zenon_Hcd. % 40.87/41.09 (* end of lemma zenon_L75_ *) % 40.87/41.09 assert (zenon_L76_ : (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((unit) = (e2)) -> ((op (e4) (e3)) = (e4)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H91 zenon_H99 zenon_H21 zenon_Hcd. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e2)) = (op (e4) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H91. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e2)) = (op (e4) (e2)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e2))) = ((op (e4) (unit)) = (op (e4) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Haf. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H95. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L57_); trivial. % 40.87/41.09 apply zenon_H96. apply refl_equal. % 40.87/41.09 apply zenon_H96. apply refl_equal. % 40.87/41.09 apply zenon_Hce. apply sym_equal. exact zenon_Hcd. % 40.87/41.09 (* end of lemma zenon_L76_ *) % 40.87/41.09 assert (zenon_L77_ : (~((op (e2) (e3)) = (op (e2) (unit)))) -> ((unit) = (e3)) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hcf zenon_H2a. % 40.87/41.09 cut (((e3) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 40.87/41.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 40.87/41.09 congruence. % 40.87/41.09 apply zenon_H7. apply refl_equal. % 40.87/41.09 apply zenon_H2b. apply sym_equal. exact zenon_H2a. % 40.87/41.09 (* end of lemma zenon_L77_ *) % 40.87/41.09 assert (zenon_L78_ : ((op (e2) (unit)) = (e2)) -> ((unit) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H58 zenon_H2a zenon_Hba zenon_H57. % 40.87/41.09 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 40.87/41.09 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e0)) = (op (e2) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H57. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H25. % 40.87/41.09 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 40.87/41.09 cut (((op (e2) (e3)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 40.87/41.09 congruence. % 40.87/41.09 cut (((op (e2) (unit)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hd0. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H58. % 40.87/41.09 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 40.87/41.09 cut (((op (e2) (unit)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 40.87/41.09 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (unit)) = (op (e2) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hd1. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H25. % 40.87/41.09 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 40.87/41.09 cut (((op (e2) (e3)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L77_); trivial. % 40.87/41.09 apply zenon_H26. apply refl_equal. % 40.87/41.09 apply zenon_H26. apply refl_equal. % 40.87/41.09 apply zenon_Hbd. apply sym_equal. exact zenon_Hba. % 40.87/41.09 apply zenon_H26. apply refl_equal. % 40.87/41.09 apply zenon_H26. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L78_ *) % 40.87/41.09 assert (zenon_L79_ : (~((op (e4) (e4)) = (op (unit) (e4)))) -> ((unit) = (e4)) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hd2 zenon_H33. % 40.87/41.09 cut (((e4) = (e4))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 40.87/41.09 cut (((e4) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 40.87/41.09 congruence. % 40.87/41.09 apply zenon_H3a. apply sym_equal. exact zenon_H33. % 40.87/41.09 apply zenon_H97. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L79_ *) % 40.87/41.09 assert (zenon_L80_ : ((op (unit) (e4)) = (e4)) -> ((unit) = (e4)) -> ((op (e4) (e3)) = (e4)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hd3 zenon_H33 zenon_Hcd zenon_Hd4. % 40.87/41.09 elim (classic ((op (e4) (e4)) = (op (e4) (e4)))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hd6 ]. % 40.87/41.09 cut (((op (e4) (e4)) = (op (e4) (e4))) = ((op (e4) (e3)) = (op (e4) (e4)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hd4. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Hd5. % 40.87/41.09 cut (((op (e4) (e4)) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 40.87/41.09 cut (((op (e4) (e4)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 40.87/41.09 congruence. % 40.87/41.09 cut (((op (unit) (e4)) = (e4)) = ((op (e4) (e4)) = (op (e4) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hd7. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Hd3. % 40.87/41.09 cut (((e4) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 40.87/41.09 cut (((op (unit) (e4)) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e4)) = (op (e4) (e4)))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hd6 ]. % 40.87/41.09 cut (((op (e4) (e4)) = (op (e4) (e4))) = ((op (unit) (e4)) = (op (e4) (e4)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hd8. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Hd5. % 40.87/41.09 cut (((op (e4) (e4)) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 40.87/41.09 cut (((op (e4) (e4)) = (op (unit) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L79_); trivial. % 40.87/41.09 apply zenon_Hd6. apply refl_equal. % 40.87/41.09 apply zenon_Hd6. apply refl_equal. % 40.87/41.09 apply zenon_Hce. apply sym_equal. exact zenon_Hcd. % 40.87/41.09 apply zenon_Hd6. apply refl_equal. % 40.87/41.09 apply zenon_Hd6. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L80_ *) % 40.87/41.09 assert (zenon_L81_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e3)) = (e4)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_Hcc zenon_Hb1 zenon_H99 zenon_H91 zenon_H57 zenon_Hba zenon_H58 zenon_Hd3 zenon_Hcd zenon_Hd4. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L74_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L75_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L76_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L78_); trivial. % 40.87/41.09 apply (zenon_L80_); trivial. % 40.87/41.09 (* end of lemma zenon_L81_ *) % 40.87/41.09 assert (zenon_L82_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hd9 zenon_H61 zenon_Hc3 zenon_H9b zenon_Hbb zenon_H83 zenon_Hb6 zenon_Hb9 zenon_H9f zenon_H5f zenon_H73 zenon_H72 zenon_H16 zenon_H34 zenon_Haa zenon_Ha1 zenon_H18 zenon_H2d zenon_H17 zenon_H2c zenon_Hc2 zenon_H92 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_Hc8 zenon_Hd4 zenon_Hd3 zenon_H58 zenon_Hba zenon_H57 zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.87/41.09 apply (zenon_L51_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.87/41.09 apply (zenon_L69_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.87/41.09 apply (zenon_L73_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.87/41.09 apply (zenon_L81_); trivial. % 40.87/41.09 exact (zenon_Hda zenon_Hde). % 40.87/41.09 (* end of lemma zenon_L82_ *) % 40.87/41.09 assert (zenon_L83_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> ((unit) = (e0)) -> ((op (e3) (e2)) = (e3)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H8e zenon_H5f zenon_H9 zenon_H76. % 40.87/41.09 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H8e. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H5f. % 40.87/41.09 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 40.87/41.09 cut (((op (e3) (unit)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H7f | zenon_intro zenon_H80 ]. % 40.87/41.09 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e3) (unit)) = (op (e3) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H7e. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H7f. % 40.87/41.09 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 40.87/41.09 cut (((op (e3) (e0)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L34_); trivial. % 40.87/41.09 apply zenon_H80. apply refl_equal. % 40.87/41.09 apply zenon_H80. apply refl_equal. % 40.87/41.09 apply zenon_H79. apply sym_equal. exact zenon_H76. % 40.87/41.09 (* end of lemma zenon_L83_ *) % 40.87/41.09 assert (zenon_L84_ : ((op (e4) (unit)) = (e4)) -> ((unit) = (e2)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H99 zenon_H21 zenon_H9a zenon_Hc8. % 40.87/41.09 elim (classic ((op (e4) (e2)) = (op (e4) (e2)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e2))) = ((op (e4) (e0)) = (op (e4) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hc8. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H95. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 40.87/41.09 congruence. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e2)) = (op (e4) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hdf. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e2)) = (op (e4) (e2)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e2))) = ((op (e4) (unit)) = (op (e4) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Haf. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H95. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L57_); trivial. % 40.87/41.09 apply zenon_H96. apply refl_equal. % 40.87/41.09 apply zenon_H96. apply refl_equal. % 40.87/41.09 apply zenon_H9d. apply sym_equal. exact zenon_H9a. % 40.87/41.09 apply zenon_H96. apply refl_equal. % 40.87/41.09 apply zenon_H96. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L84_ *) % 40.87/41.09 assert (zenon_L85_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_H5f zenon_H8e zenon_H9b zenon_Hc8 zenon_H9a zenon_H99 zenon_H77 zenon_H76 zenon_H20 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L83_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L49_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L84_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L32_); trivial. % 40.87/41.09 apply (zenon_L11_); trivial. % 40.87/41.09 (* end of lemma zenon_L85_ *) % 40.87/41.09 assert (zenon_L86_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hd9 zenon_H34 zenon_H16 zenon_H76 zenon_H77 zenon_H8e zenon_H5f zenon_Haa zenon_Hab zenon_H9b zenon_H92 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_Hc8 zenon_Hd4 zenon_Hd3 zenon_H58 zenon_Hba zenon_H57 zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.87/41.09 apply (zenon_L85_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.87/41.09 apply (zenon_L61_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.87/41.09 apply (zenon_L73_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.87/41.09 apply (zenon_L81_); trivial. % 40.87/41.09 exact (zenon_Hda zenon_Hde). % 40.87/41.09 (* end of lemma zenon_L86_ *) % 40.87/41.09 assert (zenon_L87_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (e4)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_Hb6 zenon_Hb7 zenon_H58 zenon_Hb9 zenon_H22 zenon_H1f zenon_H77 zenon_H76 zenon_H20 zenon_H91 zenon_Hc zenon_H92. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L62_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L63_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L8_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L32_); trivial. % 40.87/41.09 apply (zenon_L44_); trivial. % 40.87/41.09 (* end of lemma zenon_L87_ *) % 40.87/41.09 assert (zenon_L88_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (e3) (e4)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_H76 zenon_H5f zenon_H8e zenon_H9b zenon_Hc8 zenon_H9a zenon_H99 zenon_Hbf zenon_H83 zenon_H91 zenon_Hc zenon_H92. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L83_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L49_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L84_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L67_); trivial. % 40.87/41.09 apply (zenon_L44_); trivial. % 40.87/41.09 (* end of lemma zenon_L88_ *) % 40.87/41.09 assert (zenon_L89_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> ((unit) = (e1)) -> ((op (e3) (e2)) = (e3)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H9f zenon_H5f zenon_H14 zenon_H76. % 40.87/41.09 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H9f. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H5f. % 40.87/41.09 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 40.87/41.09 cut (((op (e3) (unit)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 40.87/41.09 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (unit)) = (op (e3) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H66. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H62. % 40.87/41.09 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 40.87/41.09 cut (((op (e3) (e1)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L23_); trivial. % 40.87/41.09 apply zenon_H63. apply refl_equal. % 40.87/41.09 apply zenon_H63. apply refl_equal. % 40.87/41.09 apply zenon_H79. apply sym_equal. exact zenon_H76. % 40.87/41.09 (* end of lemma zenon_L89_ *) % 40.87/41.09 assert (zenon_L90_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e4) (e1)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (e3) (e4)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_H9b zenon_H76 zenon_H5f zenon_H9f zenon_H32 zenon_Ha5 zenon_H99 zenon_Hbf zenon_H83 zenon_H91 zenon_Hc zenon_H92. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L55_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L89_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L58_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L67_); trivial. % 40.87/41.09 apply (zenon_L44_); trivial. % 40.87/41.09 (* end of lemma zenon_L90_ *) % 40.87/41.09 assert (zenon_L91_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hd9 zenon_H8e zenon_H83 zenon_Hbf zenon_H9f zenon_H5f zenon_H76 zenon_H9b zenon_H92 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_Hc8 zenon_Hd4 zenon_Hd3 zenon_H58 zenon_Hba zenon_H57 zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.87/41.09 apply (zenon_L88_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.87/41.09 apply (zenon_L90_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.87/41.09 apply (zenon_L73_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.87/41.09 apply (zenon_L81_); trivial. % 40.87/41.09 exact (zenon_Hda zenon_Hde). % 40.87/41.09 (* end of lemma zenon_L91_ *) % 40.87/41.09 assert (zenon_L92_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hc2 zenon_H2c zenon_H17 zenon_H2d zenon_H18 zenon_Ha1 zenon_Haa zenon_H16 zenon_H34 zenon_H77 zenon_Hb9 zenon_Hb6 zenon_Hda zenon_H3b zenon_Hcc zenon_Hb1 zenon_H99 zenon_H91 zenon_H57 zenon_Hba zenon_H58 zenon_Hd3 zenon_Hd4 zenon_Hc8 zenon_H32 zenon_H22 zenon_H20 zenon_H1f zenon_Hc zenon_H92 zenon_H9b zenon_H76 zenon_H5f zenon_H9f zenon_H83 zenon_H8e zenon_Hd9 zenon_Hc3. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.87/41.09 apply (zenon_L53_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.87/41.09 apply (zenon_L86_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.87/41.09 apply (zenon_L87_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.87/41.09 apply (zenon_L91_); trivial. % 40.87/41.09 exact (zenon_Hc3 zenon_Hc7). % 40.87/41.09 (* end of lemma zenon_L92_ *) % 40.87/41.09 assert (zenon_L93_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e3) (e3)) = (e3))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H88 zenon_H41 zenon_H42 zenon_H43 zenon_H73 zenon_Hbb zenon_H61 zenon_Hc3 zenon_Hd9 zenon_H8e zenon_H9f zenon_H9b zenon_H92 zenon_Hc zenon_H1f zenon_H22 zenon_Hc8 zenon_Hd4 zenon_Hd3 zenon_H58 zenon_Hba zenon_H57 zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_Hda zenon_Hb6 zenon_Hb9 zenon_H77 zenon_Haa zenon_Ha1 zenon_H18 zenon_H2d zenon_H17 zenon_H2c zenon_Hc2 zenon_H89 zenon_H3b zenon_H7b zenon_H81 zenon_H5f zenon_H83 zenon_H20 zenon_H87 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H60 | zenon_intro zenon_H8a ]. % 40.87/41.09 apply (zenon_L45_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H72 | zenon_intro zenon_H8b ]. % 40.87/41.09 apply (zenon_L82_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H8b); [ zenon_intro zenon_H76 | zenon_intro zenon_H8c ]. % 40.87/41.09 apply (zenon_L92_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H8d | zenon_intro zenon_H7c ]. % 40.87/41.09 exact (zenon_H89 zenon_H8d). % 40.87/41.09 apply (zenon_L40_); trivial. % 40.87/41.09 (* end of lemma zenon_L93_ *) % 40.87/41.09 assert (zenon_L94_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e3) (e3)) = (e3))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.09 do 0 intro. intros zenon_He0 zenon_Hb zenon_H50 zenon_H51 zenon_H49 zenon_H6e zenon_H68 zenon_He1 zenon_H88 zenon_H41 zenon_H42 zenon_H43 zenon_H73 zenon_Hbb zenon_H61 zenon_Hc3 zenon_Hd9 zenon_H8e zenon_H9f zenon_H9b zenon_Hc zenon_H1f zenon_H22 zenon_Hc8 zenon_Hd4 zenon_Hd3 zenon_H58 zenon_Hba zenon_H57 zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_Hda zenon_Hb6 zenon_Hb9 zenon_H77 zenon_Haa zenon_Ha1 zenon_H18 zenon_H2d zenon_H17 zenon_H2c zenon_Hc2 zenon_H89 zenon_H3b zenon_H7b zenon_H81 zenon_H5f zenon_H83 zenon_H20 zenon_H87 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.09 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.87/41.09 apply (zenon_L12_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.87/41.09 apply (zenon_L20_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.87/41.09 apply (zenon_L41_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.87/41.09 exact (zenon_He1 zenon_He5). % 40.87/41.09 apply (zenon_L93_); trivial. % 40.87/41.09 (* end of lemma zenon_L94_ *) % 40.87/41.09 assert (zenon_L95_ : (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((op (e4) (unit)) = (e4)) -> ((unit) = (e0)) -> ((op (e4) (e4)) = (e4)) -> False). % 40.87/41.09 do 0 intro. intros zenon_He6 zenon_H99 zenon_H9 zenon_Hde. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e0)) = (op (e4) (e4)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_He6. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e0)) = (op (e4) (e0)))); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha9 ]. % 40.87/41.09 cut (((op (e4) (e0)) = (op (e4) (e0))) = ((op (e4) (unit)) = (op (e4) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Ha7. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Ha8. % 40.87/41.09 cut (((op (e4) (e0)) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 40.87/41.09 cut (((op (e4) (e0)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L54_); trivial. % 40.87/41.09 apply zenon_Ha9. apply refl_equal. % 40.87/41.09 apply zenon_Ha9. apply refl_equal. % 40.87/41.09 apply zenon_He7. apply sym_equal. exact zenon_Hde. % 40.87/41.09 (* end of lemma zenon_L95_ *) % 40.87/41.09 assert (zenon_L96_ : (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (e4) (unit)) = (e4)) -> ((unit) = (e1)) -> ((op (e4) (e4)) = (e4)) -> False). % 40.87/41.09 do 0 intro. intros zenon_He8 zenon_H99 zenon_H14 zenon_Hde. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e1)) = (op (e4) (e4)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_He8. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e1)) = (op (e4) (e1)))); [ zenon_intro zenon_H37 | zenon_intro zenon_H38 ]. % 40.87/41.09 cut (((op (e4) (e1)) = (op (e4) (e1))) = ((op (e4) (unit)) = (op (e4) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H9e. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H37. % 40.87/41.09 cut (((op (e4) (e1)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 40.87/41.09 cut (((op (e4) (e1)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L48_); trivial. % 40.87/41.09 apply zenon_H38. apply refl_equal. % 40.87/41.09 apply zenon_H38. apply refl_equal. % 40.87/41.09 apply zenon_He7. apply sym_equal. exact zenon_Hde. % 40.87/41.09 (* end of lemma zenon_L96_ *) % 40.87/41.09 assert (zenon_L97_ : (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (e4) (unit)) = (e4)) -> ((unit) = (e2)) -> ((op (e4) (e4)) = (e4)) -> False). % 40.87/41.09 do 0 intro. intros zenon_He9 zenon_H99 zenon_H21 zenon_Hde. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e2)) = (op (e4) (e4)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_He9. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e2)) = (op (e4) (e2)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e2))) = ((op (e4) (unit)) = (op (e4) (e2)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Haf. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H95. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 40.87/41.09 cut (((op (e4) (e2)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L57_); trivial. % 40.87/41.09 apply zenon_H96. apply refl_equal. % 40.87/41.09 apply zenon_H96. apply refl_equal. % 40.87/41.09 apply zenon_He7. apply sym_equal. exact zenon_Hde. % 40.87/41.09 (* end of lemma zenon_L97_ *) % 40.87/41.09 assert (zenon_L98_ : (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e4) (unit)) = (e4)) -> ((unit) = (e3)) -> ((op (e4) (e4)) = (e4)) -> False). % 40.87/41.09 do 0 intro. intros zenon_Hd4 zenon_H99 zenon_H2a zenon_Hde. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e3)) = (op (e4) (e4)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hd4. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e3)) = (op (e4) (e3)))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ]. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e3))) = ((op (e4) (unit)) = (op (e4) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hb5. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Hb2. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L59_); trivial. % 40.87/41.09 apply zenon_Hb3. apply refl_equal. % 40.87/41.09 apply zenon_Hb3. apply refl_equal. % 40.87/41.09 apply zenon_He7. apply sym_equal. exact zenon_Hde. % 40.87/41.09 (* end of lemma zenon_L98_ *) % 40.87/41.09 assert (zenon_L99_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (e4) (e4)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_He6 zenon_He8 zenon_He9 zenon_Hde zenon_H99 zenon_Hd4 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L95_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L96_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L97_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L98_); trivial. % 40.87/41.09 apply (zenon_L11_); trivial. % 40.87/41.09 (* end of lemma zenon_L99_ *) % 40.87/41.09 assert (zenon_L100_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e4) (e2)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.87/41.09 do 0 intro. intros zenon_He0 zenon_H2c zenon_H17 zenon_H2d zenon_H18 zenon_Hb zenon_H50 zenon_H43 zenon_H51 zenon_H49 zenon_H41 zenon_H42 zenon_H34 zenon_H16 zenon_H87 zenon_H83 zenon_H5f zenon_H81 zenon_H7b zenon_H89 zenon_H57 zenon_H58 zenon_H6e zenon_H77 zenon_H73 zenon_H61 zenon_H68 zenon_H88 zenon_He1 zenon_H3b zenon_Hc8 zenon_H32 zenon_H22 zenon_H20 zenon_H1f zenon_Hc9 zenon_H99 zenon_H91 zenon_Hc. % 40.87/41.09 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.87/41.09 apply (zenon_L12_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.87/41.09 apply (zenon_L20_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.87/41.09 apply (zenon_L41_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.87/41.09 exact (zenon_He1 zenon_He5). % 40.87/41.09 apply (zenon_L73_); trivial. % 40.87/41.09 (* end of lemma zenon_L100_ *) % 40.87/41.09 assert (zenon_L101_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> ((unit) = (e0)) -> ((op (e3) (e3)) = (e3)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H68 zenon_H5f zenon_H9 zenon_H8d. % 40.87/41.09 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H68. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H5f. % 40.87/41.09 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 40.87/41.09 cut (((op (e3) (unit)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H7f | zenon_intro zenon_H80 ]. % 40.87/41.09 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e3) (unit)) = (op (e3) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H7e. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H7f. % 40.87/41.09 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 40.87/41.09 cut (((op (e3) (e0)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L34_); trivial. % 40.87/41.09 apply zenon_H80. apply refl_equal. % 40.87/41.09 apply zenon_H80. apply refl_equal. % 40.87/41.09 apply zenon_Hea. apply sym_equal. exact zenon_H8d. % 40.87/41.09 (* end of lemma zenon_L101_ *) % 40.87/41.09 assert (zenon_L102_ : ((op (e4) (unit)) = (e4)) -> ((unit) = (e3)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H99 zenon_H2a zenon_H9a zenon_Hcc. % 40.87/41.09 elim (classic ((op (e4) (e3)) = (op (e4) (e3)))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ]. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e3))) = ((op (e4) (e0)) = (op (e4) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hcc. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Hb2. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 40.87/41.09 congruence. % 40.87/41.09 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e3)) = (op (e4) (e0)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Heb. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H99. % 40.87/41.09 cut (((e4) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 40.87/41.09 cut (((op (e4) (unit)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e4) (e3)) = (op (e4) (e3)))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ]. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e3))) = ((op (e4) (unit)) = (op (e4) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_Hb5. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_Hb2. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 40.87/41.09 cut (((op (e4) (e3)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L59_); trivial. % 40.87/41.09 apply zenon_Hb3. apply refl_equal. % 40.87/41.09 apply zenon_Hb3. apply refl_equal. % 40.87/41.09 apply zenon_H9d. apply sym_equal. exact zenon_H9a. % 40.87/41.09 apply zenon_Hb3. apply refl_equal. % 40.87/41.09 apply zenon_Hb3. apply refl_equal. % 40.87/41.09 (* end of lemma zenon_L102_ *) % 40.87/41.09 assert (zenon_L103_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_H8d zenon_H5f zenon_H68 zenon_H9b zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L101_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L49_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L84_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L102_); trivial. % 40.87/41.09 apply (zenon_L11_); trivial. % 40.87/41.09 (* end of lemma zenon_L103_ *) % 40.87/41.09 assert (zenon_L104_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> ((unit) = (e1)) -> ((op (e3) (e3)) = (e3)) -> False). % 40.87/41.09 do 0 intro. intros zenon_H73 zenon_H5f zenon_H14 zenon_H8d. % 40.87/41.09 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e3)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H73. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H5f. % 40.87/41.09 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 40.87/41.09 cut (((op (e3) (unit)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 40.87/41.09 congruence. % 40.87/41.09 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 40.87/41.09 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (unit)) = (op (e3) (e1)))). % 40.87/41.09 intro zenon_D_pnotp. % 40.87/41.09 apply zenon_H66. % 40.87/41.09 rewrite <- zenon_D_pnotp. % 40.87/41.09 exact zenon_H62. % 40.87/41.09 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 40.87/41.09 cut (((op (e3) (e1)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 40.87/41.09 congruence. % 40.87/41.09 apply (zenon_L23_); trivial. % 40.87/41.09 apply zenon_H63. apply refl_equal. % 40.87/41.09 apply zenon_H63. apply refl_equal. % 40.87/41.09 apply zenon_Hea. apply sym_equal. exact zenon_H8d. % 40.87/41.09 (* end of lemma zenon_L104_ *) % 40.87/41.09 assert (zenon_L105_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.09 do 0 intro. intros zenon_H3b zenon_H68 zenon_H8d zenon_H5f zenon_H73 zenon_Hb1 zenon_Ha5 zenon_H99 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.09 apply (zenon_L101_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.09 apply (zenon_L104_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.09 apply (zenon_L58_); trivial. % 40.87/41.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.09 apply (zenon_L60_); trivial. % 40.87/41.09 apply (zenon_L11_); trivial. % 40.87/41.09 (* end of lemma zenon_L105_ *) % 40.87/41.09 assert (zenon_L106_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> ((unit) = (e2)) -> ((op (e3) (e3)) = (e3)) -> False). % 40.87/41.10 do 0 intro. intros zenon_H77 zenon_H5f zenon_H21 zenon_H8d. % 40.87/41.10 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e3)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H77. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H5f. % 40.87/41.10 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 40.87/41.10 cut (((op (e3) (unit)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 40.87/41.10 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (unit)) = (op (e3) (e2)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H84. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H85. % 40.87/41.10 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 40.87/41.10 cut (((op (e3) (e2)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L37_); trivial. % 40.87/41.10 apply zenon_H86. apply refl_equal. % 40.87/41.10 apply zenon_H86. apply refl_equal. % 40.87/41.10 apply zenon_Hea. apply sym_equal. exact zenon_H8d. % 40.87/41.10 (* end of lemma zenon_L106_ *) % 40.87/41.10 assert (zenon_L107_ : ((op (unit) (e4)) = (e4)) -> ((unit) = (e4)) -> ((op (e4) (e2)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hd3 zenon_H33 zenon_Hc9 zenon_He9. % 40.87/41.10 elim (classic ((op (e4) (e4)) = (op (e4) (e4)))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hd6 ]. % 40.87/41.10 cut (((op (e4) (e4)) = (op (e4) (e4))) = ((op (e4) (e2)) = (op (e4) (e4)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_He9. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_Hd5. % 40.87/41.10 cut (((op (e4) (e4)) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 40.87/41.10 cut (((op (e4) (e4)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 40.87/41.10 congruence. % 40.87/41.10 cut (((op (unit) (e4)) = (e4)) = ((op (e4) (e4)) = (op (e4) (e2)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_Hec. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_Hd3. % 40.87/41.10 cut (((e4) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 40.87/41.10 cut (((op (unit) (e4)) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e4) (e4)) = (op (e4) (e4)))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hd6 ]. % 40.87/41.10 cut (((op (e4) (e4)) = (op (e4) (e4))) = ((op (unit) (e4)) = (op (e4) (e4)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_Hd8. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_Hd5. % 40.87/41.10 cut (((op (e4) (e4)) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 40.87/41.10 cut (((op (e4) (e4)) = (op (unit) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L79_); trivial. % 40.87/41.10 apply zenon_Hd6. apply refl_equal. % 40.87/41.10 apply zenon_Hd6. apply refl_equal. % 40.87/41.10 apply zenon_Hca. apply sym_equal. exact zenon_Hc9. % 40.87/41.10 apply zenon_Hd6. apply refl_equal. % 40.87/41.10 apply zenon_Hd6. apply refl_equal. % 40.87/41.10 (* end of lemma zenon_L107_ *) % 40.87/41.10 assert (zenon_L108_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e2)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_Hc8 zenon_H32 zenon_H8d zenon_H5f zenon_H77 zenon_H91 zenon_H99 zenon_Hd3 zenon_Hc9 zenon_He9. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L70_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L71_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L106_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L72_); trivial. % 40.87/41.10 apply (zenon_L107_); trivial. % 40.87/41.10 (* end of lemma zenon_L108_ *) % 40.87/41.10 assert (zenon_L109_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e3)) = (e4)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_H68 zenon_H73 zenon_H8d zenon_H5f zenon_H77 zenon_H2d zenon_H17 zenon_H2c zenon_Hd3 zenon_Hcd zenon_Hd4. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L101_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L104_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L106_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L10_); trivial. % 40.87/41.10 apply (zenon_L80_); trivial. % 40.87/41.10 (* end of lemma zenon_L109_ *) % 40.87/41.10 assert (zenon_L110_ : ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hed zenon_He6 zenon_He8 zenon_H3b zenon_H34 zenon_H16 zenon_H32 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_H8d zenon_H5f zenon_H68 zenon_Hb1 zenon_H73 zenon_Hd3 zenon_He9 zenon_H91 zenon_H77 zenon_Hd4 zenon_H17 zenon_H2c zenon_H2d zenon_Hd9. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.87/41.10 apply (zenon_L103_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.87/41.10 apply (zenon_L105_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.87/41.10 apply (zenon_L108_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_L109_); trivial. % 40.87/41.10 exact (zenon_Hda zenon_Hde). % 40.87/41.10 apply (zenon_L99_); trivial. % 40.87/41.10 (* end of lemma zenon_L110_ *) % 40.87/41.10 assert (zenon_L111_ : ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hed zenon_He6 zenon_He8 zenon_H3b zenon_H34 zenon_H16 zenon_H32 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_H8d zenon_H5f zenon_H68 zenon_Hb1 zenon_H73 zenon_Hd3 zenon_He9 zenon_H91 zenon_H77 zenon_Hd4 zenon_Hba zenon_H58 zenon_H57 zenon_Hd9. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.87/41.10 apply (zenon_L103_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.87/41.10 apply (zenon_L105_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.87/41.10 apply (zenon_L108_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_L81_); trivial. % 40.87/41.10 exact (zenon_Hda zenon_Hde). % 40.87/41.10 apply (zenon_L99_); trivial. % 40.87/41.10 (* end of lemma zenon_L111_ *) % 40.87/41.10 assert (zenon_L112_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H3b zenon_H34 zenon_H16 zenon_H32 zenon_H68 zenon_H22 zenon_H20 zenon_H1f zenon_H5f zenon_H61 zenon_H59 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 40.87/41.10 apply (zenon_L41_); trivial. % 40.87/41.10 apply (zenon_L111_); trivial. % 40.87/41.10 (* end of lemma zenon_L112_ *) % 40.87/41.10 assert (zenon_L113_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e4) (e1)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_H8e zenon_H5f zenon_H9f zenon_Ha5 zenon_H99 zenon_H77 zenon_H76 zenon_H20 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L83_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L89_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L58_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L32_); trivial. % 40.87/41.10 apply (zenon_L11_); trivial. % 40.87/41.10 (* end of lemma zenon_L113_ *) % 40.87/41.10 assert (zenon_L114_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((unit) = (e3)) -> ((op (e3) (e3)) = (e2)) -> False). % 40.87/41.10 do 0 intro. intros zenon_H77 zenon_Hc zenon_H2a zenon_He5. % 40.87/41.10 cut (((op (unit) (e2)) = (e2)) = ((op (e3) (e2)) = (op (e3) (e3)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H77. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_Hc. % 40.87/41.10 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 40.87/41.10 cut (((op (unit) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 40.87/41.10 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (unit) (e2)) = (op (e3) (e2)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_Hc1. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H85. % 40.87/41.10 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 40.87/41.10 cut (((op (e3) (e2)) = (op (unit) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L66_); trivial. % 40.87/41.10 apply zenon_H86. apply refl_equal. % 40.87/41.10 apply zenon_H86. apply refl_equal. % 40.87/41.10 apply zenon_Hef. apply sym_equal. exact zenon_He5. % 40.87/41.10 (* end of lemma zenon_L114_ *) % 40.87/41.10 assert (zenon_L115_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e2)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_H8e zenon_H76 zenon_H5f zenon_H9f zenon_H22 zenon_H20 zenon_H1f zenon_He5 zenon_Hc zenon_H77 zenon_Hd3 zenon_Hc9 zenon_He9. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L83_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L89_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L8_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L114_); trivial. % 40.87/41.10 apply (zenon_L107_); trivial. % 40.87/41.10 (* end of lemma zenon_L115_ *) % 40.87/41.10 assert (zenon_L116_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hd9 zenon_Hc8 zenon_H9b zenon_H34 zenon_H16 zenon_H32 zenon_He9 zenon_H77 zenon_Hc zenon_He5 zenon_H1f zenon_H20 zenon_H22 zenon_H9f zenon_H5f zenon_H76 zenon_H8e zenon_Hd4 zenon_Hd3 zenon_H58 zenon_Hba zenon_H57 zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.87/41.10 apply (zenon_L85_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.87/41.10 apply (zenon_L113_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.87/41.10 apply (zenon_L115_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_L81_); trivial. % 40.87/41.10 exact (zenon_Hda zenon_Hde). % 40.87/41.10 (* end of lemma zenon_L116_ *) % 40.87/41.10 assert (zenon_L117_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e2)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_H8e zenon_H5f zenon_H9f zenon_H22 zenon_H1f zenon_H77 zenon_H76 zenon_H20 zenon_Hd3 zenon_Hc9 zenon_He9. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L83_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L89_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L8_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L32_); trivial. % 40.87/41.10 apply (zenon_L107_); trivial. % 40.87/41.10 (* end of lemma zenon_L117_ *) % 40.87/41.10 assert (zenon_L118_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hf0 zenon_Hf1 zenon_He0 zenon_H91 zenon_H8e zenon_Hd9 zenon_Hcc zenon_Hd4 zenon_Hd3 zenon_Hc8 zenon_Ha1 zenon_Hb1 zenon_Haa zenon_Hb9 zenon_Hb6 zenon_Hba zenon_Hbb zenon_Hc2 zenon_H9b zenon_H99 zenon_H9f zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_H41 zenon_H42 zenon_H43 zenon_H49 zenon_H51 zenon_H50 zenon_Hb zenon_Hc zenon_H18 zenon_H16 zenon_H17 zenon_H1f zenon_H20 zenon_H22 zenon_H2d zenon_H2c zenon_H32 zenon_H34 zenon_H3b zenon_He9 zenon_He8 zenon_He6 zenon_Hed zenon_Hee. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_He1 | zenon_intro zenon_H76 ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_L94_); trivial. % 40.87/41.10 apply (zenon_L99_); trivial. % 40.87/41.10 apply (zenon_L100_); trivial. % 40.87/41.10 apply (zenon_L110_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.87/41.10 apply (zenon_L12_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.87/41.10 apply (zenon_L20_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.87/41.10 apply (zenon_L112_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.87/41.10 apply (zenon_L116_); trivial. % 40.87/41.10 apply (zenon_L92_); trivial. % 40.87/41.10 apply (zenon_L99_); trivial. % 40.87/41.10 apply (zenon_L117_); trivial. % 40.87/41.10 (* end of lemma zenon_L118_ *) % 40.87/41.10 assert (zenon_L119_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> ((unit) = (e0)) -> ((op (e2) (e1)) = (e2)) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hbb zenon_H58 zenon_H9 zenon_Hf2. % 40.87/41.10 cut (((op (e2) (unit)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_Hbb. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H58. % 40.87/41.10 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 40.87/41.10 cut (((op (e2) (unit)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 40.87/41.10 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e2) (unit)) = (op (e2) (e0)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H5b. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H5c. % 40.87/41.10 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 40.87/41.10 cut (((op (e2) (e0)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L21_); trivial. % 40.87/41.10 apply zenon_H5d. apply refl_equal. % 40.87/41.10 apply zenon_H5d. apply refl_equal. % 40.87/41.10 apply zenon_Hf3. apply sym_equal. exact zenon_Hf2. % 40.87/41.10 (* end of lemma zenon_L119_ *) % 40.87/41.10 assert (zenon_L120_ : ((op (e2) (unit)) = (e2)) -> ((unit) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H58 zenon_H2a zenon_Hf2 zenon_H6e. % 40.87/41.10 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 40.87/41.10 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e1)) = (op (e2) (e3)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H6e. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H25. % 40.87/41.10 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 40.87/41.10 cut (((op (e2) (e3)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf4]. % 40.87/41.10 congruence. % 40.87/41.10 cut (((op (e2) (unit)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e1)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_Hf4. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H58. % 40.87/41.10 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 40.87/41.10 cut (((op (e2) (unit)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 40.87/41.10 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (unit)) = (op (e2) (e3)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_Hd1. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H25. % 40.87/41.10 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 40.87/41.10 cut (((op (e2) (e3)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L77_); trivial. % 40.87/41.10 apply zenon_H26. apply refl_equal. % 40.87/41.10 apply zenon_H26. apply refl_equal. % 40.87/41.10 apply zenon_Hf3. apply sym_equal. exact zenon_Hf2. % 40.87/41.10 apply zenon_H26. apply refl_equal. % 40.87/41.10 apply zenon_H26. apply refl_equal. % 40.87/41.10 (* end of lemma zenon_L120_ *) % 40.87/41.10 assert (zenon_L121_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_Hbb zenon_H9b zenon_H9a zenon_H99 zenon_H22 zenon_H20 zenon_H1f zenon_H6e zenon_Hf2 zenon_H58 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L119_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L49_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L8_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L120_); trivial. % 40.87/41.10 apply (zenon_L11_); trivial. % 40.87/41.10 (* end of lemma zenon_L121_ *) % 40.87/41.10 assert (zenon_L122_ : (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((unit) = (e3)) -> ((op (e2) (e4)) = (e2)) -> False). % 40.87/41.10 do 0 intro. intros zenon_H1f zenon_H58 zenon_H2a zenon_Hb7. % 40.87/41.10 cut (((op (e2) (unit)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e4)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H1f. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H58. % 40.87/41.10 cut (((e2) = (op (e2) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hb8]. % 40.87/41.10 cut (((op (e2) (unit)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 40.87/41.10 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (unit)) = (op (e2) (e3)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_Hd1. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H25. % 40.87/41.10 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 40.87/41.10 cut (((op (e2) (e3)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L77_); trivial. % 40.87/41.10 apply zenon_H26. apply refl_equal. % 40.87/41.10 apply zenon_H26. apply refl_equal. % 40.87/41.10 apply zenon_Hb8. apply sym_equal. exact zenon_Hb7. % 40.87/41.10 (* end of lemma zenon_L122_ *) % 40.87/41.10 assert (zenon_L123_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> ((op (e2) (e4)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_Hb6 zenon_Hb9 zenon_H22 zenon_H20 zenon_Hb7 zenon_H58 zenon_H1f zenon_H32 zenon_H16 zenon_H34. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L62_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L63_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L8_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L122_); trivial. % 40.87/41.10 apply (zenon_L11_); trivial. % 40.87/41.10 (* end of lemma zenon_L123_ *) % 40.87/41.10 assert (zenon_L124_ : ((op (unit) (e4)) = (e4)) -> ((unit) = (e4)) -> ((op (e4) (e1)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hd3 zenon_H33 zenon_Ha5 zenon_He8. % 40.87/41.10 elim (classic ((op (e4) (e4)) = (op (e4) (e4)))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hd6 ]. % 40.87/41.10 cut (((op (e4) (e4)) = (op (e4) (e4))) = ((op (e4) (e1)) = (op (e4) (e4)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_He8. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_Hd5. % 40.87/41.10 cut (((op (e4) (e4)) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 40.87/41.10 cut (((op (e4) (e4)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 40.87/41.10 congruence. % 40.87/41.10 cut (((op (unit) (e4)) = (e4)) = ((op (e4) (e4)) = (op (e4) (e1)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_Hf5. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_Hd3. % 40.87/41.10 cut (((e4) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 40.87/41.10 cut (((op (unit) (e4)) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e4) (e4)) = (op (e4) (e4)))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hd6 ]. % 40.87/41.10 cut (((op (e4) (e4)) = (op (e4) (e4))) = ((op (unit) (e4)) = (op (e4) (e4)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_Hd8. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_Hd5. % 40.87/41.10 cut (((op (e4) (e4)) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 40.87/41.10 cut (((op (e4) (e4)) = (op (unit) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L79_); trivial. % 40.87/41.10 apply zenon_Hd6. apply refl_equal. % 40.87/41.10 apply zenon_Hd6. apply refl_equal. % 40.87/41.10 apply zenon_Ha6. apply sym_equal. exact zenon_Ha5. % 40.87/41.10 apply zenon_Hd6. apply refl_equal. % 40.87/41.10 apply zenon_Hd6. apply refl_equal. % 40.87/41.10 (* end of lemma zenon_L124_ *) % 40.87/41.10 assert (zenon_L125_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e3) (e4)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e1)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_H32 zenon_H99 zenon_Hbf zenon_Hc zenon_H83 zenon_Hd3 zenon_Ha5 zenon_He8. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L55_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L6_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L58_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L67_); trivial. % 40.87/41.10 apply (zenon_L124_); trivial. % 40.87/41.10 (* end of lemma zenon_L125_ *) % 40.87/41.10 assert (zenon_L126_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (e4) (e3)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (e4) (e1)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hc2 zenon_H2c zenon_H2d zenon_Ha1 zenon_H92 zenon_H91 zenon_Hb1 zenon_Haa zenon_H34 zenon_H1f zenon_H58 zenon_H20 zenon_H22 zenon_Hb9 zenon_Hb6 zenon_He8 zenon_Ha5 zenon_Hd3 zenon_H83 zenon_Hc zenon_H99 zenon_H32 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H3b zenon_Hc3. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.87/41.10 apply (zenon_L53_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.87/41.10 apply (zenon_L61_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.87/41.10 apply (zenon_L123_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.87/41.10 apply (zenon_L125_); trivial. % 40.87/41.10 exact (zenon_Hc3 zenon_Hc7). % 40.87/41.10 (* end of lemma zenon_L126_ *) % 40.87/41.10 assert (zenon_L127_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e3)) = (e4)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_Hcc zenon_Hb1 zenon_H99 zenon_H91 zenon_H6e zenon_Hf2 zenon_H58 zenon_Hd3 zenon_Hcd zenon_Hd4. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L74_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L75_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L76_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L120_); trivial. % 40.87/41.10 apply (zenon_L80_); trivial. % 40.87/41.10 (* end of lemma zenon_L127_ *) % 40.87/41.10 assert (zenon_L128_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hd9 zenon_Hbb zenon_Hc3 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_H83 zenon_He8 zenon_Hb6 zenon_Hb9 zenon_H34 zenon_Haa zenon_Ha1 zenon_H2d zenon_H2c zenon_Hc2 zenon_H92 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_Hc8 zenon_Hd4 zenon_Hd3 zenon_H58 zenon_Hf2 zenon_H6e zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.87/41.10 apply (zenon_L121_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.87/41.10 apply (zenon_L126_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.87/41.10 apply (zenon_L73_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_L127_); trivial. % 40.87/41.10 exact (zenon_Hda zenon_Hde). % 40.87/41.10 (* end of lemma zenon_L128_ *) % 40.87/41.10 assert (zenon_L129_ : ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hed zenon_He6 zenon_He9 zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H17 zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H50 zenon_H51 zenon_H49 zenon_H43 zenon_H42 zenon_H41 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H89 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_He1 zenon_Hd9 zenon_Hcc zenon_Hd4 zenon_Hc8 zenon_H91 zenon_Ha1 zenon_Hb1 zenon_Haa zenon_Hb9 zenon_Hb6 zenon_Hd3 zenon_He8 zenon_Hc3 zenon_Hc2 zenon_Hbb zenon_Hf2 zenon_H9b zenon_H99 zenon_He0. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.87/41.10 apply (zenon_L12_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.87/41.10 apply (zenon_L20_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.87/41.10 apply (zenon_L41_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.87/41.10 exact (zenon_He1 zenon_He5). % 40.87/41.10 apply (zenon_L128_); trivial. % 40.87/41.10 apply (zenon_L99_); trivial. % 40.87/41.10 (* end of lemma zenon_L129_ *) % 40.87/41.10 assert (zenon_L130_ : ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hed zenon_He6 zenon_He8 zenon_H3b zenon_H34 zenon_H16 zenon_H32 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_H8d zenon_H5f zenon_H68 zenon_Hb1 zenon_H73 zenon_Hd3 zenon_He9 zenon_H91 zenon_H77 zenon_Hd4 zenon_Hf2 zenon_H58 zenon_H6e zenon_Hd9. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.87/41.10 apply (zenon_L103_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.87/41.10 apply (zenon_L105_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.87/41.10 apply (zenon_L108_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_L127_); trivial. % 40.87/41.10 exact (zenon_Hda zenon_Hde). % 40.87/41.10 apply (zenon_L99_); trivial. % 40.87/41.10 (* end of lemma zenon_L130_ *) % 40.87/41.10 assert (zenon_L131_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hee zenon_Hed zenon_He6 zenon_He9 zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H17 zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H50 zenon_H51 zenon_H49 zenon_H43 zenon_H42 zenon_H41 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_He1 zenon_Hd9 zenon_Hcc zenon_Hd4 zenon_Hc8 zenon_H91 zenon_Ha1 zenon_Hb1 zenon_Haa zenon_Hb9 zenon_Hb6 zenon_Hd3 zenon_He8 zenon_Hc2 zenon_Hbb zenon_Hf2 zenon_H9b zenon_H99 zenon_He0 zenon_Hf1. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 40.87/41.10 apply (zenon_L129_); trivial. % 40.87/41.10 apply (zenon_L100_); trivial. % 40.87/41.10 apply (zenon_L130_); trivial. % 40.87/41.10 (* end of lemma zenon_L131_ *) % 40.87/41.10 assert (zenon_L132_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hee zenon_Hd9 zenon_H2d zenon_H2c zenon_H17 zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H3b zenon_H34 zenon_H16 zenon_H32 zenon_H68 zenon_H22 zenon_H20 zenon_H1f zenon_H5f zenon_H61 zenon_H59 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 40.87/41.10 apply (zenon_L41_); trivial. % 40.87/41.10 apply (zenon_L110_); trivial. % 40.87/41.10 (* end of lemma zenon_L132_ *) % 40.87/41.10 assert (zenon_L133_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hd9 zenon_Hc8 zenon_H9b zenon_H34 zenon_H16 zenon_H32 zenon_He9 zenon_H77 zenon_Hc zenon_He5 zenon_H1f zenon_H20 zenon_H22 zenon_H9f zenon_H5f zenon_H76 zenon_H8e zenon_Hd4 zenon_Hd3 zenon_H58 zenon_Hf2 zenon_H6e zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.87/41.10 apply (zenon_L85_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.87/41.10 apply (zenon_L113_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.87/41.10 apply (zenon_L115_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_L127_); trivial. % 40.87/41.10 exact (zenon_Hda zenon_Hde). % 40.87/41.10 (* end of lemma zenon_L133_ *) % 40.87/41.10 assert (zenon_L134_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hf0 zenon_H9f zenon_H8e zenon_Hf1 zenon_He0 zenon_H99 zenon_H9b zenon_Hf2 zenon_Hbb zenon_Hc2 zenon_He8 zenon_Hd3 zenon_Hb6 zenon_Hb9 zenon_Haa zenon_Hb1 zenon_Ha1 zenon_H91 zenon_Hc8 zenon_Hd4 zenon_Hcc zenon_Hd9 zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_H41 zenon_H42 zenon_H43 zenon_H49 zenon_H51 zenon_H50 zenon_Hb zenon_Hc zenon_H18 zenon_H16 zenon_H17 zenon_H1f zenon_H20 zenon_H22 zenon_H2d zenon_H2c zenon_H32 zenon_H34 zenon_H3b zenon_He9 zenon_He6 zenon_Hed zenon_Hee. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_He1 | zenon_intro zenon_H76 ]. % 40.87/41.10 apply (zenon_L131_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.87/41.10 apply (zenon_L12_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.87/41.10 apply (zenon_L20_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.87/41.10 apply (zenon_L132_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.87/41.10 apply (zenon_L133_); trivial. % 40.87/41.10 apply (zenon_L128_); trivial. % 40.87/41.10 apply (zenon_L99_); trivial. % 40.87/41.10 apply (zenon_L117_); trivial. % 40.87/41.10 (* end of lemma zenon_L134_ *) % 40.87/41.10 assert (zenon_L135_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hf6 zenon_H18 zenon_Hc zenon_Hb zenon_H50 zenon_H51 zenon_H49 zenon_H43 zenon_H42 zenon_H41 zenon_Ha1 zenon_Haa zenon_Hc2 zenon_Hbb zenon_He0 zenon_Hf1 zenon_H8e zenon_H9f zenon_Hf0 zenon_Hf7 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H61 zenon_H5f zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_H91 zenon_Hd4 zenon_H17 zenon_H2c zenon_H2d zenon_Hd9 zenon_Hee zenon_H3b zenon_Hb6 zenon_Hb9 zenon_H22 zenon_H20 zenon_H58 zenon_H1f zenon_H32 zenon_H16 zenon_H34. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hba | zenon_intro zenon_Hf8 ]. % 40.87/41.10 apply (zenon_L118_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf9 ]. % 40.87/41.10 apply (zenon_L134_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hfa ]. % 40.87/41.10 exact (zenon_Hf7 zenon_Hfb). % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H59 | zenon_intro zenon_Hb7 ]. % 40.87/41.10 apply (zenon_L132_); trivial. % 40.87/41.10 apply (zenon_L123_); trivial. % 40.87/41.10 (* end of lemma zenon_L135_ *) % 40.87/41.10 assert (zenon_L136_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (unit)) = (e2)) -> ((unit) = (e0)) -> ((op (e2) (e2)) = (e2)) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hfc zenon_H58 zenon_H9 zenon_Hfb. % 40.87/41.10 cut (((op (e2) (unit)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e2)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_Hfc. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H58. % 40.87/41.10 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfd]. % 40.87/41.10 cut (((op (e2) (unit)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 40.87/41.10 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e2) (unit)) = (op (e2) (e0)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H5b. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H5c. % 40.87/41.10 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 40.87/41.10 cut (((op (e2) (e0)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L21_); trivial. % 40.87/41.10 apply zenon_H5d. apply refl_equal. % 40.87/41.10 apply zenon_H5d. apply refl_equal. % 40.87/41.10 apply zenon_Hfd. apply sym_equal. exact zenon_Hfb. % 40.87/41.10 (* end of lemma zenon_L136_ *) % 40.87/41.10 assert (zenon_L137_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (unit)) = (e2)) -> ((unit) = (e1)) -> ((op (e2) (e2)) = (e2)) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hfe zenon_H58 zenon_H14 zenon_Hfb. % 40.87/41.10 cut (((op (e2) (unit)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e2)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_Hfe. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H58. % 40.87/41.10 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfd]. % 40.87/41.10 cut (((op (e2) (unit)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H70 | zenon_intro zenon_H71 ]. % 40.87/41.10 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (unit)) = (op (e2) (e1)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H6f. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H70. % 40.87/41.10 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 40.87/41.10 cut (((op (e2) (e1)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L28_); trivial. % 40.87/41.10 apply zenon_H71. apply refl_equal. % 40.87/41.10 apply zenon_H71. apply refl_equal. % 40.87/41.10 apply zenon_Hfd. apply sym_equal. exact zenon_Hfb. % 40.87/41.10 (* end of lemma zenon_L137_ *) % 40.87/41.10 assert (zenon_L138_ : ((op (e2) (unit)) = (e2)) -> ((unit) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H58 zenon_H2a zenon_Hfb zenon_Hff. % 40.87/41.10 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 40.87/41.10 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e2)) = (op (e2) (e3)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_Hff. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H25. % 40.87/41.10 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 40.87/41.10 cut (((op (e2) (e3)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 40.87/41.10 congruence. % 40.87/41.10 cut (((op (e2) (unit)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e2)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H100. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H58. % 40.87/41.10 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfd]. % 40.87/41.10 cut (((op (e2) (unit)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 40.87/41.10 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (unit)) = (op (e2) (e3)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_Hd1. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H25. % 40.87/41.10 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 40.87/41.10 cut (((op (e2) (e3)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L77_); trivial. % 40.87/41.10 apply zenon_H26. apply refl_equal. % 40.87/41.10 apply zenon_H26. apply refl_equal. % 40.87/41.10 apply zenon_Hfd. apply sym_equal. exact zenon_Hfb. % 40.87/41.10 apply zenon_H26. apply refl_equal. % 40.87/41.10 apply zenon_H26. apply refl_equal. % 40.87/41.10 (* end of lemma zenon_L138_ *) % 40.87/41.10 assert (zenon_L139_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_Hfc zenon_Hfe zenon_H22 zenon_H20 zenon_H1f zenon_Hff zenon_Hfb zenon_H58 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L136_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L137_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L8_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L138_); trivial. % 40.87/41.10 apply (zenon_L11_); trivial. % 40.87/41.10 (* end of lemma zenon_L139_ *) % 40.87/41.10 assert (zenon_L140_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H101 zenon_Hfc zenon_Hfe zenon_Hff zenon_Hf0 zenon_Hf1 zenon_He0 zenon_H91 zenon_H8e zenon_Hd9 zenon_Hcc zenon_Hd4 zenon_Hd3 zenon_Hc8 zenon_Ha1 zenon_Hb1 zenon_Haa zenon_Hb9 zenon_Hb6 zenon_Hbb zenon_Hc2 zenon_H9b zenon_H99 zenon_H9f zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_H41 zenon_H42 zenon_H43 zenon_H49 zenon_H51 zenon_H50 zenon_Hb zenon_Hc zenon_H18 zenon_H16 zenon_H17 zenon_H1f zenon_H20 zenon_H22 zenon_H2d zenon_H2c zenon_H32 zenon_H34 zenon_H3b zenon_He9 zenon_He8 zenon_He6 zenon_Hed zenon_Hee zenon_Hf6. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hfb ]. % 40.87/41.10 apply (zenon_L135_); trivial. % 40.87/41.10 apply (zenon_L139_); trivial. % 40.87/41.10 (* end of lemma zenon_L140_ *) % 40.87/41.10 assert (zenon_L141_ : (~((op (e1) (e0)) = (op (e1) (unit)))) -> ((unit) = (e0)) -> False). % 40.87/41.10 do 0 intro. intros zenon_H102 zenon_H9. % 40.87/41.10 cut (((e0) = (unit))); [idtac | apply NNPP; zenon_intro zenon_Ha]. % 40.87/41.10 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 40.87/41.10 congruence. % 40.87/41.10 apply zenon_H12. apply refl_equal. % 40.87/41.10 apply zenon_Ha. apply sym_equal. exact zenon_H9. % 40.87/41.10 (* end of lemma zenon_L141_ *) % 40.87/41.10 assert (zenon_L142_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (unit)) = (e1)) -> ((unit) = (e0)) -> ((op (e1) (e2)) = (e1)) -> False). % 40.87/41.10 do 0 intro. intros zenon_H103 zenon_H2c zenon_H9 zenon_H104. % 40.87/41.10 cut (((op (e1) (unit)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e2)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H103. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H2c. % 40.87/41.10 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 40.87/41.10 cut (((op (e1) (unit)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H107 | zenon_intro zenon_H108 ]. % 40.87/41.10 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (unit)) = (op (e1) (e0)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H106. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H107. % 40.87/41.10 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 40.87/41.10 cut (((op (e1) (e0)) = (op (e1) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L141_); trivial. % 40.87/41.10 apply zenon_H108. apply refl_equal. % 40.87/41.10 apply zenon_H108. apply refl_equal. % 40.87/41.10 apply zenon_H105. apply sym_equal. exact zenon_H104. % 40.87/41.10 (* end of lemma zenon_L142_ *) % 40.87/41.10 assert (zenon_L143_ : (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((unit) = (e1)) -> ((op (e1) (e2)) = (e1)) -> False). % 40.87/41.10 do 0 intro. intros zenon_H109 zenon_H16 zenon_H14 zenon_H104. % 40.87/41.10 cut (((op (unit) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e2)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H109. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H16. % 40.87/41.10 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 40.87/41.10 cut (((op (unit) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H19 | zenon_intro zenon_H1a ]. % 40.87/41.10 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (unit) (e1)) = (op (e1) (e1)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H1d. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H19. % 40.87/41.10 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 40.87/41.10 cut (((op (e1) (e1)) = (op (unit) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L5_); trivial. % 40.87/41.10 apply zenon_H1a. apply refl_equal. % 40.87/41.10 apply zenon_H1a. apply refl_equal. % 40.87/41.10 apply zenon_H105. apply sym_equal. exact zenon_H104. % 40.87/41.10 (* end of lemma zenon_L143_ *) % 40.87/41.10 assert (zenon_L144_ : ((op (e1) (unit)) = (e1)) -> ((unit) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H2c zenon_H2a zenon_H104 zenon_H49. % 40.87/41.10 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 40.87/41.10 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e2)) = (op (e1) (e3)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H49. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H2e. % 40.87/41.10 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 40.87/41.10 cut (((op (e1) (e3)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 40.87/41.10 congruence. % 40.87/41.10 cut (((op (e1) (unit)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e2)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H10a. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H2c. % 40.87/41.10 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 40.87/41.10 cut (((op (e1) (unit)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 40.87/41.10 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (unit)) = (op (e1) (e3)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H31. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H2e. % 40.87/41.10 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 40.87/41.10 cut (((op (e1) (e3)) = (op (e1) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L9_); trivial. % 40.87/41.10 apply zenon_H2f. apply refl_equal. % 40.87/41.10 apply zenon_H2f. apply refl_equal. % 40.87/41.10 apply zenon_H105. apply sym_equal. exact zenon_H104. % 40.87/41.10 apply zenon_H2f. apply refl_equal. % 40.87/41.10 apply zenon_H2f. apply refl_equal. % 40.87/41.10 (* end of lemma zenon_L144_ *) % 40.87/41.10 assert (zenon_L145_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_H103 zenon_H109 zenon_H22 zenon_H20 zenon_H1f zenon_H49 zenon_H104 zenon_H2c zenon_H32 zenon_H16 zenon_H34. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L142_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L143_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L8_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L144_); trivial. % 40.87/41.10 apply (zenon_L11_); trivial. % 40.87/41.10 (* end of lemma zenon_L145_ *) % 40.87/41.10 assert (zenon_L146_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (unit) (e0)) = (e0)) -> ((unit) = (e0)) -> ((op (e0) (e2)) = (e0)) -> False). % 40.87/41.10 do 0 intro. intros zenon_H10b zenon_H42 zenon_H9 zenon_H10c. % 40.87/41.10 cut (((op (unit) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e0) (e2)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H10b. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H42. % 40.87/41.10 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 40.87/41.10 cut (((op (unit) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e0) (e0)) = (op (e0) (e0)))); [ zenon_intro zenon_H46 | zenon_intro zenon_H47 ]. % 40.87/41.10 cut (((op (e0) (e0)) = (op (e0) (e0))) = ((op (unit) (e0)) = (op (e0) (e0)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H45. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H46. % 40.87/41.10 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 40.87/41.10 cut (((op (e0) (e0)) = (op (unit) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L14_); trivial. % 40.87/41.10 apply zenon_H47. apply refl_equal. % 40.87/41.10 apply zenon_H47. apply refl_equal. % 40.87/41.10 apply zenon_H10d. apply sym_equal. exact zenon_H10c. % 40.87/41.10 (* end of lemma zenon_L146_ *) % 40.87/41.10 assert (zenon_L147_ : ((op (e0) (unit)) = (e0)) -> ((unit) = (e3)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H50 zenon_H2a zenon_H10c zenon_Hb. % 40.87/41.10 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 40.87/41.10 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e2)) = (op (e0) (e3)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_Hb. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H52. % 40.87/41.10 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 40.87/41.10 cut (((op (e0) (e3)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10e]. % 40.87/41.10 congruence. % 40.87/41.10 cut (((op (e0) (unit)) = (e0)) = ((op (e0) (e3)) = (op (e0) (e2)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H10e. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H50. % 40.87/41.10 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 40.87/41.10 cut (((op (e0) (unit)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 40.87/41.10 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (unit)) = (op (e0) (e3)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H55. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H52. % 40.87/41.10 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 40.87/41.10 cut (((op (e0) (e3)) = (op (e0) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L18_); trivial. % 40.87/41.10 apply zenon_H53. apply refl_equal. % 40.87/41.10 apply zenon_H53. apply refl_equal. % 40.87/41.10 apply zenon_H10d. apply sym_equal. exact zenon_H10c. % 40.87/41.10 apply zenon_H53. apply refl_equal. % 40.87/41.10 apply zenon_H53. apply refl_equal. % 40.87/41.10 (* end of lemma zenon_L147_ *) % 40.87/41.10 assert (zenon_L148_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_H42 zenon_H10b zenon_H4a zenon_Hc zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_Hb zenon_H10c zenon_H50 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L146_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L17_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L8_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L147_); trivial. % 40.87/41.10 apply (zenon_L11_); trivial. % 40.87/41.10 (* end of lemma zenon_L148_ *) % 40.87/41.10 assert (zenon_L149_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_H42 zenon_H10b zenon_H18 zenon_H17 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_Hb zenon_H10c zenon_H50 zenon_H91 zenon_Hc zenon_H92. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L146_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L6_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L8_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L147_); trivial. % 40.87/41.10 apply (zenon_L44_); trivial. % 40.87/41.10 (* end of lemma zenon_L149_ *) % 40.87/41.10 assert (zenon_L150_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.87/41.10 do 0 intro. intros zenon_He0 zenon_H2c zenon_H2d zenon_H49 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_H32 zenon_H34 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H3b zenon_H42 zenon_H10b zenon_H18 zenon_H17 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_Hb zenon_H10c zenon_H50 zenon_H91 zenon_Hc. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.87/41.10 apply (zenon_L12_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.87/41.10 apply (zenon_L148_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.87/41.10 apply (zenon_L112_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.87/41.10 exact (zenon_He1 zenon_He5). % 40.87/41.10 apply (zenon_L149_); trivial. % 40.87/41.10 (* end of lemma zenon_L150_ *) % 40.87/41.10 assert (zenon_L151_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hf0 zenon_H8e zenon_H9f zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H17 zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H50 zenon_H49 zenon_H10c zenon_H42 zenon_H10b zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_He0. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_He1 | zenon_intro zenon_H76 ]. % 40.87/41.10 apply (zenon_L150_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.87/41.10 apply (zenon_L12_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.87/41.10 apply (zenon_L148_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.87/41.10 apply (zenon_L112_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.87/41.10 apply (zenon_L116_); trivial. % 40.87/41.10 apply (zenon_L149_); trivial. % 40.87/41.10 apply (zenon_L99_); trivial. % 40.87/41.10 (* end of lemma zenon_L151_ *) % 40.87/41.10 assert (zenon_L152_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hee zenon_Hd9 zenon_Hf2 zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H3b zenon_H34 zenon_H16 zenon_H32 zenon_H68 zenon_H22 zenon_H20 zenon_H1f zenon_H5f zenon_H61 zenon_H59 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 40.87/41.10 apply (zenon_L41_); trivial. % 40.87/41.10 apply (zenon_L130_); trivial. % 40.87/41.10 (* end of lemma zenon_L152_ *) % 40.87/41.10 assert (zenon_L153_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.87/41.10 do 0 intro. intros zenon_He0 zenon_H2c zenon_H2d zenon_H49 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_H32 zenon_H34 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hf2 zenon_Hd9 zenon_Hee zenon_He1 zenon_H3b zenon_H42 zenon_H10b zenon_H18 zenon_H17 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_Hb zenon_H10c zenon_H50 zenon_H91 zenon_Hc. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.87/41.10 apply (zenon_L12_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.87/41.10 apply (zenon_L148_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.87/41.10 apply (zenon_L152_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.87/41.10 exact (zenon_He1 zenon_He5). % 40.87/41.10 apply (zenon_L149_); trivial. % 40.87/41.10 (* end of lemma zenon_L153_ *) % 40.87/41.10 assert (zenon_L154_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hf0 zenon_H8e zenon_H9f zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H17 zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H50 zenon_H49 zenon_H10c zenon_H42 zenon_H10b zenon_Hee zenon_Hd9 zenon_Hf2 zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_He0. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_He1 | zenon_intro zenon_H76 ]. % 40.87/41.10 apply (zenon_L153_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.87/41.10 apply (zenon_L12_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.87/41.10 apply (zenon_L148_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.87/41.10 apply (zenon_L152_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.87/41.10 apply (zenon_L133_); trivial. % 40.87/41.10 apply (zenon_L149_); trivial. % 40.87/41.10 apply (zenon_L99_); trivial. % 40.87/41.10 (* end of lemma zenon_L154_ *) % 40.87/41.10 assert (zenon_L155_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H101 zenon_Hfc zenon_Hfe zenon_Hff zenon_Hf0 zenon_H8e zenon_H9f zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H17 zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H50 zenon_H49 zenon_H10c zenon_H42 zenon_H10b zenon_Hee zenon_Hd9 zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_He0 zenon_Hb9 zenon_Hb6 zenon_Hf6. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hfb ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hba | zenon_intro zenon_Hf8 ]. % 40.87/41.10 apply (zenon_L151_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf9 ]. % 40.87/41.10 apply (zenon_L154_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hfa ]. % 40.87/41.10 exact (zenon_Hf7 zenon_Hfb). % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H59 | zenon_intro zenon_Hb7 ]. % 40.87/41.10 apply (zenon_L132_); trivial. % 40.87/41.10 apply (zenon_L123_); trivial. % 40.87/41.10 apply (zenon_L139_); trivial. % 40.87/41.10 (* end of lemma zenon_L155_ *) % 40.87/41.10 assert (zenon_L156_ : (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> ((unit) = (e0)) -> ((op (e1) (e3)) = (e1)) -> False). % 40.87/41.10 do 0 intro. intros zenon_H2d zenon_H2c zenon_H9 zenon_H10f. % 40.87/41.10 cut (((op (e1) (unit)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e3)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H2d. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H2c. % 40.87/41.10 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 40.87/41.10 cut (((op (e1) (unit)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H107 | zenon_intro zenon_H108 ]. % 40.87/41.10 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (unit)) = (op (e1) (e0)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H106. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H107. % 40.87/41.10 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 40.87/41.10 cut (((op (e1) (e0)) = (op (e1) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L141_); trivial. % 40.87/41.10 apply zenon_H108. apply refl_equal. % 40.87/41.10 apply zenon_H108. apply refl_equal. % 40.87/41.10 apply zenon_H110. apply sym_equal. exact zenon_H10f. % 40.87/41.10 (* end of lemma zenon_L156_ *) % 40.87/41.10 assert (zenon_L157_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_H10f zenon_H2c zenon_H2d zenon_Hbb zenon_H22 zenon_H20 zenon_H1f zenon_H57 zenon_Hba zenon_H58 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L156_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L65_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L8_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L78_); trivial. % 40.87/41.10 apply (zenon_L11_); trivial. % 40.87/41.10 (* end of lemma zenon_L157_ *) % 40.87/41.10 assert (zenon_L158_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (unit) (e1)) = (e1)) -> ((unit) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 40.87/41.10 do 0 intro. intros zenon_H111 zenon_H16 zenon_H14 zenon_H10f. % 40.87/41.10 cut (((op (unit) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e3)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H111. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H16. % 40.87/41.10 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 40.87/41.10 cut (((op (unit) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H19 | zenon_intro zenon_H1a ]. % 40.87/41.10 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (unit) (e1)) = (op (e1) (e1)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H1d. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H19. % 40.87/41.10 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 40.87/41.10 cut (((op (e1) (e1)) = (op (unit) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L5_); trivial. % 40.87/41.10 apply zenon_H1a. apply refl_equal. % 40.87/41.10 apply zenon_H1a. apply refl_equal. % 40.87/41.10 apply zenon_H110. apply sym_equal. exact zenon_H10f. % 40.87/41.10 (* end of lemma zenon_L158_ *) % 40.87/41.10 assert (zenon_L159_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_H2c zenon_H2d zenon_H10f zenon_H111 zenon_H22 zenon_H20 zenon_H1f zenon_H6e zenon_Hf2 zenon_H58 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L156_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L158_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L8_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L120_); trivial. % 40.87/41.10 apply (zenon_L11_); trivial. % 40.87/41.10 (* end of lemma zenon_L159_ *) % 40.87/41.10 assert (zenon_L160_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e3)) = (e4)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_H2c zenon_H2d zenon_H10f zenon_H16 zenon_H111 zenon_H8d zenon_H5f zenon_H77 zenon_Hb zenon_H10c zenon_H50 zenon_Hd3 zenon_Hcd zenon_Hd4. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L156_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L158_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L106_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L147_); trivial. % 40.87/41.10 apply (zenon_L80_); trivial. % 40.87/41.10 (* end of lemma zenon_L160_ *) % 40.87/41.10 assert (zenon_L161_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hee zenon_Hd9 zenon_H2d zenon_H2c zenon_H10f zenon_H111 zenon_Hb zenon_H50 zenon_H10c zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H3b zenon_H34 zenon_H16 zenon_H32 zenon_H68 zenon_H22 zenon_H20 zenon_H1f zenon_H5f zenon_H61 zenon_H59 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 40.87/41.10 apply (zenon_L41_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.87/41.10 apply (zenon_L103_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.87/41.10 apply (zenon_L105_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.87/41.10 apply (zenon_L108_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.87/41.10 apply (zenon_L160_); trivial. % 40.87/41.10 exact (zenon_Hda zenon_Hde). % 40.87/41.10 apply (zenon_L99_); trivial. % 40.87/41.10 (* end of lemma zenon_L161_ *) % 40.87/41.10 assert (zenon_L162_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.10 do 0 intro. intros zenon_Hf6 zenon_Hbb zenon_Hf7 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H61 zenon_H5f zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_H91 zenon_Hd4 zenon_H10c zenon_H50 zenon_Hb zenon_H111 zenon_H10f zenon_H2c zenon_H2d zenon_Hd9 zenon_Hee zenon_H3b zenon_Hb6 zenon_Hb9 zenon_H22 zenon_H20 zenon_H58 zenon_H1f zenon_H32 zenon_H16 zenon_H34. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hba | zenon_intro zenon_Hf8 ]. % 40.87/41.10 apply (zenon_L157_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf9 ]. % 40.87/41.10 apply (zenon_L159_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hfa ]. % 40.87/41.10 exact (zenon_Hf7 zenon_Hfb). % 40.87/41.10 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H59 | zenon_intro zenon_Hb7 ]. % 40.87/41.10 apply (zenon_L161_); trivial. % 40.87/41.10 apply (zenon_L123_); trivial. % 40.87/41.10 (* end of lemma zenon_L162_ *) % 40.87/41.10 assert (zenon_L163_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H101 zenon_Hfc zenon_Hfe zenon_Hff zenon_H3b zenon_H34 zenon_H16 zenon_H32 zenon_H57 zenon_H22 zenon_H20 zenon_H1f zenon_H58 zenon_Hbb zenon_H10f zenon_H2c zenon_H2d zenon_H6e zenon_H111 zenon_Hee zenon_Hd9 zenon_Hb zenon_H50 zenon_H10c zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H73 zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_Hb9 zenon_Hb6 zenon_Hf6. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hfb ]. % 40.87/41.10 apply (zenon_L162_); trivial. % 40.87/41.10 apply (zenon_L139_); trivial. % 40.87/41.10 (* end of lemma zenon_L163_ *) % 40.87/41.10 assert (zenon_L164_ : (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((unit) = (e0)) -> ((op (e1) (e4)) = (e1)) -> False). % 40.87/41.10 do 0 intro. intros zenon_H112 zenon_H2c zenon_H9 zenon_H113. % 40.87/41.10 cut (((op (e1) (unit)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e4)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H112. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H2c. % 40.87/41.10 cut (((e1) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 40.87/41.10 cut (((op (e1) (unit)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H107 | zenon_intro zenon_H108 ]. % 40.87/41.10 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (unit)) = (op (e1) (e0)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H106. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H107. % 40.87/41.10 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 40.87/41.10 cut (((op (e1) (e0)) = (op (e1) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L141_); trivial. % 40.87/41.10 apply zenon_H108. apply refl_equal. % 40.87/41.10 apply zenon_H108. apply refl_equal. % 40.87/41.10 apply zenon_H114. apply sym_equal. exact zenon_H113. % 40.87/41.10 (* end of lemma zenon_L164_ *) % 40.87/41.10 assert (zenon_L165_ : (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((unit) = (e1)) -> ((op (e1) (e4)) = (e1)) -> False). % 40.87/41.10 do 0 intro. intros zenon_H115 zenon_H16 zenon_H14 zenon_H113. % 40.87/41.10 cut (((op (unit) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e4)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H115. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H16. % 40.87/41.10 cut (((e1) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 40.87/41.10 cut (((op (unit) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H19 | zenon_intro zenon_H1a ]. % 40.87/41.10 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (unit) (e1)) = (op (e1) (e1)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H1d. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H19. % 40.87/41.10 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 40.87/41.10 cut (((op (e1) (e1)) = (op (unit) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L5_); trivial. % 40.87/41.10 apply zenon_H1a. apply refl_equal. % 40.87/41.10 apply zenon_H1a. apply refl_equal. % 40.87/41.10 apply zenon_H114. apply sym_equal. exact zenon_H113. % 40.87/41.10 (* end of lemma zenon_L165_ *) % 40.87/41.10 assert (zenon_L166_ : (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((unit) = (e3)) -> ((op (e1) (e4)) = (e1)) -> False). % 40.87/41.10 do 0 intro. intros zenon_H116 zenon_H2c zenon_H2a zenon_H113. % 40.87/41.10 cut (((op (e1) (unit)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e4)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H116. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H2c. % 40.87/41.10 cut (((e1) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 40.87/41.10 cut (((op (e1) (unit)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 40.87/41.10 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (unit)) = (op (e1) (e3)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H31. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H2e. % 40.87/41.10 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 40.87/41.10 cut (((op (e1) (e3)) = (op (e1) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L9_); trivial. % 40.87/41.10 apply zenon_H2f. apply refl_equal. % 40.87/41.10 apply zenon_H2f. apply refl_equal. % 40.87/41.10 apply zenon_H114. apply sym_equal. exact zenon_H113. % 40.87/41.10 (* end of lemma zenon_L166_ *) % 40.87/41.10 assert (zenon_L167_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e1) (e4)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_H112 zenon_H115 zenon_H22 zenon_H20 zenon_H1f zenon_H113 zenon_H2c zenon_H116 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L164_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L165_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L8_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L166_); trivial. % 40.87/41.10 apply (zenon_L11_); trivial. % 40.87/41.10 (* end of lemma zenon_L167_ *) % 40.87/41.10 assert (zenon_L168_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e3)) = (e1))\/((op (e1) (e4)) = (e1)))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (unit) (e0)) = (e0)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H117 zenon_He0 zenon_H10b zenon_H42 zenon_Hc zenon_H18 zenon_H9f zenon_H8e zenon_Hf0 zenon_H118 zenon_H49 zenon_H109 zenon_H103 zenon_Hf6 zenon_Hb6 zenon_Hb9 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H73 zenon_H61 zenon_H5f zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_H91 zenon_Hd4 zenon_H10c zenon_H50 zenon_Hb zenon_Hd9 zenon_Hee zenon_H111 zenon_H6e zenon_H2d zenon_Hbb zenon_H58 zenon_H57 zenon_Hff zenon_Hfe zenon_Hfc zenon_H101 zenon_H3b zenon_H112 zenon_H115 zenon_H22 zenon_H20 zenon_H1f zenon_H2c zenon_H116 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H17 | zenon_intro zenon_H119 ]. % 40.87/41.10 apply (zenon_L155_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H11b | zenon_intro zenon_H11a ]. % 40.87/41.10 exact (zenon_H118 zenon_H11b). % 40.87/41.10 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H104 | zenon_intro zenon_H11c ]. % 40.87/41.10 apply (zenon_L145_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H10f | zenon_intro zenon_H113 ]. % 40.87/41.10 apply (zenon_L163_); trivial. % 40.87/41.10 apply (zenon_L167_); trivial. % 40.87/41.10 (* end of lemma zenon_L168_ *) % 40.87/41.10 assert (zenon_L169_ : (~((op (op (e4) (e2)) (op (e4) (e2))) = (op (e1) (e1)))) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H11d zenon_H34. % 40.87/41.10 cut (((op (e4) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 40.87/41.10 cut (((op (e4) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 40.87/41.10 congruence. % 40.87/41.10 apply zenon_H11e. apply sym_equal. exact zenon_H34. % 40.87/41.10 apply zenon_H11e. apply sym_equal. exact zenon_H34. % 40.87/41.10 (* end of lemma zenon_L169_ *) % 40.87/41.10 assert (zenon_L170_ : ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H11f zenon_H120 zenon_H34 zenon_H109. % 40.87/41.10 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 40.87/41.10 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e1)) = (op (e1) (e2)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H109. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H4d. % 40.87/41.10 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 40.87/41.10 cut (((op (e1) (e2)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 40.87/41.10 congruence. % 40.87/41.10 cut (((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) = ((op (e1) (e2)) = (op (e1) (e1)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H121. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H11f. % 40.87/41.10 cut (((op (op (e4) (e2)) (op (e4) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 40.87/41.10 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 40.87/41.10 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((e0) = (op (e1) (e2)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H122. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H4d. % 40.87/41.10 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 40.87/41.10 cut (((op (e1) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 40.87/41.10 congruence. % 40.87/41.10 exact (zenon_H123 zenon_H120). % 40.87/41.10 apply zenon_H4e. apply refl_equal. % 40.87/41.10 apply zenon_H4e. apply refl_equal. % 40.87/41.10 apply (zenon_L169_); trivial. % 40.87/41.10 apply zenon_H4e. apply refl_equal. % 40.87/41.10 apply zenon_H4e. apply refl_equal. % 40.87/41.10 (* end of lemma zenon_L170_ *) % 40.87/41.10 assert (zenon_L171_ : (~((op (e3) (e0)) = (op (unit) (e0)))) -> ((unit) = (e3)) -> False). % 40.87/41.10 do 0 intro. intros zenon_H124 zenon_H2a. % 40.87/41.10 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 40.87/41.10 cut (((e3) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 40.87/41.10 congruence. % 40.87/41.10 apply zenon_H2b. apply sym_equal. exact zenon_H2a. % 40.87/41.10 apply zenon_H3f. apply refl_equal. % 40.87/41.10 (* end of lemma zenon_L171_ *) % 40.87/41.10 assert (zenon_L172_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (unit) (e0)) = (e0)) -> ((unit) = (e3)) -> ((op (e3) (e2)) = (e0)) -> False). % 40.87/41.10 do 0 intro. intros zenon_H8e zenon_H42 zenon_H2a zenon_H125. % 40.87/41.10 cut (((op (unit) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H8e. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H42. % 40.87/41.10 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H126]. % 40.87/41.10 cut (((op (unit) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H127]. % 40.87/41.10 congruence. % 40.87/41.10 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H7f | zenon_intro zenon_H80 ]. % 40.87/41.10 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (unit) (e0)) = (op (e3) (e0)))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H127. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H7f. % 40.87/41.10 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 40.87/41.10 cut (((op (e3) (e0)) = (op (unit) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 40.87/41.10 congruence. % 40.87/41.10 apply (zenon_L171_); trivial. % 40.87/41.10 apply zenon_H80. apply refl_equal. % 40.87/41.10 apply zenon_H80. apply refl_equal. % 40.87/41.10 apply zenon_H126. apply sym_equal. exact zenon_H125. % 40.87/41.10 (* end of lemma zenon_L172_ *) % 40.87/41.10 assert (zenon_L173_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e2)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H3b zenon_H2c zenon_H2d zenon_H10f zenon_H111 zenon_H22 zenon_H20 zenon_H1f zenon_H125 zenon_H42 zenon_H8e zenon_H32 zenon_H16 zenon_H34. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.10 apply (zenon_L156_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.10 apply (zenon_L158_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.10 apply (zenon_L8_); trivial. % 40.87/41.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.10 apply (zenon_L172_); trivial. % 40.87/41.10 apply (zenon_L11_); trivial. % 40.87/41.10 (* end of lemma zenon_L173_ *) % 40.87/41.10 assert (zenon_L174_ : ((e1) = (op (e4) (e2))) -> ((op (e4) (e2)) = (e0)) -> (~((e0) = (e1))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H34 zenon_H128 zenon_H129. % 40.87/41.10 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12 ]. % 40.87/41.10 cut (((e1) = (e1)) = ((e0) = (e1))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H129. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H12a. % 40.87/41.10 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 40.87/41.10 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 40.87/41.10 congruence. % 40.87/41.10 cut (((e1) = (op (e4) (e2))) = ((e1) = (e0))). % 40.87/41.10 intro zenon_D_pnotp. % 40.87/41.10 apply zenon_H12b. % 40.87/41.10 rewrite <- zenon_D_pnotp. % 40.87/41.10 exact zenon_H34. % 40.87/41.10 cut (((op (e4) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 40.87/41.10 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 40.87/41.10 congruence. % 40.87/41.10 apply zenon_H12. apply refl_equal. % 40.87/41.10 exact (zenon_H12c zenon_H128). % 40.87/41.10 apply zenon_H12. apply refl_equal. % 40.87/41.10 apply zenon_H12. apply refl_equal. % 40.87/41.10 (* end of lemma zenon_L174_ *) % 40.87/41.10 assert (zenon_L175_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e4) (e2)) = (e0)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e3)) = (e1))\/((op (e1) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((e0) = (e1))) -> False). % 40.87/41.10 do 0 intro. intros zenon_H12d zenon_H116 zenon_H115 zenon_H112 zenon_H101 zenon_Hfc zenon_Hfe zenon_Hff zenon_H57 zenon_H58 zenon_Hbb zenon_H6e zenon_Hee zenon_Hd9 zenon_Hb zenon_H50 zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H73 zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_Hb9 zenon_Hb6 zenon_Hf6 zenon_H103 zenon_H49 zenon_H118 zenon_Hf0 zenon_H9f zenon_H18 zenon_Hc zenon_H10b zenon_He0 zenon_H117 zenon_H109 zenon_H11f zenon_H12e zenon_H16 zenon_H32 zenon_H8e zenon_H42 zenon_H1f zenon_H20 zenon_H22 zenon_H111 zenon_H10f zenon_H2d zenon_H2c zenon_H3b zenon_H34 zenon_H129. % 40.87/41.11 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H10c | zenon_intro zenon_H12f ]. % 40.87/41.11 apply (zenon_L168_); trivial. % 40.87/41.11 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H120 | zenon_intro zenon_H130 ]. % 40.87/41.11 apply (zenon_L170_); trivial. % 40.87/41.11 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H132 | zenon_intro zenon_H131 ]. % 40.87/41.11 exact (zenon_H12e zenon_H132). % 40.87/41.11 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H125 | zenon_intro zenon_H128 ]. % 40.87/41.11 apply (zenon_L173_); trivial. % 40.87/41.11 apply (zenon_L174_); trivial. % 40.87/41.11 (* end of lemma zenon_L175_ *) % 40.87/41.11 assert (zenon_L176_ : (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e3)) = (e1))\/((op (e1) (e4)) = (e1)))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e4) (e2)) = (e0)))))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.11 do 0 intro. intros zenon_H51 zenon_H43 zenon_H41 zenon_Hc2 zenon_Haa zenon_Ha1 zenon_Hf1 zenon_H129 zenon_H2d zenon_H111 zenon_H42 zenon_H8e zenon_H12e zenon_H11f zenon_H109 zenon_H117 zenon_He0 zenon_H10b zenon_Hc zenon_H18 zenon_H9f zenon_Hf0 zenon_H118 zenon_H49 zenon_H103 zenon_Hf6 zenon_Hb6 zenon_Hb9 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H73 zenon_H61 zenon_H5f zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_H91 zenon_Hd4 zenon_H50 zenon_Hb zenon_Hd9 zenon_Hee zenon_H6e zenon_Hbb zenon_H58 zenon_H57 zenon_Hff zenon_Hfe zenon_Hfc zenon_H101 zenon_H12d zenon_H3b zenon_H112 zenon_H115 zenon_H22 zenon_H20 zenon_H1f zenon_H2c zenon_H116 zenon_H32 zenon_H16 zenon_H34. % 40.87/41.11 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H17 | zenon_intro zenon_H119 ]. % 40.87/41.11 apply (zenon_L140_); trivial. % 40.87/41.11 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H11b | zenon_intro zenon_H11a ]. % 40.87/41.11 exact (zenon_H118 zenon_H11b). % 40.87/41.11 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H104 | zenon_intro zenon_H11c ]. % 40.87/41.11 apply (zenon_L145_); trivial. % 40.87/41.11 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H10f | zenon_intro zenon_H113 ]. % 40.87/41.11 apply (zenon_L175_); trivial. % 40.87/41.11 apply (zenon_L167_); trivial. % 40.87/41.11 (* end of lemma zenon_L176_ *) % 40.87/41.11 assert (zenon_L177_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.87/41.11 do 0 intro. intros zenon_H3b zenon_H103 zenon_Hbb zenon_Hba zenon_H58 zenon_H22 zenon_H20 zenon_H1f zenon_H49 zenon_H104 zenon_H2c zenon_H32 zenon_H16 zenon_H34. % 40.87/41.11 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.87/41.11 apply (zenon_L142_); trivial. % 40.87/41.11 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.87/41.11 apply (zenon_L65_); trivial. % 40.87/41.11 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.87/41.11 apply (zenon_L8_); trivial. % 40.87/41.11 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.87/41.11 apply (zenon_L144_); trivial. % 40.87/41.11 apply (zenon_L11_); trivial. % 40.87/41.11 (* end of lemma zenon_L177_ *) % 40.87/41.11 assert (zenon_L178_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e1) (e4)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H3b zenon_H113 zenon_H2c zenon_H112 zenon_Hbb zenon_H22 zenon_H20 zenon_H1f zenon_H57 zenon_Hba zenon_H58 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.11 apply (zenon_L164_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.11 apply (zenon_L65_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.11 apply (zenon_L8_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.11 apply (zenon_L78_); trivial. % 40.94/41.11 apply (zenon_L11_); trivial. % 40.94/41.11 (* end of lemma zenon_L178_ *) % 40.94/41.11 assert (zenon_L179_ : (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (unit)) = (e1)) -> ((unit) = (e0)) -> ((op (e1) (e1)) = (e1)) -> False). % 40.94/41.11 do 0 intro. intros zenon_H18 zenon_H2c zenon_H9 zenon_H11b. % 40.94/41.11 cut (((op (e1) (unit)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e1)))). % 40.94/41.11 intro zenon_D_pnotp. % 40.94/41.11 apply zenon_H18. % 40.94/41.11 rewrite <- zenon_D_pnotp. % 40.94/41.11 exact zenon_H2c. % 40.94/41.11 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 40.94/41.11 cut (((op (e1) (unit)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 40.94/41.11 congruence. % 40.94/41.11 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H107 | zenon_intro zenon_H108 ]. % 40.94/41.11 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (unit)) = (op (e1) (e0)))). % 40.94/41.11 intro zenon_D_pnotp. % 40.94/41.11 apply zenon_H106. % 40.94/41.11 rewrite <- zenon_D_pnotp. % 40.94/41.11 exact zenon_H107. % 40.94/41.11 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 40.94/41.11 cut (((op (e1) (e0)) = (op (e1) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 40.94/41.11 congruence. % 40.94/41.11 apply (zenon_L141_); trivial. % 40.94/41.11 apply zenon_H108. apply refl_equal. % 40.94/41.11 apply zenon_H108. apply refl_equal. % 40.94/41.11 apply zenon_H133. apply sym_equal. exact zenon_H11b. % 40.94/41.11 (* end of lemma zenon_L179_ *) % 40.94/41.11 assert (zenon_L180_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H3b zenon_H11b zenon_H2c zenon_H18 zenon_Hbb zenon_H22 zenon_H20 zenon_H1f zenon_H57 zenon_Hba zenon_H58 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.11 apply (zenon_L179_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.11 apply (zenon_L65_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.11 apply (zenon_L8_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.11 apply (zenon_L78_); trivial. % 40.94/41.11 apply (zenon_L11_); trivial. % 40.94/41.11 (* end of lemma zenon_L180_ *) % 40.94/41.11 assert (zenon_L181_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H3b zenon_Hbb zenon_H61 zenon_H60 zenon_H5f zenon_H22 zenon_H20 zenon_H1f zenon_H6e zenon_Hf2 zenon_H58 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.11 apply (zenon_L119_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.11 apply (zenon_L24_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.11 apply (zenon_L8_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.11 apply (zenon_L120_); trivial. % 40.94/41.11 apply (zenon_L11_); trivial. % 40.94/41.11 (* end of lemma zenon_L181_ *) % 40.94/41.11 assert (zenon_L182_ : (~((op (e0) (e1)) = (op (e0) (unit)))) -> ((unit) = (e1)) -> False). % 40.94/41.11 do 0 intro. intros zenon_H134 zenon_H14. % 40.94/41.11 cut (((e1) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 40.94/41.11 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 40.94/41.11 congruence. % 40.94/41.11 apply zenon_H3f. apply refl_equal. % 40.94/41.11 apply zenon_H15. apply sym_equal. exact zenon_H14. % 40.94/41.11 (* end of lemma zenon_L182_ *) % 40.94/41.11 assert (zenon_L183_ : ((op (e1) (unit)) = (e1)) -> ((unit) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H2c zenon_H2a zenon_H11b zenon_H111. % 40.94/41.11 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 40.94/41.11 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e1)) = (op (e1) (e3)))). % 40.94/41.11 intro zenon_D_pnotp. % 40.94/41.11 apply zenon_H111. % 40.94/41.11 rewrite <- zenon_D_pnotp. % 40.94/41.11 exact zenon_H2e. % 40.94/41.11 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 40.94/41.11 cut (((op (e1) (e3)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 40.94/41.11 congruence. % 40.94/41.11 cut (((op (e1) (unit)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e1)))). % 40.94/41.11 intro zenon_D_pnotp. % 40.94/41.11 apply zenon_H135. % 40.94/41.11 rewrite <- zenon_D_pnotp. % 40.94/41.11 exact zenon_H2c. % 40.94/41.11 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 40.94/41.11 cut (((op (e1) (unit)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 40.94/41.11 congruence. % 40.94/41.11 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 40.94/41.11 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (unit)) = (op (e1) (e3)))). % 40.94/41.11 intro zenon_D_pnotp. % 40.94/41.11 apply zenon_H31. % 40.94/41.11 rewrite <- zenon_D_pnotp. % 40.94/41.11 exact zenon_H2e. % 40.94/41.11 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 40.94/41.11 cut (((op (e1) (e3)) = (op (e1) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 40.94/41.11 congruence. % 40.94/41.11 apply (zenon_L9_); trivial. % 40.94/41.11 apply zenon_H2f. apply refl_equal. % 40.94/41.11 apply zenon_H2f. apply refl_equal. % 40.94/41.11 apply zenon_H133. apply sym_equal. exact zenon_H11b. % 40.94/41.11 apply zenon_H2f. apply refl_equal. % 40.94/41.11 apply zenon_H2f. apply refl_equal. % 40.94/41.11 (* end of lemma zenon_L183_ *) % 40.94/41.11 assert (zenon_L184_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e1)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H3b zenon_H18 zenon_H10c zenon_H50 zenon_H136 zenon_H9f zenon_H72 zenon_H5f zenon_H111 zenon_H11b zenon_H2c zenon_Hd3 zenon_Ha5 zenon_He8. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.11 apply (zenon_L179_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.11 cut (((op (e0) (unit)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e2)))). % 40.94/41.11 intro zenon_D_pnotp. % 40.94/41.11 apply zenon_H136. % 40.94/41.11 rewrite <- zenon_D_pnotp. % 40.94/41.11 exact zenon_H50. % 40.94/41.11 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 40.94/41.11 cut (((op (e0) (unit)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 40.94/41.11 congruence. % 40.94/41.11 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 40.94/41.11 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (unit)) = (op (e0) (e1)))). % 40.94/41.11 intro zenon_D_pnotp. % 40.94/41.11 apply zenon_H137. % 40.94/41.11 rewrite <- zenon_D_pnotp. % 40.94/41.11 exact zenon_H138. % 40.94/41.11 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 40.94/41.11 cut (((op (e0) (e1)) = (op (e0) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 40.94/41.11 congruence. % 40.94/41.11 apply (zenon_L182_); trivial. % 40.94/41.11 apply zenon_H139. apply refl_equal. % 40.94/41.11 apply zenon_H139. apply refl_equal. % 40.94/41.11 apply zenon_H10d. apply sym_equal. exact zenon_H10c. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.11 apply (zenon_L50_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.11 apply (zenon_L183_); trivial. % 40.94/41.11 apply (zenon_L124_); trivial. % 40.94/41.11 (* end of lemma zenon_L184_ *) % 40.94/41.11 assert (zenon_L185_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e2)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H3b zenon_Hd zenon_Hc zenon_Hb zenon_H32 zenon_H9f zenon_H72 zenon_H5f zenon_H91 zenon_H99 zenon_Hd3 zenon_Hc9 zenon_He9. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.11 apply (zenon_L3_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.11 apply (zenon_L71_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.11 apply (zenon_L50_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.11 apply (zenon_L72_); trivial. % 40.94/41.11 apply (zenon_L107_); trivial. % 40.94/41.11 (* end of lemma zenon_L185_ *) % 40.94/41.11 assert (zenon_L186_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e3)) = (e4)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H3b zenon_Hcc zenon_Hb1 zenon_H99 zenon_H91 zenon_H111 zenon_H11b zenon_H2c zenon_Hd3 zenon_Hcd zenon_Hd4. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.11 apply (zenon_L74_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.11 apply (zenon_L75_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.11 apply (zenon_L76_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.11 apply (zenon_L183_); trivial. % 40.94/41.11 apply (zenon_L80_); trivial. % 40.94/41.11 (* end of lemma zenon_L186_ *) % 40.94/41.11 assert (zenon_L187_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (e3) (unit)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.11 do 0 intro. intros zenon_Hd9 zenon_H34 zenon_H16 zenon_H20 zenon_H73 zenon_H9b zenon_H61 zenon_He8 zenon_H136 zenon_H50 zenon_H10c zenon_H18 zenon_He9 zenon_H5f zenon_H72 zenon_H9f zenon_H32 zenon_Hb zenon_Hc zenon_Hd zenon_Hd4 zenon_Hd3 zenon_H2c zenon_H11b zenon_H111 zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.94/41.11 apply (zenon_L51_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.94/41.11 apply (zenon_L184_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.94/41.11 apply (zenon_L185_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.94/41.11 apply (zenon_L186_); trivial. % 40.94/41.11 exact (zenon_Hda zenon_Hde). % 40.94/41.11 (* end of lemma zenon_L187_ *) % 40.94/41.11 assert (zenon_L188_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H3b zenon_H18 zenon_H4a zenon_Hc zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_H111 zenon_H11b zenon_H2c zenon_H32 zenon_H16 zenon_H34. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.11 apply (zenon_L179_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.11 apply (zenon_L17_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.11 apply (zenon_L8_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.11 apply (zenon_L183_); trivial. % 40.94/41.11 apply (zenon_L11_); trivial. % 40.94/41.11 (* end of lemma zenon_L188_ *) % 40.94/41.11 assert (zenon_L189_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e4)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e4) (e2)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.11 do 0 intro. intros zenon_H3b zenon_Ha2 zenon_Ha1 zenon_H32 zenon_H22 zenon_H20 zenon_H1f zenon_Hc9 zenon_H99 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.11 apply (zenon_L52_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.11 apply (zenon_L71_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.11 apply (zenon_L8_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.11 apply (zenon_L72_); trivial. % 40.94/41.11 apply (zenon_L44_); trivial. % 40.94/41.11 (* end of lemma zenon_L189_ *) % 40.94/41.11 assert (zenon_L190_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e4)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H3b zenon_H18 zenon_Hab zenon_Hc zenon_Haa zenon_H22 zenon_H20 zenon_H1f zenon_H111 zenon_H11b zenon_H2c zenon_H32 zenon_H16 zenon_H34. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.11 apply (zenon_L179_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.11 apply (zenon_L56_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.11 apply (zenon_L8_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.11 apply (zenon_L183_); trivial. % 40.94/41.11 apply (zenon_L11_); trivial. % 40.94/41.11 (* end of lemma zenon_L190_ *) % 40.94/41.11 assert (zenon_L191_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> ((op (e3) (e4)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e2)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H3b zenon_Hc8 zenon_H99 zenon_H32 zenon_H9f zenon_H72 zenon_H5f zenon_Hbf zenon_Hc zenon_H83 zenon_Hd3 zenon_Hc9 zenon_He9. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.11 apply (zenon_L70_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.11 apply (zenon_L71_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.11 apply (zenon_L50_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.11 apply (zenon_L67_); trivial. % 40.94/41.11 apply (zenon_L107_); trivial. % 40.94/41.11 (* end of lemma zenon_L191_ *) % 40.94/41.11 assert (zenon_L192_ : (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((unit) = (e4)) -> ((op (e4) (e4)) = (e2)) -> False). % 40.94/41.11 do 0 intro. intros zenon_He9 zenon_Hc zenon_H33 zenon_Hc7. % 40.94/41.11 cut (((op (unit) (e2)) = (e2)) = ((op (e4) (e2)) = (op (e4) (e4)))). % 40.94/41.11 intro zenon_D_pnotp. % 40.94/41.11 apply zenon_He9. % 40.94/41.11 rewrite <- zenon_D_pnotp. % 40.94/41.11 exact zenon_Hc. % 40.94/41.11 cut (((e2) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 40.94/41.11 cut (((op (unit) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 40.94/41.11 congruence. % 40.94/41.11 elim (classic ((op (e4) (e2)) = (op (e4) (e2)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 40.94/41.11 cut (((op (e4) (e2)) = (op (e4) (e2))) = ((op (unit) (e2)) = (op (e4) (e2)))). % 40.94/41.11 intro zenon_D_pnotp. % 40.94/41.11 apply zenon_H94. % 40.94/41.11 rewrite <- zenon_D_pnotp. % 40.94/41.11 exact zenon_H95. % 40.94/41.11 cut (((op (e4) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 40.94/41.11 cut (((op (e4) (e2)) = (op (unit) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 40.94/41.11 congruence. % 40.94/41.11 apply (zenon_L43_); trivial. % 40.94/41.11 apply zenon_H96. apply refl_equal. % 40.94/41.11 apply zenon_H96. apply refl_equal. % 40.94/41.11 apply zenon_H13a. apply sym_equal. exact zenon_Hc7. % 40.94/41.11 (* end of lemma zenon_L192_ *) % 40.94/41.11 assert (zenon_L193_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (e2)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e4)) = (e2)) -> False). % 40.94/41.11 do 0 intro. intros zenon_H3b zenon_Hc8 zenon_H32 zenon_H22 zenon_H20 zenon_H1f zenon_H91 zenon_Hc9 zenon_H99 zenon_He9 zenon_Hc zenon_Hc7. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.11 apply (zenon_L70_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.11 apply (zenon_L71_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.11 apply (zenon_L8_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.11 apply (zenon_L72_); trivial. % 40.94/41.11 apply (zenon_L192_); trivial. % 40.94/41.11 (* end of lemma zenon_L193_ *) % 40.94/41.11 assert (zenon_L194_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e4) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (e2)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.11 do 0 intro. intros zenon_Hc2 zenon_H92 zenon_Ha1 zenon_H2c zenon_H11b zenon_H111 zenon_Haa zenon_H18 zenon_H34 zenon_H16 zenon_H58 zenon_Hb9 zenon_Hb6 zenon_Hd3 zenon_H83 zenon_H5f zenon_H72 zenon_H9f zenon_H3b zenon_Hc8 zenon_H32 zenon_H22 zenon_H20 zenon_H1f zenon_H91 zenon_Hc9 zenon_H99 zenon_He9 zenon_Hc. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.11 apply (zenon_L189_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.11 apply (zenon_L190_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.11 apply (zenon_L123_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.11 apply (zenon_L191_); trivial. % 40.94/41.11 apply (zenon_L193_); trivial. % 40.94/41.11 (* end of lemma zenon_L194_ *) % 40.94/41.11 assert (zenon_L195_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (e4) (e3)) = (e2)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.11 do 0 intro. intros zenon_Hd9 zenon_Hf2 zenon_H6e zenon_H9b zenon_Hbb zenon_He8 zenon_H136 zenon_H50 zenon_H10c zenon_Hc zenon_He9 zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_Hc8 zenon_H9f zenon_H72 zenon_H5f zenon_H83 zenon_Hb6 zenon_Hb9 zenon_H58 zenon_H16 zenon_H34 zenon_H18 zenon_Haa zenon_Ha1 zenon_H92 zenon_Hc2 zenon_Hd4 zenon_Hd3 zenon_H2c zenon_H11b zenon_H111 zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.94/41.11 apply (zenon_L121_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.94/41.11 apply (zenon_L184_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.94/41.11 apply (zenon_L194_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.94/41.11 apply (zenon_L186_); trivial. % 40.94/41.11 exact (zenon_Hda zenon_Hde). % 40.94/41.11 (* end of lemma zenon_L195_ *) % 40.94/41.11 assert (zenon_L196_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H3b zenon_H8e zenon_H9f zenon_H72 zenon_H5f zenon_H77 zenon_H76 zenon_H20 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.11 apply (zenon_L83_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.11 apply (zenon_L89_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.11 apply (zenon_L50_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.11 apply (zenon_L32_); trivial. % 40.94/41.11 apply (zenon_L11_); trivial. % 40.94/41.11 (* end of lemma zenon_L196_ *) % 40.94/41.11 assert (zenon_L197_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> False). % 40.94/41.11 do 0 intro. intros zenon_Hf0 zenon_H8e zenon_He0 zenon_Hbb zenon_Hc2 zenon_Hb6 zenon_Hb9 zenon_Haa zenon_Ha1 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H57 zenon_H58 zenon_H68 zenon_Hed zenon_He6 zenon_Hc8 zenon_Hf2 zenon_Hee zenon_H49 zenon_H1f zenon_H22 zenon_H3b zenon_H34 zenon_H16 zenon_H32 zenon_H20 zenon_H73 zenon_H9f zenon_H99 zenon_H9b zenon_H72 zenon_H5f zenon_H61 zenon_Hd3 zenon_He8 zenon_H111 zenon_H10c zenon_H50 zenon_H136 zenon_H11b zenon_H2c zenon_H18 zenon_He9 zenon_H91 zenon_Hc zenon_Hb zenon_Hd4 zenon_Hb1 zenon_Hcc zenon_Hd9. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_He1 | zenon_intro zenon_H76 ]. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.94/41.11 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.11 apply (zenon_L187_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.11 apply (zenon_L188_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.11 apply (zenon_L152_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.11 exact (zenon_He1 zenon_He5). % 40.94/41.11 apply (zenon_L195_); trivial. % 40.94/41.11 apply (zenon_L99_); trivial. % 40.94/41.11 apply (zenon_L196_); trivial. % 40.94/41.11 (* end of lemma zenon_L197_ *) % 40.94/41.11 assert (zenon_L198_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.11 do 0 intro. intros zenon_Hd9 zenon_Hc8 zenon_H9b zenon_H34 zenon_H16 zenon_H32 zenon_He9 zenon_H20 zenon_H76 zenon_H77 zenon_H1f zenon_H22 zenon_H9f zenon_H5f zenon_H8e zenon_Hd4 zenon_Hd3 zenon_H2c zenon_H11b zenon_H111 zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.94/41.11 apply (zenon_L85_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.94/41.11 apply (zenon_L113_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.94/41.11 apply (zenon_L117_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.94/41.11 apply (zenon_L186_); trivial. % 40.94/41.11 exact (zenon_Hda zenon_Hde). % 40.94/41.11 (* end of lemma zenon_L198_ *) % 40.94/41.11 assert (zenon_L199_ : ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> False). % 40.94/41.11 do 0 intro. intros zenon_Hed zenon_He6 zenon_He8 zenon_H3b zenon_H34 zenon_H16 zenon_H32 zenon_H20 zenon_H77 zenon_Hc8 zenon_H99 zenon_H9b zenon_H76 zenon_H5f zenon_H8e zenon_H9f zenon_Hd3 zenon_He9 zenon_H22 zenon_H1f zenon_Hd4 zenon_H11b zenon_H2c zenon_H111 zenon_H91 zenon_Hb1 zenon_Hcc zenon_Hd9. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.94/41.11 apply (zenon_L198_); trivial. % 40.94/41.11 apply (zenon_L99_); trivial. % 40.94/41.11 (* end of lemma zenon_L199_ *) % 40.94/41.11 assert (zenon_L200_ : (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e3)) = (e3))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.11 do 0 intro. intros zenon_Hb zenon_Hc zenon_H18 zenon_H136 zenon_H50 zenon_H10c zenon_H61 zenon_H73 zenon_H49 zenon_Hee zenon_Hf2 zenon_H68 zenon_H58 zenon_H57 zenon_H6e zenon_H88 zenon_Ha1 zenon_Haa zenon_Hb9 zenon_Hb6 zenon_Hc2 zenon_Hbb zenon_He0 zenon_Hf0 zenon_Hd9 zenon_Hcc zenon_Hb1 zenon_H91 zenon_H111 zenon_H2c zenon_H11b zenon_Hd4 zenon_H1f zenon_H22 zenon_He9 zenon_Hd3 zenon_H9f zenon_H8e zenon_H9b zenon_H99 zenon_Hc8 zenon_H77 zenon_He8 zenon_He6 zenon_Hed zenon_H89 zenon_H3b zenon_H7b zenon_H81 zenon_H5f zenon_H83 zenon_H20 zenon_H87 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H60 | zenon_intro zenon_H8a ]. % 40.94/41.11 apply (zenon_L181_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H72 | zenon_intro zenon_H8b ]. % 40.94/41.11 apply (zenon_L197_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H8b); [ zenon_intro zenon_H76 | zenon_intro zenon_H8c ]. % 40.94/41.11 apply (zenon_L199_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H8d | zenon_intro zenon_H7c ]. % 40.94/41.11 exact (zenon_H89 zenon_H8d). % 40.94/41.11 apply (zenon_L40_); trivial. % 40.94/41.11 (* end of lemma zenon_L200_ *) % 40.94/41.11 assert (zenon_L201_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H3b zenon_H34 zenon_H16 zenon_H32 zenon_H6e zenon_H22 zenon_H20 zenon_H1f zenon_H5f zenon_H61 zenon_Hf2 zenon_H58 zenon_Hbb zenon_Hf0 zenon_H8e zenon_He0 zenon_Hc2 zenon_Hb6 zenon_Hb9 zenon_Haa zenon_Ha1 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H57 zenon_H68 zenon_Hed zenon_He6 zenon_Hc8 zenon_Hee zenon_H49 zenon_H73 zenon_H9f zenon_H99 zenon_H9b zenon_Hd3 zenon_He8 zenon_H111 zenon_H10c zenon_H50 zenon_H136 zenon_H11b zenon_H2c zenon_H18 zenon_He9 zenon_H91 zenon_Hc zenon_Hb zenon_Hd4 zenon_Hb1 zenon_Hcc zenon_Hd9. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 40.94/41.11 apply (zenon_L200_); trivial. % 40.94/41.11 apply (zenon_L130_); trivial. % 40.94/41.11 (* end of lemma zenon_L201_ *) % 40.94/41.11 assert (zenon_L202_ : ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> False). % 40.94/41.11 do 0 intro. intros zenon_Hed zenon_He6 zenon_He8 zenon_H3b zenon_H34 zenon_H16 zenon_H32 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_H8d zenon_H5f zenon_H68 zenon_Hb1 zenon_H73 zenon_Hd3 zenon_He9 zenon_H91 zenon_H77 zenon_Hd4 zenon_H11b zenon_H2c zenon_H111 zenon_Hd9. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.94/41.11 apply (zenon_L103_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.94/41.11 apply (zenon_L105_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.94/41.11 apply (zenon_L108_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.94/41.11 apply (zenon_L186_); trivial. % 40.94/41.11 exact (zenon_Hda zenon_Hde). % 40.94/41.11 apply (zenon_L99_); trivial. % 40.94/41.11 (* end of lemma zenon_L202_ *) % 40.94/41.11 assert (zenon_L203_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> False). % 40.94/41.11 do 0 intro. intros zenon_Hee zenon_Hd9 zenon_H111 zenon_H2c zenon_H11b zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H3b zenon_H34 zenon_H16 zenon_H32 zenon_H68 zenon_H22 zenon_H20 zenon_H1f zenon_H5f zenon_H61 zenon_H59 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 40.94/41.11 apply (zenon_L41_); trivial. % 40.94/41.11 apply (zenon_L202_); trivial. % 40.94/41.11 (* end of lemma zenon_L203_ *) % 40.94/41.11 assert (zenon_L204_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e3)) = (e1))\/((op (e1) (e4)) = (e1)))))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H13b zenon_H136 zenon_Ha1 zenon_Haa zenon_Hc2 zenon_H101 zenon_Hfc zenon_Hfe zenon_Hff zenon_Hf0 zenon_H8e zenon_H9f zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H50 zenon_H49 zenon_H10c zenon_H42 zenon_H10b zenon_Hee zenon_Hd9 zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_He0 zenon_Hb9 zenon_Hb6 zenon_Hf6 zenon_H109 zenon_H103 zenon_Hbb zenon_H111 zenon_H116 zenon_H115 zenon_H112 zenon_H117. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H118 | zenon_intro zenon_H11b ]. % 40.94/41.11 apply (zenon_L168_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hfb ]. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hba | zenon_intro zenon_Hf8 ]. % 40.94/41.11 apply (zenon_L180_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf9 ]. % 40.94/41.11 apply (zenon_L201_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hfa ]. % 40.94/41.11 exact (zenon_Hf7 zenon_Hfb). % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H59 | zenon_intro zenon_Hb7 ]. % 40.94/41.11 apply (zenon_L203_); trivial. % 40.94/41.11 apply (zenon_L123_); trivial. % 40.94/41.11 apply (zenon_L139_); trivial. % 40.94/41.11 (* end of lemma zenon_L204_ *) % 40.94/41.11 assert (zenon_L205_ : (~((op (e1) (e0)) = (op (unit) (e0)))) -> ((unit) = (e1)) -> False). % 40.94/41.11 do 0 intro. intros zenon_H13c zenon_H14. % 40.94/41.11 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 40.94/41.11 cut (((e1) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 40.94/41.11 congruence. % 40.94/41.11 apply zenon_H15. apply sym_equal. exact zenon_H14. % 40.94/41.11 apply zenon_H3f. apply refl_equal. % 40.94/41.11 (* end of lemma zenon_L205_ *) % 40.94/41.11 assert (zenon_L206_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (unit) (e0)) = (e0)) -> ((unit) = (e1)) -> ((op (e1) (e2)) = (e0)) -> False). % 40.94/41.11 do 0 intro. intros zenon_H103 zenon_H42 zenon_H14 zenon_H120. % 40.94/41.11 cut (((op (unit) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e1) (e2)))). % 40.94/41.11 intro zenon_D_pnotp. % 40.94/41.11 apply zenon_H103. % 40.94/41.11 rewrite <- zenon_D_pnotp. % 40.94/41.11 exact zenon_H42. % 40.94/41.11 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 40.94/41.11 cut (((op (unit) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 40.94/41.11 congruence. % 40.94/41.11 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H107 | zenon_intro zenon_H108 ]. % 40.94/41.11 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (unit) (e0)) = (op (e1) (e0)))). % 40.94/41.11 intro zenon_D_pnotp. % 40.94/41.11 apply zenon_H13d. % 40.94/41.11 rewrite <- zenon_D_pnotp. % 40.94/41.11 exact zenon_H107. % 40.94/41.11 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 40.94/41.11 cut (((op (e1) (e0)) = (op (unit) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13c]. % 40.94/41.11 congruence. % 40.94/41.11 apply (zenon_L205_); trivial. % 40.94/41.11 apply zenon_H108. apply refl_equal. % 40.94/41.11 apply zenon_H108. apply refl_equal. % 40.94/41.11 apply zenon_H122. apply sym_equal. exact zenon_H120. % 40.94/41.11 (* end of lemma zenon_L206_ *) % 40.94/41.11 assert (zenon_L207_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H3b zenon_H18 zenon_H120 zenon_H42 zenon_H103 zenon_H22 zenon_H20 zenon_H1f zenon_H111 zenon_H11b zenon_H2c zenon_H32 zenon_H16 zenon_H34. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.11 apply (zenon_L179_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.11 apply (zenon_L206_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.11 apply (zenon_L8_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.11 apply (zenon_L183_); trivial. % 40.94/41.11 apply (zenon_L11_); trivial. % 40.94/41.11 (* end of lemma zenon_L207_ *) % 40.94/41.11 assert (zenon_L208_ : ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e0))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e4) (e4)) = (e3))) -> (((op (e4) (e4)) = (e0))\/(((op (e4) (e4)) = (e1))\/(((op (e4) (e4)) = (e2))\/(((op (e4) (e4)) = (e3))\/((op (e4) (e4)) = (e4)))))) -> False). % 40.94/41.11 do 0 intro. intros zenon_Hed zenon_He6 zenon_H99 zenon_He8 zenon_Hd4 zenon_H32 zenon_H16 zenon_H3b zenon_H13e zenon_He9 zenon_H34 zenon_Hc3 zenon_H13f zenon_H140. % 40.94/41.11 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H142 | zenon_intro zenon_H141 ]. % 40.94/41.11 exact (zenon_H13e zenon_H142). % 40.94/41.11 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H144 | zenon_intro zenon_H143 ]. % 40.94/41.11 elim (classic ((op (e4) (e4)) = (op (e4) (e4)))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hd6 ]. % 40.94/41.11 cut (((op (e4) (e4)) = (op (e4) (e4))) = ((op (e4) (e2)) = (op (e4) (e4)))). % 40.94/41.11 intro zenon_D_pnotp. % 40.94/41.11 apply zenon_He9. % 40.94/41.11 rewrite <- zenon_D_pnotp. % 40.94/41.11 exact zenon_Hd5. % 40.94/41.11 cut (((op (e4) (e4)) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 40.94/41.11 cut (((op (e4) (e4)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 40.94/41.11 congruence. % 40.94/41.11 cut (((e1) = (op (e4) (e2))) = ((op (e4) (e4)) = (op (e4) (e2)))). % 40.94/41.11 intro zenon_D_pnotp. % 40.94/41.11 apply zenon_Hec. % 40.94/41.11 rewrite <- zenon_D_pnotp. % 40.94/41.11 exact zenon_H34. % 40.94/41.11 cut (((op (e4) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 40.94/41.11 cut (((e1) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H145]. % 40.94/41.11 congruence. % 40.94/41.11 elim (classic ((op (e4) (e4)) = (op (e4) (e4)))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hd6 ]. % 40.94/41.11 cut (((op (e4) (e4)) = (op (e4) (e4))) = ((e1) = (op (e4) (e4)))). % 40.94/41.11 intro zenon_D_pnotp. % 40.94/41.11 apply zenon_H145. % 40.94/41.11 rewrite <- zenon_D_pnotp. % 40.94/41.11 exact zenon_Hd5. % 40.94/41.11 cut (((op (e4) (e4)) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 40.94/41.11 cut (((op (e4) (e4)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 40.94/41.11 congruence. % 40.94/41.11 exact (zenon_H146 zenon_H144). % 40.94/41.11 apply zenon_Hd6. apply refl_equal. % 40.94/41.11 apply zenon_Hd6. apply refl_equal. % 40.94/41.11 apply zenon_H96. apply refl_equal. % 40.94/41.11 apply zenon_Hd6. apply refl_equal. % 40.94/41.11 apply zenon_Hd6. apply refl_equal. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H147 ]. % 40.94/41.11 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.11 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H148 | zenon_intro zenon_Hde ]. % 40.94/41.11 exact (zenon_H13f zenon_H148). % 40.94/41.11 exact (zenon_Hda zenon_Hde). % 40.94/41.11 apply (zenon_L99_); trivial. % 40.94/41.11 (* end of lemma zenon_L208_ *) % 40.94/41.11 assert (zenon_L209_ : ((~((op (e4) (e4)) = (e3)))\/((op (e4) (e3)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> ((op (unit) (e4)) = (e4)) -> (((op (e4) (e4)) = (e0))\/(((op (e4) (e4)) = (e1))\/(((op (e4) (e4)) = (e2))\/(((op (e4) (e4)) = (e3))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e4)) = (e0))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H149 zenon_Hcc zenon_Hb1 zenon_H91 zenon_H6e zenon_H58 zenon_Hf2 zenon_Hd3 zenon_H140 zenon_Hc3 zenon_H34 zenon_He9 zenon_H13e zenon_H3b zenon_H16 zenon_H32 zenon_Hd4 zenon_He8 zenon_H99 zenon_He6 zenon_Hed. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H13f | zenon_intro zenon_Hcd ]. % 40.94/41.11 apply (zenon_L208_); trivial. % 40.94/41.11 apply (zenon_L127_); trivial. % 40.94/41.11 (* end of lemma zenon_L209_ *) % 40.94/41.11 assert (zenon_L210_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e4) (e2)) = (e4)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e3)) = (e3))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H88 zenon_H58 zenon_Hf2 zenon_H6e zenon_H61 zenon_Hbb zenon_Hc9 zenon_Hb zenon_Hc zenon_Hd zenon_Hd9 zenon_Hcc zenon_Hb1 zenon_H91 zenon_H111 zenon_H2c zenon_H11b zenon_Hd4 zenon_H1f zenon_H22 zenon_He9 zenon_Hd3 zenon_H9f zenon_H8e zenon_H9b zenon_H99 zenon_Hc8 zenon_H77 zenon_He8 zenon_He6 zenon_Hed zenon_H89 zenon_H3b zenon_H7b zenon_H81 zenon_H5f zenon_H83 zenon_H20 zenon_H87 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H60 | zenon_intro zenon_H8a ]. % 40.94/41.11 apply (zenon_L181_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H72 | zenon_intro zenon_H8b ]. % 40.94/41.11 apply (zenon_L185_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H8b); [ zenon_intro zenon_H76 | zenon_intro zenon_H8c ]. % 40.94/41.11 apply (zenon_L199_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H8d | zenon_intro zenon_H7c ]. % 40.94/41.11 exact (zenon_H89 zenon_H8d). % 40.94/41.11 apply (zenon_L40_); trivial. % 40.94/41.11 (* end of lemma zenon_L210_ *) % 40.94/41.11 assert (zenon_L211_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e3) (e4)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e2)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H3b zenon_Hc8 zenon_H32 zenon_H7c zenon_H5f zenon_H83 zenon_H91 zenon_H99 zenon_Hd3 zenon_Hc9 zenon_He9. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.11 apply (zenon_L70_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.11 apply (zenon_L71_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.11 apply (zenon_L38_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.11 apply (zenon_L72_); trivial. % 40.94/41.11 apply (zenon_L107_); trivial. % 40.94/41.11 (* end of lemma zenon_L211_ *) % 40.94/41.11 assert (zenon_L212_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e2)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> False). % 40.94/41.11 do 0 intro. intros zenon_H88 zenon_H68 zenon_H61 zenon_H73 zenon_H34 zenon_H16 zenon_H20 zenon_H77 zenon_H1f zenon_H22 zenon_H6e zenon_H58 zenon_H59 zenon_H57 zenon_H89 zenon_H3b zenon_Hc8 zenon_H32 zenon_H5f zenon_H83 zenon_H91 zenon_H99 zenon_Hd3 zenon_Hc9 zenon_He9. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H60 | zenon_intro zenon_H8a ]. % 40.94/41.11 apply (zenon_L27_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H72 | zenon_intro zenon_H8b ]. % 40.94/41.11 apply (zenon_L31_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H8b); [ zenon_intro zenon_H76 | zenon_intro zenon_H8c ]. % 40.94/41.11 apply (zenon_L33_); trivial. % 40.94/41.11 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H8d | zenon_intro zenon_H7c ]. % 40.94/41.12 exact (zenon_H89 zenon_H8d). % 40.94/41.12 apply (zenon_L211_); trivial. % 40.94/41.12 (* end of lemma zenon_L212_ *) % 40.94/41.12 assert (zenon_L213_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4))) -> ((~((op (e4) (e4)) = (e3)))\/((op (e4) (e3)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> ((op (unit) (e4)) = (e4)) -> (((op (e4) (e4)) = (e0))\/(((op (e4) (e4)) = (e1))\/(((op (e4) (e4)) = (e2))\/(((op (e4) (e4)) = (e3))\/((op (e4) (e4)) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 40.94/41.12 do 0 intro. intros zenon_Hf0 zenon_H14a zenon_H149 zenon_Hcc zenon_Hb1 zenon_H91 zenon_H6e zenon_H58 zenon_Hf2 zenon_Hd3 zenon_H140 zenon_H34 zenon_He9 zenon_H3b zenon_H16 zenon_H32 zenon_Hd4 zenon_He8 zenon_H99 zenon_He6 zenon_Hed zenon_He0 zenon_H68 zenon_H57 zenon_H73 zenon_H41 zenon_H42 zenon_H43 zenon_H49 zenon_H51 zenon_H50 zenon_H22 zenon_H20 zenon_H1f zenon_H5f zenon_H61 zenon_Hbb zenon_H9f zenon_Hc zenon_Hb zenon_H77 zenon_Hc8 zenon_H9b zenon_H8e zenon_H11b zenon_H2c zenon_H111 zenon_Hd9 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_Hf1 zenon_Hee. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_He1 | zenon_intro zenon_H76 ]. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H13e | zenon_intro zenon_H9a ]. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 40.94/41.12 apply (zenon_L209_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.12 apply (zenon_L210_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.12 apply (zenon_L20_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.12 apply (zenon_L212_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.12 exact (zenon_He1 zenon_He5). % 40.94/41.12 apply (zenon_L73_); trivial. % 40.94/41.12 apply (zenon_L121_); trivial. % 40.94/41.12 apply (zenon_L202_); trivial. % 40.94/41.12 apply (zenon_L199_); trivial. % 40.94/41.12 (* end of lemma zenon_L213_ *) % 40.94/41.12 assert (zenon_L214_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (e4)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e2)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_Hb6 zenon_Hb7 zenon_H58 zenon_Hb9 zenon_H22 zenon_H20 zenon_H1f zenon_H125 zenon_H42 zenon_H8e zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L62_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L63_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L8_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L172_); trivial. % 40.94/41.12 apply (zenon_L11_); trivial. % 40.94/41.12 (* end of lemma zenon_L214_ *) % 40.94/41.12 assert (zenon_L215_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e4) (e4)) = (e0))\/(((op (e4) (e4)) = (e1))\/(((op (e4) (e4)) = (e2))\/(((op (e4) (e4)) = (e3))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e4) (e4)) = (e3)))\/((op (e4) (e3)) = (e4))) -> ((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e3)) = (e1))\/((op (e1) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e4) (e2)) = (e0)))))) -> (~((op (e1) (e0)) = (op (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) (e4)) = (e2)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H13b zenon_H136 zenon_H140 zenon_H149 zenon_H14a zenon_H117 zenon_H112 zenon_H115 zenon_H116 zenon_H111 zenon_H10b zenon_H11f zenon_H129 zenon_H12d zenon_H103 zenon_H109 zenon_Hf6 zenon_Hee zenon_Hed zenon_He6 zenon_He8 zenon_He9 zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H50 zenon_H51 zenon_H49 zenon_H43 zenon_H42 zenon_H41 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_H9f zenon_H99 zenon_H9b zenon_Hc2 zenon_Hbb zenon_Hb6 zenon_Hb9 zenon_Haa zenon_Hb1 zenon_Ha1 zenon_Hc8 zenon_Hd3 zenon_Hd4 zenon_Hcc zenon_Hd9 zenon_H8e zenon_H91 zenon_He0 zenon_Hf1 zenon_Hf0 zenon_Hff zenon_Hfe zenon_Hfc zenon_H101 zenon_H14b. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H118 | zenon_intro zenon_H11b ]. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H12e | zenon_intro zenon_Hba ]. % 40.94/41.12 apply (zenon_L176_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hfb ]. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H17 | zenon_intro zenon_H119 ]. % 40.94/41.12 apply (zenon_L135_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H11b | zenon_intro zenon_H11a ]. % 40.94/41.12 exact (zenon_H118 zenon_H11b). % 40.94/41.12 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H104 | zenon_intro zenon_H11c ]. % 40.94/41.12 apply (zenon_L177_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H10f | zenon_intro zenon_H113 ]. % 40.94/41.12 apply (zenon_L157_); trivial. % 40.94/41.12 apply (zenon_L178_); trivial. % 40.94/41.12 apply (zenon_L139_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H12e | zenon_intro zenon_Hba ]. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hfb ]. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H10c | zenon_intro zenon_H12f ]. % 40.94/41.12 apply (zenon_L204_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H120 | zenon_intro zenon_H130 ]. % 40.94/41.12 apply (zenon_L207_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H132 | zenon_intro zenon_H131 ]. % 40.94/41.12 exact (zenon_H12e zenon_H132). % 40.94/41.12 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H125 | zenon_intro zenon_H128 ]. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hba | zenon_intro zenon_Hf8 ]. % 40.94/41.12 apply (zenon_L180_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf9 ]. % 40.94/41.12 apply (zenon_L213_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hfa ]. % 40.94/41.12 exact (zenon_Hf7 zenon_Hfb). % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H59 | zenon_intro zenon_Hb7 ]. % 40.94/41.12 apply (zenon_L203_); trivial. % 40.94/41.12 apply (zenon_L214_); trivial. % 40.94/41.12 apply (zenon_L174_); trivial. % 40.94/41.12 apply (zenon_L139_); trivial. % 40.94/41.12 apply (zenon_L180_); trivial. % 40.94/41.12 (* end of lemma zenon_L215_ *) % 40.94/41.12 assert (zenon_L216_ : ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e2) (e1)) = (e0)) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H11f zenon_H14c zenon_H34 zenon_H14d. % 40.94/41.12 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H70 | zenon_intro zenon_H71 ]. % 40.94/41.12 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e1) (e1)) = (op (e2) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H14d. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H70. % 40.94/41.12 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 40.94/41.12 cut (((op (e2) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14e]. % 40.94/41.12 congruence. % 40.94/41.12 cut (((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) = ((op (e2) (e1)) = (op (e1) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H14e. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H11f. % 40.94/41.12 cut (((op (op (e4) (e2)) (op (e4) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 40.94/41.12 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 40.94/41.12 congruence. % 40.94/41.12 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H70 | zenon_intro zenon_H71 ]. % 40.94/41.12 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((e0) = (op (e2) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H14f. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H70. % 40.94/41.12 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 40.94/41.12 cut (((op (e2) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 40.94/41.12 congruence. % 40.94/41.12 exact (zenon_H150 zenon_H14c). % 40.94/41.12 apply zenon_H71. apply refl_equal. % 40.94/41.12 apply zenon_H71. apply refl_equal. % 40.94/41.12 apply (zenon_L169_); trivial. % 40.94/41.12 apply zenon_H71. apply refl_equal. % 40.94/41.12 apply zenon_H71. apply refl_equal. % 40.94/41.12 (* end of lemma zenon_L216_ *) % 40.94/41.12 assert (zenon_L217_ : ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e3) (e1)) = (e0)) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H11f zenon_H151 zenon_H34 zenon_H152. % 40.94/41.12 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 40.94/41.12 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e1) (e1)) = (op (e3) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H152. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H62. % 40.94/41.12 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 40.94/41.12 cut (((op (e3) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 40.94/41.12 congruence. % 40.94/41.12 cut (((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) = ((op (e3) (e1)) = (op (e1) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H153. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H11f. % 40.94/41.12 cut (((op (op (e4) (e2)) (op (e4) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 40.94/41.12 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 40.94/41.12 congruence. % 40.94/41.12 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 40.94/41.12 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((e0) = (op (e3) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H154. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H62. % 40.94/41.12 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 40.94/41.12 cut (((op (e3) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 40.94/41.12 congruence. % 40.94/41.12 exact (zenon_H155 zenon_H151). % 40.94/41.12 apply zenon_H63. apply refl_equal. % 40.94/41.12 apply zenon_H63. apply refl_equal. % 40.94/41.12 apply (zenon_L169_); trivial. % 40.94/41.12 apply zenon_H63. apply refl_equal. % 40.94/41.12 apply zenon_H63. apply refl_equal. % 40.94/41.12 (* end of lemma zenon_L217_ *) % 40.94/41.12 assert (zenon_L218_ : ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e4) (e1)) = (e0)) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H11f zenon_H156 zenon_H34 zenon_H157. % 40.94/41.12 elim (classic ((op (e4) (e1)) = (op (e4) (e1)))); [ zenon_intro zenon_H37 | zenon_intro zenon_H38 ]. % 40.94/41.12 cut (((op (e4) (e1)) = (op (e4) (e1))) = ((op (e1) (e1)) = (op (e4) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H157. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H37. % 40.94/41.12 cut (((op (e4) (e1)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 40.94/41.12 cut (((op (e4) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H158]. % 40.94/41.12 congruence. % 40.94/41.12 cut (((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) = ((op (e4) (e1)) = (op (e1) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H158. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H11f. % 40.94/41.12 cut (((op (op (e4) (e2)) (op (e4) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 40.94/41.12 cut (((e0) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 40.94/41.12 congruence. % 40.94/41.12 elim (classic ((op (e4) (e1)) = (op (e4) (e1)))); [ zenon_intro zenon_H37 | zenon_intro zenon_H38 ]. % 40.94/41.12 cut (((op (e4) (e1)) = (op (e4) (e1))) = ((e0) = (op (e4) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H159. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H37. % 40.94/41.12 cut (((op (e4) (e1)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 40.94/41.12 cut (((op (e4) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H15a]. % 40.94/41.12 congruence. % 40.94/41.12 exact (zenon_H15a zenon_H156). % 40.94/41.12 apply zenon_H38. apply refl_equal. % 40.94/41.12 apply zenon_H38. apply refl_equal. % 40.94/41.12 apply (zenon_L169_); trivial. % 40.94/41.12 apply zenon_H38. apply refl_equal. % 40.94/41.12 apply zenon_H38. apply refl_equal. % 40.94/41.12 (* end of lemma zenon_L218_ *) % 40.94/41.12 assert (zenon_L219_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e4) (e2)) = (e0)))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e3)) = (e1))\/((op (e1) (e4)) = (e1)))))) -> ((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4))) -> ((~((op (e4) (e4)) = (e3)))\/((op (e4) (e3)) = (e4))) -> (((op (e4) (e4)) = (e0))\/(((op (e4) (e4)) = (e1))\/(((op (e4) (e4)) = (e2))\/(((op (e4) (e4)) = (e3))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H15b zenon_H14b zenon_H101 zenon_Hfc zenon_Hfe zenon_Hff zenon_Hf0 zenon_Hf1 zenon_He0 zenon_H91 zenon_H8e zenon_Hd9 zenon_Hcc zenon_Hd4 zenon_Hd3 zenon_Hc8 zenon_Ha1 zenon_Hb1 zenon_Haa zenon_Hb9 zenon_Hb6 zenon_Hbb zenon_Hc2 zenon_H9b zenon_H99 zenon_H9f zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_H41 zenon_H42 zenon_H49 zenon_H51 zenon_H50 zenon_Hb zenon_Hc zenon_H18 zenon_H16 zenon_H1f zenon_H20 zenon_H22 zenon_H2d zenon_H2c zenon_H32 zenon_H3b zenon_He9 zenon_He8 zenon_He6 zenon_Hed zenon_Hee zenon_Hf6 zenon_H109 zenon_H103 zenon_H12d zenon_H129 zenon_H10b zenon_H111 zenon_H116 zenon_H115 zenon_H112 zenon_H117 zenon_H14a zenon_H149 zenon_H140 zenon_H136 zenon_H13b zenon_H15c zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 40.94/41.12 apply (zenon_L215_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 40.94/41.12 exact (zenon_H15c zenon_H15f). % 40.94/41.12 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 40.94/41.12 apply (zenon_L216_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 40.94/41.12 apply (zenon_L217_); trivial. % 40.94/41.12 apply (zenon_L218_); trivial. % 40.94/41.12 (* end of lemma zenon_L219_ *) % 40.94/41.12 assert (zenon_L220_ : (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (unit) (e0)) = (e0)) -> ((unit) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H161 zenon_H42 zenon_H9 zenon_H162. % 40.94/41.12 cut (((op (unit) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e0) (e3)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H161. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H42. % 40.94/41.12 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H163]. % 40.94/41.12 cut (((op (unit) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 40.94/41.12 congruence. % 40.94/41.12 elim (classic ((op (e0) (e0)) = (op (e0) (e0)))); [ zenon_intro zenon_H46 | zenon_intro zenon_H47 ]. % 40.94/41.12 cut (((op (e0) (e0)) = (op (e0) (e0))) = ((op (unit) (e0)) = (op (e0) (e0)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H45. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H46. % 40.94/41.12 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 40.94/41.12 cut (((op (e0) (e0)) = (op (unit) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 40.94/41.12 congruence. % 40.94/41.12 apply (zenon_L14_); trivial. % 40.94/41.12 apply zenon_H47. apply refl_equal. % 40.94/41.12 apply zenon_H47. apply refl_equal. % 40.94/41.12 apply zenon_H163. apply sym_equal. exact zenon_H162. % 40.94/41.12 (* end of lemma zenon_L220_ *) % 40.94/41.12 assert (zenon_L221_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e3)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H162 zenon_H42 zenon_H161 zenon_H4a zenon_Hc zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L220_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L17_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L8_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L10_); trivial. % 40.94/41.12 apply (zenon_L11_); trivial. % 40.94/41.12 (* end of lemma zenon_L221_ *) % 40.94/41.12 assert (zenon_L222_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e3)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H162 zenon_H42 zenon_H161 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc zenon_H92. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L220_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L6_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L8_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L10_); trivial. % 40.94/41.12 apply (zenon_L44_); trivial. % 40.94/41.12 (* end of lemma zenon_L222_ *) % 40.94/41.12 assert (zenon_L223_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e3)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.12 do 0 intro. intros zenon_He0 zenon_Hb zenon_H49 zenon_H34 zenon_H32 zenon_H87 zenon_H83 zenon_H5f zenon_H81 zenon_H7b zenon_H89 zenon_H57 zenon_H58 zenon_H6e zenon_H77 zenon_H73 zenon_H61 zenon_H68 zenon_H88 zenon_He1 zenon_H3b zenon_H162 zenon_H42 zenon_H161 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.12 apply (zenon_L12_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.12 apply (zenon_L221_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.12 apply (zenon_L41_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.12 exact (zenon_He1 zenon_He5). % 40.94/41.12 apply (zenon_L222_); trivial. % 40.94/41.12 (* end of lemma zenon_L223_ *) % 40.94/41.12 assert (zenon_L224_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> False). % 40.94/41.12 do 0 intro. intros zenon_Hee zenon_Hd9 zenon_Hd4 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H17 zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H49 zenon_H162 zenon_H42 zenon_H161 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_He1 zenon_H91 zenon_He0. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 40.94/41.12 apply (zenon_L223_); trivial. % 40.94/41.12 apply (zenon_L110_); trivial. % 40.94/41.12 (* end of lemma zenon_L224_ *) % 40.94/41.12 assert (zenon_L225_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H68 zenon_H73 zenon_H8d zenon_H5f zenon_H77 zenon_H76 zenon_H20 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L101_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L104_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L106_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L32_); trivial. % 40.94/41.12 apply (zenon_L11_); trivial. % 40.94/41.12 (* end of lemma zenon_L225_ *) % 40.94/41.12 assert (zenon_L226_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 40.94/41.12 do 0 intro. intros zenon_Hf0 zenon_Hba zenon_H9f zenon_H8e zenon_He0 zenon_H91 zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_H161 zenon_H42 zenon_H162 zenon_H49 zenon_Hb zenon_Hc zenon_H18 zenon_H16 zenon_H17 zenon_H1f zenon_H20 zenon_H22 zenon_H2d zenon_H2c zenon_H32 zenon_H34 zenon_H3b zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hd9 zenon_Hee. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_He1 | zenon_intro zenon_H76 ]. % 40.94/41.12 apply (zenon_L224_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.12 apply (zenon_L12_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.12 apply (zenon_L221_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.12 apply (zenon_L41_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.12 apply (zenon_L116_); trivial. % 40.94/41.12 apply (zenon_L222_); trivial. % 40.94/41.12 apply (zenon_L99_); trivial. % 40.94/41.12 apply (zenon_L225_); trivial. % 40.94/41.12 (* end of lemma zenon_L226_ *) % 40.94/41.12 assert (zenon_L227_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 40.94/41.12 do 0 intro. intros zenon_Hf0 zenon_Hf2 zenon_H9f zenon_H8e zenon_He0 zenon_H91 zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_H161 zenon_H42 zenon_H162 zenon_H49 zenon_Hb zenon_Hc zenon_H18 zenon_H16 zenon_H17 zenon_H1f zenon_H20 zenon_H22 zenon_H2d zenon_H2c zenon_H32 zenon_H34 zenon_H3b zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hd9 zenon_Hee. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_He1 | zenon_intro zenon_H76 ]. % 40.94/41.12 apply (zenon_L224_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.12 apply (zenon_L12_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.12 apply (zenon_L221_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.12 apply (zenon_L41_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.12 apply (zenon_L133_); trivial. % 40.94/41.12 apply (zenon_L222_); trivial. % 40.94/41.12 apply (zenon_L99_); trivial. % 40.94/41.12 apply (zenon_L225_); trivial. % 40.94/41.12 (* end of lemma zenon_L227_ *) % 40.94/41.12 assert (zenon_L228_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_Hf6 zenon_H18 zenon_Hc zenon_Hb zenon_H49 zenon_H162 zenon_H42 zenon_H161 zenon_He0 zenon_H8e zenon_H9f zenon_Hf0 zenon_Hf7 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H61 zenon_H5f zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_H91 zenon_Hd4 zenon_H17 zenon_H2c zenon_H2d zenon_Hd9 zenon_Hee zenon_H3b zenon_Hb6 zenon_Hb9 zenon_H22 zenon_H20 zenon_H58 zenon_H1f zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hba | zenon_intro zenon_Hf8 ]. % 40.94/41.12 apply (zenon_L226_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf9 ]. % 40.94/41.12 apply (zenon_L227_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hfa ]. % 40.94/41.12 exact (zenon_Hf7 zenon_Hfb). % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H59 | zenon_intro zenon_Hb7 ]. % 40.94/41.12 apply (zenon_L132_); trivial. % 40.94/41.12 apply (zenon_L123_); trivial. % 40.94/41.12 (* end of lemma zenon_L228_ *) % 40.94/41.12 assert (zenon_L229_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H101 zenon_Hfc zenon_Hfe zenon_Hff zenon_Hf0 zenon_H9f zenon_H8e zenon_He0 zenon_H91 zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_H161 zenon_H42 zenon_H162 zenon_H49 zenon_Hb zenon_Hc zenon_H18 zenon_H16 zenon_H17 zenon_H1f zenon_H20 zenon_H22 zenon_H2d zenon_H2c zenon_H32 zenon_H34 zenon_H3b zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hd9 zenon_Hee zenon_Hb9 zenon_Hb6 zenon_Hf6. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hfb ]. % 40.94/41.12 apply (zenon_L228_); trivial. % 40.94/41.12 apply (zenon_L139_); trivial. % 40.94/41.12 (* end of lemma zenon_L229_ *) % 40.94/41.12 assert (zenon_L230_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e4) (e4)) = (e0))\/(((op (e4) (e4)) = (e1))\/(((op (e4) (e4)) = (e2))\/(((op (e4) (e4)) = (e3))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e4) (e4)) = (e3)))\/((op (e4) (e3)) = (e4))) -> ((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e3)) = (e1))\/((op (e1) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e4) (e2)) = (e0)))))) -> (~((op (e1) (e0)) = (op (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) (e4)) = (e2)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H164 zenon_H162 zenon_H161 zenon_H13b zenon_H136 zenon_H140 zenon_H149 zenon_H14a zenon_H117 zenon_H112 zenon_H115 zenon_H116 zenon_H111 zenon_H10b zenon_H11f zenon_H129 zenon_H12d zenon_H103 zenon_H109 zenon_Hf6 zenon_Hee zenon_Hed zenon_He6 zenon_He8 zenon_He9 zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H50 zenon_H51 zenon_H49 zenon_H42 zenon_H41 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_H9f zenon_H99 zenon_H9b zenon_Hc2 zenon_Hbb zenon_Hb6 zenon_Hb9 zenon_Haa zenon_Hb1 zenon_Ha1 zenon_Hc8 zenon_Hd3 zenon_Hd4 zenon_Hcc zenon_Hd9 zenon_H8e zenon_H91 zenon_He0 zenon_Hf1 zenon_Hf0 zenon_Hff zenon_Hfe zenon_Hfc zenon_H101 zenon_H14b zenon_H14d zenon_H152 zenon_H157 zenon_H15b. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H15c | zenon_intro zenon_H17 ]. % 40.94/41.12 apply (zenon_L219_); trivial. % 40.94/41.12 apply (zenon_L229_); trivial. % 40.94/41.12 (* end of lemma zenon_L230_ *) % 40.94/41.12 assert (zenon_L231_ : (~((op (e0) (e0)) = (op (e0) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((unit) = (e0)) -> ((op (e0) (e4)) = (e0)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H165 zenon_H42 zenon_H9 zenon_H166. % 40.94/41.12 cut (((op (unit) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e0) (e4)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H165. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H42. % 40.94/41.12 cut (((e0) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 40.94/41.12 cut (((op (unit) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 40.94/41.12 congruence. % 40.94/41.12 elim (classic ((op (e0) (e0)) = (op (e0) (e0)))); [ zenon_intro zenon_H46 | zenon_intro zenon_H47 ]. % 40.94/41.12 cut (((op (e0) (e0)) = (op (e0) (e0))) = ((op (unit) (e0)) = (op (e0) (e0)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H45. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H46. % 40.94/41.12 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 40.94/41.12 cut (((op (e0) (e0)) = (op (unit) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 40.94/41.12 congruence. % 40.94/41.12 apply (zenon_L14_); trivial. % 40.94/41.12 apply zenon_H47. apply refl_equal. % 40.94/41.12 apply zenon_H47. apply refl_equal. % 40.94/41.12 apply zenon_H167. apply sym_equal. exact zenon_H166. % 40.94/41.12 (* end of lemma zenon_L231_ *) % 40.94/41.12 assert (zenon_L232_ : (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e0) (unit)) = (e0)) -> ((unit) = (e1)) -> ((op (e0) (e4)) = (e0)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H168 zenon_H50 zenon_H14 zenon_H166. % 40.94/41.12 cut (((op (e0) (unit)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e4)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H168. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H50. % 40.94/41.12 cut (((e0) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 40.94/41.12 cut (((op (e0) (unit)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 40.94/41.12 congruence. % 40.94/41.12 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 40.94/41.12 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (unit)) = (op (e0) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H137. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H138. % 40.94/41.12 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 40.94/41.12 cut (((op (e0) (e1)) = (op (e0) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 40.94/41.12 congruence. % 40.94/41.12 apply (zenon_L182_); trivial. % 40.94/41.12 apply zenon_H139. apply refl_equal. % 40.94/41.12 apply zenon_H139. apply refl_equal. % 40.94/41.12 apply zenon_H167. apply sym_equal. exact zenon_H166. % 40.94/41.12 (* end of lemma zenon_L232_ *) % 40.94/41.12 assert (zenon_L233_ : (~((op (e0) (e3)) = (op (e0) (e4)))) -> ((op (e0) (unit)) = (e0)) -> ((unit) = (e3)) -> ((op (e0) (e4)) = (e0)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H169 zenon_H50 zenon_H2a zenon_H166. % 40.94/41.12 cut (((op (e0) (unit)) = (e0)) = ((op (e0) (e3)) = (op (e0) (e4)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H169. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H50. % 40.94/41.12 cut (((e0) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 40.94/41.12 cut (((op (e0) (unit)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 40.94/41.12 congruence. % 40.94/41.12 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 40.94/41.12 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (unit)) = (op (e0) (e3)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H55. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H52. % 40.94/41.12 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 40.94/41.12 cut (((op (e0) (e3)) = (op (e0) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 40.94/41.12 congruence. % 40.94/41.12 apply (zenon_L18_); trivial. % 40.94/41.12 apply zenon_H53. apply refl_equal. % 40.94/41.12 apply zenon_H53. apply refl_equal. % 40.94/41.12 apply zenon_H167. apply sym_equal. exact zenon_H166. % 40.94/41.12 (* end of lemma zenon_L233_ *) % 40.94/41.12 assert (zenon_L234_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e0) (e4)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H42 zenon_H165 zenon_H168 zenon_H22 zenon_H20 zenon_H1f zenon_H166 zenon_H50 zenon_H169 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L231_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L232_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L8_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L233_); trivial. % 40.94/41.12 apply (zenon_L11_); trivial. % 40.94/41.12 (* end of lemma zenon_L234_ *) % 40.94/41.12 assert (zenon_L235_ : ((~((op (e4) (e4)) = (e3)))\/((op (e4) (e3)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> ((op (unit) (e4)) = (e4)) -> (((op (e4) (e4)) = (e0))\/(((op (e4) (e4)) = (e1))\/(((op (e4) (e4)) = (e2))\/(((op (e4) (e4)) = (e3))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e4)) = (e0))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H149 zenon_Hcc zenon_Hb1 zenon_H91 zenon_H57 zenon_H58 zenon_Hba zenon_Hd3 zenon_H140 zenon_Hc3 zenon_H34 zenon_He9 zenon_H13e zenon_H3b zenon_H16 zenon_H32 zenon_Hd4 zenon_He8 zenon_H99 zenon_He6 zenon_Hed. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H13f | zenon_intro zenon_Hcd ]. % 40.94/41.12 apply (zenon_L208_); trivial. % 40.94/41.12 apply (zenon_L81_); trivial. % 40.94/41.12 (* end of lemma zenon_L235_ *) % 40.94/41.12 assert (zenon_L236_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/(((op (e0) (e3)) = (e0))\/((op (e0) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e4) (e2)) = (e4)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e4) (e2)) = (e0)))))) -> (~((e0) = (e1))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e3)) = (e1))\/((op (e1) (e4)) = (e1)))))) -> ((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4))) -> ((~((op (e4) (e4)) = (e3)))\/((op (e4) (e3)) = (e4))) -> (((op (e4) (e4)) = (e0))\/(((op (e4) (e4)) = (e1))\/(((op (e4) (e4)) = (e2))\/(((op (e4) (e4)) = (e3))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H16a zenon_H16b zenon_Hc9 zenon_He1 zenon_H89 zenon_H17 zenon_H15b zenon_H157 zenon_H152 zenon_H14d zenon_H14b zenon_H101 zenon_Hfc zenon_Hfe zenon_Hff zenon_Hf0 zenon_Hf1 zenon_He0 zenon_H91 zenon_H8e zenon_Hd9 zenon_Hcc zenon_Hd4 zenon_Hd3 zenon_Hc8 zenon_Ha1 zenon_Hb1 zenon_Haa zenon_Hb9 zenon_Hb6 zenon_Hbb zenon_Hc2 zenon_H9b zenon_H99 zenon_H9f zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_H41 zenon_H49 zenon_H51 zenon_Hb zenon_Hc zenon_H18 zenon_H2d zenon_H2c zenon_He9 zenon_He8 zenon_He6 zenon_Hed zenon_Hee zenon_Hf6 zenon_H109 zenon_H103 zenon_H12d zenon_H129 zenon_H11f zenon_H10b zenon_H111 zenon_H116 zenon_H115 zenon_H112 zenon_H117 zenon_H14a zenon_H149 zenon_H140 zenon_H136 zenon_H13b zenon_H161 zenon_H164 zenon_H3b zenon_H42 zenon_H165 zenon_H168 zenon_H22 zenon_H20 zenon_H1f zenon_H50 zenon_H169 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H16d | zenon_intro zenon_H16c ]. % 40.94/41.12 exact (zenon_H16b zenon_H16d). % 40.94/41.12 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H43 | zenon_intro zenon_H16e ]. % 40.94/41.12 apply (zenon_L100_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H10c | zenon_intro zenon_H16f ]. % 40.94/41.12 apply (zenon_L204_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H162 | zenon_intro zenon_H166 ]. % 40.94/41.12 apply (zenon_L230_); trivial. % 40.94/41.12 apply (zenon_L234_); trivial. % 40.94/41.12 (* end of lemma zenon_L236_ *) % 40.94/41.12 assert (zenon_L237_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (e4)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H7c zenon_H5f zenon_H7b zenon_H9b zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L35_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L49_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L84_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L102_); trivial. % 40.94/41.12 apply (zenon_L11_); trivial. % 40.94/41.12 (* end of lemma zenon_L237_ *) % 40.94/41.12 assert (zenon_L238_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H88 zenon_H68 zenon_H1f zenon_H22 zenon_H57 zenon_H58 zenon_H59 zenon_H73 zenon_H9f zenon_H61 zenon_H20 zenon_H77 zenon_H8e zenon_H89 zenon_H3b zenon_H5f zenon_H7b zenon_H9b zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H60 | zenon_intro zenon_H8a ]. % 40.94/41.12 apply (zenon_L27_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H72 | zenon_intro zenon_H8b ]. % 40.94/41.12 apply (zenon_L51_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H8b); [ zenon_intro zenon_H76 | zenon_intro zenon_H8c ]. % 40.94/41.12 apply (zenon_L85_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H8d | zenon_intro zenon_H7c ]. % 40.94/41.12 exact (zenon_H89 zenon_H8d). % 40.94/41.12 apply (zenon_L237_); trivial. % 40.94/41.12 (* end of lemma zenon_L238_ *) % 40.94/41.12 assert (zenon_L239_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (e4)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H7c zenon_H5f zenon_H7b zenon_H9b zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L35_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L49_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L84_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L102_); trivial. % 40.94/41.12 apply (zenon_L44_); trivial. % 40.94/41.12 (* end of lemma zenon_L239_ *) % 40.94/41.12 assert (zenon_L240_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e3) (e3)) = (e3))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.12 do 0 intro. intros zenon_He0 zenon_Hb zenon_H50 zenon_H51 zenon_H49 zenon_H68 zenon_He1 zenon_H88 zenon_H41 zenon_H42 zenon_H43 zenon_H73 zenon_Hbb zenon_H61 zenon_Hc3 zenon_Hd9 zenon_H8e zenon_H83 zenon_H9f zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_Hd4 zenon_Hd3 zenon_H58 zenon_Hba zenon_H57 zenon_Hb1 zenon_Hda zenon_Hb6 zenon_Hb9 zenon_H77 zenon_H34 zenon_H16 zenon_Haa zenon_Ha1 zenon_H18 zenon_H2d zenon_H17 zenon_H2c zenon_Hc2 zenon_H89 zenon_H3b zenon_H5f zenon_H7b zenon_H9b zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.12 apply (zenon_L12_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.12 apply (zenon_L20_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.12 apply (zenon_L238_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.12 exact (zenon_He1 zenon_He5). % 40.94/41.12 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H60 | zenon_intro zenon_H8a ]. % 40.94/41.12 apply (zenon_L45_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H72 | zenon_intro zenon_H8b ]. % 40.94/41.12 apply (zenon_L82_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H8b); [ zenon_intro zenon_H76 | zenon_intro zenon_H8c ]. % 40.94/41.12 apply (zenon_L92_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H8d | zenon_intro zenon_H7c ]. % 40.94/41.12 exact (zenon_H89 zenon_H8d). % 40.94/41.12 apply (zenon_L239_); trivial. % 40.94/41.12 (* end of lemma zenon_L240_ *) % 40.94/41.12 assert (zenon_L241_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e3)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.12 do 0 intro. intros zenon_He0 zenon_Hb zenon_H49 zenon_H34 zenon_H32 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H9b zenon_H7b zenon_H5f zenon_H89 zenon_H8e zenon_H77 zenon_H61 zenon_H9f zenon_H73 zenon_H58 zenon_H57 zenon_H68 zenon_H88 zenon_He1 zenon_H3b zenon_H162 zenon_H42 zenon_H161 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.12 apply (zenon_L12_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.12 apply (zenon_L221_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.12 apply (zenon_L238_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.12 exact (zenon_He1 zenon_He5). % 40.94/41.12 apply (zenon_L222_); trivial. % 40.94/41.12 (* end of lemma zenon_L241_ *) % 40.94/41.12 assert (zenon_L242_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H166 zenon_H42 zenon_H165 zenon_H4a zenon_Hc zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L231_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L17_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L8_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L10_); trivial. % 40.94/41.12 apply (zenon_L11_); trivial. % 40.94/41.12 (* end of lemma zenon_L242_ *) % 40.94/41.12 assert (zenon_L243_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H166 zenon_H42 zenon_H165 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc zenon_H92. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L231_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L6_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L8_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L10_); trivial. % 40.94/41.12 apply (zenon_L44_); trivial. % 40.94/41.12 (* end of lemma zenon_L243_ *) % 40.94/41.12 assert (zenon_L244_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.12 do 0 intro. intros zenon_He0 zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_H32 zenon_H34 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H3b zenon_H166 zenon_H42 zenon_H165 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.12 apply (zenon_L12_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.12 apply (zenon_L242_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.12 apply (zenon_L112_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.12 exact (zenon_He1 zenon_He5). % 40.94/41.12 apply (zenon_L243_); trivial. % 40.94/41.12 (* end of lemma zenon_L244_ *) % 40.94/41.12 assert (zenon_L245_ : (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/(((op (e0) (e3)) = (e0))\/((op (e0) (e4)) = (e0)))))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H16b zenon_He0 zenon_H91 zenon_Hd9 zenon_Hd4 zenon_Hd3 zenon_Ha1 zenon_Hb1 zenon_Haa zenon_Hb9 zenon_Hb6 zenon_H83 zenon_Hba zenon_Hbb zenon_Hc3 zenon_Hc2 zenon_He1 zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H9f zenon_H9a zenon_H99 zenon_H9b zenon_H77 zenon_Hc8 zenon_H8e zenon_H89 zenon_Hcc zenon_H7b zenon_H88 zenon_H41 zenon_H42 zenon_H49 zenon_H51 zenon_H50 zenon_Hb zenon_Hc zenon_H18 zenon_H16 zenon_H17 zenon_H1f zenon_H20 zenon_H22 zenon_H2d zenon_H2c zenon_H32 zenon_H34 zenon_H3b zenon_Hf0 zenon_H10b zenon_Hee zenon_He9 zenon_He8 zenon_He6 zenon_Hed zenon_H6e zenon_H87 zenon_H81 zenon_H161 zenon_H165 zenon_H16a. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H16d | zenon_intro zenon_H16c ]. % 40.94/41.12 exact (zenon_H16b zenon_H16d). % 40.94/41.12 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H43 | zenon_intro zenon_H16e ]. % 40.94/41.12 apply (zenon_L240_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H10c | zenon_intro zenon_H16f ]. % 40.94/41.12 apply (zenon_L151_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H162 | zenon_intro zenon_H166 ]. % 40.94/41.12 apply (zenon_L241_); trivial. % 40.94/41.12 apply (zenon_L244_); trivial. % 40.94/41.12 apply (zenon_L99_); trivial. % 40.94/41.12 (* end of lemma zenon_L245_ *) % 40.94/41.12 assert (zenon_L246_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e2)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H32 zenon_Hc8 zenon_H9a zenon_H91 zenon_H99 zenon_Hd3 zenon_Hc9 zenon_He9. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L70_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L71_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L84_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L72_); trivial. % 40.94/41.12 apply (zenon_L107_); trivial. % 40.94/41.12 (* end of lemma zenon_L246_ *) % 40.94/41.12 assert (zenon_L247_ : ((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((~((op (e4) (e4)) = (e3)))\/((op (e4) (e3)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> ((op (unit) (e4)) = (e4)) -> (((op (e4) (e4)) = (e0))\/(((op (e4) (e4)) = (e1))\/(((op (e4) (e4)) = (e2))\/(((op (e4) (e4)) = (e3))\/((op (e4) (e4)) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H14a zenon_H9b zenon_Hc8 zenon_H149 zenon_Hcc zenon_Hb1 zenon_H91 zenon_H57 zenon_H58 zenon_Hba zenon_Hd3 zenon_H140 zenon_H34 zenon_He9 zenon_H3b zenon_H16 zenon_H32 zenon_Hd4 zenon_He8 zenon_H99 zenon_He6 zenon_Hed zenon_H77 zenon_H22 zenon_H20 zenon_H1f zenon_H9f zenon_H76 zenon_H5f zenon_H8e zenon_Hf1. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H13e | zenon_intro zenon_H9a ]. % 40.94/41.12 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 40.94/41.12 apply (zenon_L235_); trivial. % 40.94/41.12 apply (zenon_L117_); trivial. % 40.94/41.12 apply (zenon_L85_); trivial. % 40.94/41.12 (* end of lemma zenon_L247_ *) % 40.94/41.12 assert (zenon_L248_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H18 zenon_H17 zenon_H22 zenon_H20 zenon_H1f zenon_H111 zenon_H11b zenon_H2c zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L179_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L6_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L8_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L183_); trivial. % 40.94/41.12 apply (zenon_L11_); trivial. % 40.94/41.12 (* end of lemma zenon_L248_ *) % 40.94/41.12 assert (zenon_L249_ : ((op (e0) (unit)) = (e0)) -> ((unit) = (e1)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H50 zenon_H14 zenon_H16d zenon_H41. % 40.94/41.12 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 40.94/41.12 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (e0)) = (op (e0) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H41. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H138. % 40.94/41.12 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 40.94/41.12 cut (((op (e0) (e1)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H170]. % 40.94/41.12 congruence. % 40.94/41.12 cut (((op (e0) (unit)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e0)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H170. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H50. % 40.94/41.12 cut (((e0) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 40.94/41.12 cut (((op (e0) (unit)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 40.94/41.12 congruence. % 40.94/41.12 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 40.94/41.12 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (unit)) = (op (e0) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H137. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H138. % 40.94/41.12 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 40.94/41.12 cut (((op (e0) (e1)) = (op (e0) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 40.94/41.12 congruence. % 40.94/41.12 apply (zenon_L182_); trivial. % 40.94/41.12 apply zenon_H139. apply refl_equal. % 40.94/41.12 apply zenon_H139. apply refl_equal. % 40.94/41.12 apply zenon_H171. apply sym_equal. exact zenon_H16d. % 40.94/41.12 apply zenon_H139. apply refl_equal. % 40.94/41.12 apply zenon_H139. apply refl_equal. % 40.94/41.12 (* end of lemma zenon_L249_ *) % 40.94/41.12 assert (zenon_L250_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H42 zenon_H41 zenon_H16d zenon_H22 zenon_H20 zenon_H1f zenon_H51 zenon_H43 zenon_H50 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L15_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L249_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L8_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L19_); trivial. % 40.94/41.12 apply (zenon_L11_); trivial. % 40.94/41.12 (* end of lemma zenon_L250_ *) % 40.94/41.12 assert (zenon_L251_ : ((~((op (e0) (e0)) = (op (e0) (e0))))/\(((op (op (e0) (e0)) (e0)) = (e0))/\(~((op (op (e0) (e0)) (e0)) = (e0))))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H172. % 40.94/41.12 apply (zenon_and_s _ _ zenon_H172). zenon_intro zenon_H47. zenon_intro zenon_H173. % 40.94/41.12 apply zenon_H47. apply refl_equal. % 40.94/41.12 (* end of lemma zenon_L251_ *) % 40.94/41.12 assert (zenon_L252_ : (~((op (e0) (e1)) = (op (unit) (e1)))) -> ((unit) = (e0)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H174 zenon_H9. % 40.94/41.12 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 40.94/41.12 cut (((e0) = (unit))); [idtac | apply NNPP; zenon_intro zenon_Ha]. % 40.94/41.12 congruence. % 40.94/41.12 apply zenon_Ha. apply sym_equal. exact zenon_H9. % 40.94/41.12 apply zenon_H12. apply refl_equal. % 40.94/41.12 (* end of lemma zenon_L252_ *) % 40.94/41.12 assert (zenon_L253_ : (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((unit) = (e0)) -> ((op (e0) (e2)) = (e1)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H136 zenon_H16 zenon_H9 zenon_H175. % 40.94/41.12 cut (((op (unit) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e0) (e2)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H136. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H16. % 40.94/41.12 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 40.94/41.12 cut (((op (unit) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 40.94/41.12 congruence. % 40.94/41.12 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 40.94/41.12 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (unit) (e1)) = (op (e0) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H177. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H138. % 40.94/41.12 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 40.94/41.12 cut (((op (e0) (e1)) = (op (unit) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H174]. % 40.94/41.12 congruence. % 40.94/41.12 apply (zenon_L252_); trivial. % 40.94/41.12 apply zenon_H139. apply refl_equal. % 40.94/41.12 apply zenon_H139. apply refl_equal. % 40.94/41.12 apply zenon_H176. apply sym_equal. exact zenon_H175. % 40.94/41.12 (* end of lemma zenon_L253_ *) % 40.94/41.12 assert (zenon_L254_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H175 zenon_H136 zenon_H4a zenon_Hc zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L253_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L17_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L8_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L10_); trivial. % 40.94/41.12 apply (zenon_L11_); trivial. % 40.94/41.12 (* end of lemma zenon_L254_ *) % 40.94/41.12 assert (zenon_L255_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H175 zenon_H136 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc zenon_H92. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L253_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L6_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L8_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L10_); trivial. % 40.94/41.12 apply (zenon_L44_); trivial. % 40.94/41.12 (* end of lemma zenon_L255_ *) % 40.94/41.12 assert (zenon_L256_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.12 do 0 intro. intros zenon_He0 zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_H32 zenon_H34 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H3b zenon_H175 zenon_H136 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.12 apply (zenon_L12_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.12 apply (zenon_L254_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.12 apply (zenon_L112_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.12 exact (zenon_He1 zenon_He5). % 40.94/41.12 apply (zenon_L255_); trivial. % 40.94/41.12 (* end of lemma zenon_L256_ *) % 40.94/41.12 assert (zenon_L257_ : (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (unit) (e1)) = (e1)) -> ((unit) = (e0)) -> ((op (e0) (e3)) = (e1)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H51 zenon_H16 zenon_H9 zenon_H178. % 40.94/41.12 cut (((op (unit) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e0) (e3)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H51. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H16. % 40.94/41.12 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 40.94/41.12 cut (((op (unit) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 40.94/41.12 congruence. % 40.94/41.12 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 40.94/41.12 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (unit) (e1)) = (op (e0) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H177. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H138. % 40.94/41.12 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 40.94/41.12 cut (((op (e0) (e1)) = (op (unit) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H174]. % 40.94/41.12 congruence. % 40.94/41.12 apply (zenon_L252_); trivial. % 40.94/41.12 apply zenon_H139. apply refl_equal. % 40.94/41.12 apply zenon_H139. apply refl_equal. % 40.94/41.12 apply zenon_H179. apply sym_equal. exact zenon_H178. % 40.94/41.12 (* end of lemma zenon_L257_ *) % 40.94/41.12 assert (zenon_L258_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H178 zenon_H51 zenon_H4a zenon_Hc zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L257_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L17_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L8_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L10_); trivial. % 40.94/41.12 apply (zenon_L11_); trivial. % 40.94/41.12 (* end of lemma zenon_L258_ *) % 40.94/41.12 assert (zenon_L259_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H178 zenon_H51 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc zenon_H92. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L257_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L6_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L8_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L10_); trivial. % 40.94/41.12 apply (zenon_L44_); trivial. % 40.94/41.12 (* end of lemma zenon_L259_ *) % 40.94/41.12 assert (zenon_L260_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.12 do 0 intro. intros zenon_He0 zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_H32 zenon_H34 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H3b zenon_H178 zenon_H51 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.12 apply (zenon_L12_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.12 apply (zenon_L258_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.12 apply (zenon_L112_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.12 exact (zenon_He1 zenon_He5). % 40.94/41.12 apply (zenon_L259_); trivial. % 40.94/41.12 (* end of lemma zenon_L260_ *) % 40.94/41.12 assert (zenon_L261_ : (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((unit) = (e0)) -> ((op (e0) (e4)) = (e1)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H168 zenon_H16 zenon_H9 zenon_H17a. % 40.94/41.12 cut (((op (unit) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e0) (e4)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H168. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H16. % 40.94/41.12 cut (((e1) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 40.94/41.12 cut (((op (unit) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 40.94/41.12 congruence. % 40.94/41.12 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 40.94/41.12 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (unit) (e1)) = (op (e0) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H177. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H138. % 40.94/41.12 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 40.94/41.12 cut (((op (e0) (e1)) = (op (unit) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H174]. % 40.94/41.12 congruence. % 40.94/41.12 apply (zenon_L252_); trivial. % 40.94/41.12 apply zenon_H139. apply refl_equal. % 40.94/41.12 apply zenon_H139. apply refl_equal. % 40.94/41.12 apply zenon_H17b. apply sym_equal. exact zenon_H17a. % 40.94/41.12 (* end of lemma zenon_L261_ *) % 40.94/41.12 assert (zenon_L262_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e4)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H17a zenon_H168 zenon_H4a zenon_Hc zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L261_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L17_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L8_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L10_); trivial. % 40.94/41.12 apply (zenon_L11_); trivial. % 40.94/41.12 (* end of lemma zenon_L262_ *) % 40.94/41.12 assert (zenon_L263_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e4)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H17a zenon_H168 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc zenon_H92. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L261_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L6_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L8_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L10_); trivial. % 40.94/41.12 apply (zenon_L44_); trivial. % 40.94/41.12 (* end of lemma zenon_L263_ *) % 40.94/41.12 assert (zenon_L264_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e4)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.12 do 0 intro. intros zenon_He0 zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_H32 zenon_H34 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H3b zenon_H17a zenon_H168 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.12 apply (zenon_L12_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.12 apply (zenon_L262_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.12 apply (zenon_L112_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.12 exact (zenon_He1 zenon_He5). % 40.94/41.12 apply (zenon_L263_); trivial. % 40.94/41.12 (* end of lemma zenon_L264_ *) % 40.94/41.12 assert (zenon_L265_ : ((~((op (e1) (e0)) = (op (e0) (e1))))/\(((op (op (e0) (e1)) (e1)) = (e0))/\(~((op (op (e0) (e1)) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e3)) = (e1))\/((op (e0) (e4)) = (e1)))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H17c zenon_H17d zenon_H17e zenon_H136 zenon_H51 zenon_He0 zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_H32 zenon_H34 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H3b zenon_H168 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc. % 40.94/41.12 apply (zenon_and_s _ _ zenon_H17c). zenon_intro zenon_H180. zenon_intro zenon_H17f. % 40.94/41.12 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H182. zenon_intro zenon_H181. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H184 | zenon_intro zenon_H183 ]. % 40.94/41.12 exact (zenon_H17e zenon_H184). % 40.94/41.12 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ]. % 40.94/41.12 cut (((op (e1) (e0)) = (e1)) = ((op (op (e0) (e1)) (e0)) = (e1))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H181. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H17. % 40.94/41.12 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 40.94/41.12 cut (((op (e1) (e0)) = (op (op (e0) (e1)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 40.94/41.12 congruence. % 40.94/41.12 elim (classic ((op (op (e0) (e1)) (e0)) = (op (op (e0) (e1)) (e0)))); [ zenon_intro zenon_H188 | zenon_intro zenon_H189 ]. % 40.94/41.12 cut (((op (op (e0) (e1)) (e0)) = (op (op (e0) (e1)) (e0))) = ((op (e1) (e0)) = (op (op (e0) (e1)) (e0)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H187. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H188. % 40.94/41.12 cut (((op (op (e0) (e1)) (e0)) = (op (op (e0) (e1)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 40.94/41.12 cut (((op (op (e0) (e1)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18a]. % 40.94/41.12 congruence. % 40.94/41.12 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 40.94/41.12 cut (((op (e0) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H18b]. % 40.94/41.12 congruence. % 40.94/41.12 exact (zenon_H18b zenon_H186). % 40.94/41.12 apply zenon_H3f. apply refl_equal. % 40.94/41.12 apply zenon_H189. apply refl_equal. % 40.94/41.12 apply zenon_H189. apply refl_equal. % 40.94/41.12 apply zenon_H12. apply refl_equal. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 40.94/41.12 apply (zenon_L256_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H178 | zenon_intro zenon_H17a ]. % 40.94/41.12 apply (zenon_L260_); trivial. % 40.94/41.12 apply (zenon_L264_); trivial. % 40.94/41.12 (* end of lemma zenon_L265_ *) % 40.94/41.12 assert (zenon_L266_ : ((e3) = (op (e2) (e4))) -> ((op (e2) (e4)) = (e1)) -> (~((e1) = (e3))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H22 zenon_H18d zenon_H18e. % 40.94/41.12 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H18f | zenon_intro zenon_H1e ]. % 40.94/41.12 cut (((e3) = (e3)) = ((e1) = (e3))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H18e. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H18f. % 40.94/41.12 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 40.94/41.12 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 40.94/41.12 congruence. % 40.94/41.12 cut (((e3) = (op (e2) (e4))) = ((e3) = (e1))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H190. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H22. % 40.94/41.12 cut (((op (e2) (e4)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 40.94/41.12 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 40.94/41.12 congruence. % 40.94/41.12 apply zenon_H1e. apply refl_equal. % 40.94/41.12 exact (zenon_H191 zenon_H18d). % 40.94/41.12 apply zenon_H1e. apply refl_equal. % 40.94/41.12 apply zenon_H1e. apply refl_equal. % 40.94/41.12 (* end of lemma zenon_L266_ *) % 40.94/41.12 assert (zenon_L267_ : (~((op (e0) (e3)) = (op (unit) (e3)))) -> ((unit) = (e0)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H192 zenon_H9. % 40.94/41.12 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 40.94/41.12 cut (((e0) = (unit))); [idtac | apply NNPP; zenon_intro zenon_Ha]. % 40.94/41.12 congruence. % 40.94/41.12 apply zenon_Ha. apply sym_equal. exact zenon_H9. % 40.94/41.12 apply zenon_H1e. apply refl_equal. % 40.94/41.12 (* end of lemma zenon_L267_ *) % 40.94/41.12 assert (zenon_L268_ : ((op (unit) (e3)) = (e3)) -> ((unit) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H20 zenon_H9 zenon_H193 zenon_H51. % 40.94/41.12 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 40.94/41.12 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e1)) = (op (e0) (e3)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H51. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H52. % 40.94/41.12 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 40.94/41.12 cut (((op (e0) (e3)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 40.94/41.12 congruence. % 40.94/41.12 cut (((op (unit) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e0) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H54. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H20. % 40.94/41.12 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 40.94/41.12 cut (((op (unit) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 40.94/41.12 congruence. % 40.94/41.12 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 40.94/41.12 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (unit) (e3)) = (op (e0) (e3)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H195. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H52. % 40.94/41.12 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 40.94/41.12 cut (((op (e0) (e3)) = (op (unit) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 40.94/41.12 congruence. % 40.94/41.12 apply (zenon_L267_); trivial. % 40.94/41.12 apply zenon_H53. apply refl_equal. % 40.94/41.12 apply zenon_H53. apply refl_equal. % 40.94/41.12 apply zenon_H194. apply sym_equal. exact zenon_H193. % 40.94/41.12 apply zenon_H53. apply refl_equal. % 40.94/41.12 apply zenon_H53. apply refl_equal. % 40.94/41.12 (* end of lemma zenon_L268_ *) % 40.94/41.12 assert (zenon_L269_ : (~((op (e3) (e1)) = (op (unit) (e1)))) -> ((unit) = (e3)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H196 zenon_H2a. % 40.94/41.12 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 40.94/41.12 cut (((e3) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 40.94/41.12 congruence. % 40.94/41.12 apply zenon_H2b. apply sym_equal. exact zenon_H2a. % 40.94/41.12 apply zenon_H12. apply refl_equal. % 40.94/41.12 (* end of lemma zenon_L269_ *) % 40.94/41.12 assert (zenon_L270_ : (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((unit) = (e3)) -> ((op (e3) (e4)) = (e1)) -> False). % 40.94/41.12 do 0 intro. intros zenon_H81 zenon_H16 zenon_H2a zenon_H197. % 40.94/41.12 cut (((op (unit) (e1)) = (e1)) = ((op (e3) (e1)) = (op (e3) (e4)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H81. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H16. % 40.94/41.12 cut (((e1) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 40.94/41.12 cut (((op (unit) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 40.94/41.12 congruence. % 40.94/41.12 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 40.94/41.12 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (unit) (e1)) = (op (e3) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H199. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H62. % 40.94/41.12 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 40.94/41.12 cut (((op (e3) (e1)) = (op (unit) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 40.94/41.12 congruence. % 40.94/41.12 apply (zenon_L269_); trivial. % 40.94/41.12 apply zenon_H63. apply refl_equal. % 40.94/41.12 apply zenon_H63. apply refl_equal. % 40.94/41.12 apply zenon_H198. apply sym_equal. exact zenon_H197. % 40.94/41.12 (* end of lemma zenon_L270_ *) % 40.94/41.12 assert (zenon_L271_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H51 zenon_H193 zenon_H41 zenon_H16d zenon_H50 zenon_H22 zenon_H20 zenon_H1f zenon_H197 zenon_H81 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.12 apply (zenon_L268_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.12 apply (zenon_L249_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.12 apply (zenon_L8_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.12 apply (zenon_L270_); trivial. % 40.94/41.12 apply (zenon_L11_); trivial. % 40.94/41.12 (* end of lemma zenon_L271_ *) % 40.94/41.12 assert (zenon_L272_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H19a zenon_Hc zenon_H91 zenon_H17 zenon_H2d zenon_H18 zenon_H168 zenon_He1 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H7b zenon_H88 zenon_H49 zenon_Hb zenon_He0 zenon_H116 zenon_H2c zenon_H115 zenon_H112 zenon_H18e zenon_H34 zenon_H16 zenon_H32 zenon_H81 zenon_H1f zenon_H20 zenon_H22 zenon_H50 zenon_H16d zenon_H41 zenon_H193 zenon_H51 zenon_H3b zenon_H146. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.12 apply (zenon_L264_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.12 apply (zenon_L167_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.12 apply (zenon_L266_); trivial. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.12 apply (zenon_L271_); trivial. % 40.94/41.12 exact (zenon_H146 zenon_H144). % 40.94/41.12 (* end of lemma zenon_L272_ *) % 40.94/41.12 assert (zenon_L273_ : (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (e2) (e1)) = (e3)) -> False). % 40.94/41.12 do 0 intro. intros zenon_Hb9 zenon_H22 zenon_H19e. % 40.94/41.12 cut (((e3) = (op (e2) (e4))) = ((op (e2) (e1)) = (op (e2) (e4)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_Hb9. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H22. % 40.94/41.12 cut (((op (e2) (e4)) = (op (e2) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 40.94/41.12 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 40.94/41.12 congruence. % 40.94/41.12 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H70 | zenon_intro zenon_H71 ]. % 40.94/41.12 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((e3) = (op (e2) (e1)))). % 40.94/41.12 intro zenon_D_pnotp. % 40.94/41.12 apply zenon_H1a0. % 40.94/41.12 rewrite <- zenon_D_pnotp. % 40.94/41.12 exact zenon_H70. % 40.94/41.12 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 40.94/41.12 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 40.94/41.12 congruence. % 40.94/41.12 exact (zenon_H1a1 zenon_H19e). % 40.94/41.12 apply zenon_H71. apply refl_equal. % 40.94/41.12 apply zenon_H71. apply refl_equal. % 40.94/41.12 apply zenon_H19f. apply refl_equal. % 40.94/41.12 (* end of lemma zenon_L273_ *) % 40.94/41.12 assert (zenon_L274_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.12 do 0 intro. intros zenon_H3b zenon_H61 zenon_H60 zenon_H9f zenon_H5f zenon_H73 zenon_H72 zenon_H20 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.12 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.13 apply (zenon_L46_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.13 apply (zenon_L24_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.13 apply (zenon_L50_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.13 apply (zenon_L30_); trivial. % 40.94/41.13 apply (zenon_L11_); trivial. % 40.94/41.13 (* end of lemma zenon_L274_ *) % 40.94/41.13 assert (zenon_L275_ : ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (e4)) = (e0)) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> False). % 40.94/41.13 do 0 intro. intros zenon_H11f zenon_H1a2 zenon_H34 zenon_H115. % 40.94/41.13 elim (classic ((op (e1) (e4)) = (op (e1) (e4)))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a4 ]. % 40.94/41.13 cut (((op (e1) (e4)) = (op (e1) (e4))) = ((op (e1) (e1)) = (op (e1) (e4)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H115. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H1a3. % 40.94/41.13 cut (((op (e1) (e4)) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1a4]. % 40.94/41.13 cut (((op (e1) (e4)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 40.94/41.13 congruence. % 40.94/41.13 cut (((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) = ((op (e1) (e4)) = (op (e1) (e1)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H1a5. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H11f. % 40.94/41.13 cut (((op (op (e4) (e2)) (op (e4) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 40.94/41.13 cut (((e0) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1a6]. % 40.94/41.13 congruence. % 40.94/41.13 elim (classic ((op (e1) (e4)) = (op (e1) (e4)))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a4 ]. % 40.94/41.13 cut (((op (e1) (e4)) = (op (e1) (e4))) = ((e0) = (op (e1) (e4)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H1a6. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H1a3. % 40.94/41.13 cut (((op (e1) (e4)) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1a4]. % 40.94/41.13 cut (((op (e1) (e4)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 40.94/41.13 congruence. % 40.94/41.13 exact (zenon_H1a7 zenon_H1a2). % 40.94/41.13 apply zenon_H1a4. apply refl_equal. % 40.94/41.13 apply zenon_H1a4. apply refl_equal. % 40.94/41.13 apply (zenon_L169_); trivial. % 40.94/41.13 apply zenon_H1a4. apply refl_equal. % 40.94/41.13 apply zenon_H1a4. apply refl_equal. % 40.94/41.13 (* end of lemma zenon_L275_ *) % 40.94/41.13 assert (zenon_L276_ : ((e3) = (op (e2) (e4))) -> ((op (e2) (e4)) = (e0)) -> (~((e0) = (e3))) -> False). % 40.94/41.13 do 0 intro. intros zenon_H22 zenon_H1a8 zenon_H1a9. % 40.94/41.13 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H18f | zenon_intro zenon_H1e ]. % 40.94/41.13 cut (((e3) = (e3)) = ((e0) = (e3))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H1a9. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H18f. % 40.94/41.13 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 40.94/41.13 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 40.94/41.13 congruence. % 40.94/41.13 cut (((e3) = (op (e2) (e4))) = ((e3) = (e0))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H1aa. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H22. % 40.94/41.13 cut (((op (e2) (e4)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 40.94/41.13 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 40.94/41.13 congruence. % 40.94/41.13 apply zenon_H1e. apply refl_equal. % 40.94/41.13 exact (zenon_H1ab zenon_H1a8). % 40.94/41.13 apply zenon_H1e. apply refl_equal. % 40.94/41.13 apply zenon_H1e. apply refl_equal. % 40.94/41.13 (* end of lemma zenon_L276_ *) % 40.94/41.13 assert (zenon_L277_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e4)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.13 do 0 intro. intros zenon_H3b zenon_Ha2 zenon_Hc zenon_Ha1 zenon_H18 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H32 zenon_H16 zenon_H34. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.13 apply (zenon_L52_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.13 apply (zenon_L6_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.13 apply (zenon_L8_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.13 apply (zenon_L10_); trivial. % 40.94/41.13 apply (zenon_L11_); trivial. % 40.94/41.13 (* end of lemma zenon_L277_ *) % 40.94/41.13 assert (zenon_L278_ : ((op (e1) (e4)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> False). % 40.94/41.13 do 0 intro. intros zenon_Hab zenon_H4a zenon_H116. % 40.94/41.13 elim (classic ((op (e1) (e4)) = (op (e1) (e4)))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a4 ]. % 40.94/41.13 cut (((op (e1) (e4)) = (op (e1) (e4))) = ((op (e1) (e3)) = (op (e1) (e4)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H116. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H1a3. % 40.94/41.13 cut (((op (e1) (e4)) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1a4]. % 40.94/41.13 cut (((op (e1) (e4)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ac]. % 40.94/41.13 congruence. % 40.94/41.13 cut (((op (e1) (e4)) = (e2)) = ((op (e1) (e4)) = (op (e1) (e3)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H1ac. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_Hab. % 40.94/41.13 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 40.94/41.13 cut (((op (e1) (e4)) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1a4]. % 40.94/41.13 congruence. % 40.94/41.13 apply zenon_H1a4. apply refl_equal. % 40.94/41.13 apply zenon_H4b. apply sym_equal. exact zenon_H4a. % 40.94/41.13 apply zenon_H1a4. apply refl_equal. % 40.94/41.13 apply zenon_H1a4. apply refl_equal. % 40.94/41.13 (* end of lemma zenon_L278_ *) % 40.94/41.13 assert (zenon_L279_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e2) (e4)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.13 do 0 intro. intros zenon_H3b zenon_Hb7 zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H20 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.13 apply (zenon_L62_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.13 apply (zenon_L24_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.13 apply (zenon_L42_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.13 apply (zenon_L26_); trivial. % 40.94/41.13 apply (zenon_L11_); trivial. % 40.94/41.13 (* end of lemma zenon_L279_ *) % 40.94/41.13 assert (zenon_L280_ : (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((op (e1) (e4)) = (e2)) -> ((op (e3) (e4)) = (e2)) -> False). % 40.94/41.13 do 0 intro. intros zenon_H1ad zenon_Hab zenon_Hbf. % 40.94/41.13 cut (((op (e1) (e4)) = (e2)) = ((op (e1) (e4)) = (op (e3) (e4)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H1ad. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_Hab. % 40.94/41.13 cut (((e2) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 40.94/41.13 cut (((op (e1) (e4)) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1a4]. % 40.94/41.13 congruence. % 40.94/41.13 apply zenon_H1a4. apply refl_equal. % 40.94/41.13 apply zenon_Hc0. apply sym_equal. exact zenon_Hbf. % 40.94/41.13 (* end of lemma zenon_L280_ *) % 40.94/41.13 assert (zenon_L281_ : (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (e1) (e4)) = (e3)) -> False). % 40.94/41.13 do 0 intro. intros zenon_H1ae zenon_H22 zenon_H1af. % 40.94/41.13 cut (((e3) = (op (e2) (e4))) = ((op (e1) (e4)) = (op (e2) (e4)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H1ae. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H22. % 40.94/41.13 cut (((op (e2) (e4)) = (op (e2) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 40.94/41.13 cut (((e3) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 40.94/41.13 congruence. % 40.94/41.13 elim (classic ((op (e1) (e4)) = (op (e1) (e4)))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a4 ]. % 40.94/41.13 cut (((op (e1) (e4)) = (op (e1) (e4))) = ((e3) = (op (e1) (e4)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H1b0. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H1a3. % 40.94/41.13 cut (((op (e1) (e4)) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1a4]. % 40.94/41.13 cut (((op (e1) (e4)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1b1]. % 40.94/41.13 congruence. % 40.94/41.13 exact (zenon_H1b1 zenon_H1af). % 40.94/41.13 apply zenon_H1a4. apply refl_equal. % 40.94/41.13 apply zenon_H1a4. apply refl_equal. % 40.94/41.13 apply zenon_H19f. apply refl_equal. % 40.94/41.13 (* end of lemma zenon_L281_ *) % 40.94/41.13 assert (zenon_L282_ : (~((op (e0) (e4)) = (op (unit) (e4)))) -> ((unit) = (e0)) -> False). % 40.94/41.13 do 0 intro. intros zenon_H1b2 zenon_H9. % 40.94/41.13 cut (((e4) = (e4))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 40.94/41.13 cut (((e0) = (unit))); [idtac | apply NNPP; zenon_intro zenon_Ha]. % 40.94/41.13 congruence. % 40.94/41.13 apply zenon_Ha. apply sym_equal. exact zenon_H9. % 40.94/41.13 apply zenon_H97. apply refl_equal. % 40.94/41.13 (* end of lemma zenon_L282_ *) % 40.94/41.13 assert (zenon_L283_ : (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((unit) = (e0)) -> ((op (e1) (e4)) = (e4)) -> False). % 40.94/41.13 do 0 intro. intros zenon_H1b3 zenon_Hd3 zenon_H9 zenon_H1b4. % 40.94/41.13 cut (((op (unit) (e4)) = (e4)) = ((op (e0) (e4)) = (op (e1) (e4)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H1b3. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_Hd3. % 40.94/41.13 cut (((e4) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 40.94/41.13 cut (((op (unit) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 40.94/41.13 congruence. % 40.94/41.13 elim (classic ((op (e0) (e4)) = (op (e0) (e4)))); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H1b8 ]. % 40.94/41.13 cut (((op (e0) (e4)) = (op (e0) (e4))) = ((op (unit) (e4)) = (op (e0) (e4)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H1b6. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H1b7. % 40.94/41.13 cut (((op (e0) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 40.94/41.13 cut (((op (e0) (e4)) = (op (unit) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 40.94/41.13 congruence. % 40.94/41.13 apply (zenon_L282_); trivial. % 40.94/41.13 apply zenon_H1b8. apply refl_equal. % 40.94/41.13 apply zenon_H1b8. apply refl_equal. % 40.94/41.13 apply zenon_H1b5. apply sym_equal. exact zenon_H1b4. % 40.94/41.13 (* end of lemma zenon_L283_ *) % 40.94/41.13 assert (zenon_L284_ : (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e3) (e4)) = (e2)) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((unit) = (e0)) -> False). % 40.94/41.13 do 0 intro. intros zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_Hbf zenon_H1ad zenon_H22 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H9. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1ba ]. % 40.94/41.13 apply (zenon_L275_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H113 | zenon_intro zenon_H1bb ]. % 40.94/41.13 apply (zenon_L164_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_Hab | zenon_intro zenon_H1bc ]. % 40.94/41.13 apply (zenon_L280_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H1af | zenon_intro zenon_H1b4 ]. % 40.94/41.13 apply (zenon_L281_); trivial. % 40.94/41.13 apply (zenon_L283_); trivial. % 40.94/41.13 (* end of lemma zenon_L284_ *) % 40.94/41.13 assert (zenon_L285_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.13 do 0 intro. intros zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H4a zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_Hbf zenon_Hc zenon_H83 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.13 apply (zenon_L284_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.13 apply (zenon_L17_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.13 apply (zenon_L8_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.13 apply (zenon_L67_); trivial. % 40.94/41.13 apply (zenon_L11_); trivial. % 40.94/41.13 (* end of lemma zenon_L285_ *) % 40.94/41.13 assert (zenon_L286_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.13 do 0 intro. intros zenon_H3b zenon_H57 zenon_H59 zenon_H58 zenon_H6e zenon_H22 zenon_H20 zenon_H1f zenon_H197 zenon_H81 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.13 apply (zenon_L22_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.13 apply (zenon_L29_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.13 apply (zenon_L8_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.13 apply (zenon_L270_); trivial. % 40.94/41.13 apply (zenon_L11_); trivial. % 40.94/41.13 (* end of lemma zenon_L286_ *) % 40.94/41.13 assert (zenon_L287_ : (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((unit) = (e1)) -> ((op (e1) (e1)) = (e0)) -> False). % 40.94/41.13 do 0 intro. intros zenon_H18 zenon_H42 zenon_H14 zenon_H15f. % 40.94/41.13 cut (((op (unit) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e1) (e1)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H18. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H42. % 40.94/41.13 cut (((e0) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1bd]. % 40.94/41.13 cut (((op (unit) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 40.94/41.13 congruence. % 40.94/41.13 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H107 | zenon_intro zenon_H108 ]. % 40.94/41.13 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (unit) (e0)) = (op (e1) (e0)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H13d. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H107. % 40.94/41.13 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 40.94/41.13 cut (((op (e1) (e0)) = (op (unit) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13c]. % 40.94/41.13 congruence. % 40.94/41.13 apply (zenon_L205_); trivial. % 40.94/41.13 apply zenon_H108. apply refl_equal. % 40.94/41.13 apply zenon_H108. apply refl_equal. % 40.94/41.13 apply zenon_H1bd. apply sym_equal. exact zenon_H15f. % 40.94/41.13 (* end of lemma zenon_L287_ *) % 40.94/41.13 assert (zenon_L288_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.13 do 0 intro. intros zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H22 zenon_H1ad zenon_Hbf zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.13 apply (zenon_L284_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.13 apply (zenon_L287_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.13 apply (zenon_L84_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.13 apply (zenon_L102_); trivial. % 40.94/41.13 apply (zenon_L44_); trivial. % 40.94/41.13 (* end of lemma zenon_L288_ *) % 40.94/41.13 assert (zenon_L289_ : (~((op (e4) (e3)) = (op (unit) (e3)))) -> ((unit) = (e4)) -> False). % 40.94/41.13 do 0 intro. intros zenon_H1be zenon_H33. % 40.94/41.13 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 40.94/41.13 cut (((e4) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 40.94/41.13 congruence. % 40.94/41.13 apply zenon_H3a. apply sym_equal. exact zenon_H33. % 40.94/41.13 apply zenon_H1e. apply refl_equal. % 40.94/41.13 (* end of lemma zenon_L289_ *) % 40.94/41.13 assert (zenon_L290_ : ((op (unit) (e3)) = (e3)) -> ((unit) = (e4)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.94/41.13 do 0 intro. intros zenon_H20 zenon_H33 zenon_H1bf zenon_Hb1. % 40.94/41.13 elim (classic ((op (e4) (e3)) = (op (e4) (e3)))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ]. % 40.94/41.13 cut (((op (e4) (e3)) = (op (e4) (e3))) = ((op (e4) (e1)) = (op (e4) (e3)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_Hb1. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_Hb2. % 40.94/41.13 cut (((op (e4) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 40.94/41.13 cut (((op (e4) (e3)) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 40.94/41.13 congruence. % 40.94/41.13 cut (((op (unit) (e3)) = (e3)) = ((op (e4) (e3)) = (op (e4) (e1)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_Hb4. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H20. % 40.94/41.13 cut (((e3) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 40.94/41.13 cut (((op (unit) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1c1]. % 40.94/41.13 congruence. % 40.94/41.13 elim (classic ((op (e4) (e3)) = (op (e4) (e3)))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ]. % 40.94/41.13 cut (((op (e4) (e3)) = (op (e4) (e3))) = ((op (unit) (e3)) = (op (e4) (e3)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H1c1. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_Hb2. % 40.94/41.13 cut (((op (e4) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 40.94/41.13 cut (((op (e4) (e3)) = (op (unit) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 40.94/41.13 congruence. % 40.94/41.13 apply (zenon_L289_); trivial. % 40.94/41.13 apply zenon_Hb3. apply refl_equal. % 40.94/41.13 apply zenon_Hb3. apply refl_equal. % 40.94/41.13 apply zenon_H1c0. apply sym_equal. exact zenon_H1bf. % 40.94/41.13 apply zenon_Hb3. apply refl_equal. % 40.94/41.13 apply zenon_Hb3. apply refl_equal. % 40.94/41.13 (* end of lemma zenon_L290_ *) % 40.94/41.13 assert (zenon_L291_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e2)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.94/41.13 do 0 intro. intros zenon_H3b zenon_Hc8 zenon_Hc9 zenon_H99 zenon_H32 zenon_H22 zenon_H1f zenon_Hbf zenon_Hc zenon_H83 zenon_H20 zenon_H1bf zenon_Hb1. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.13 apply (zenon_L70_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.13 apply (zenon_L71_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.13 apply (zenon_L8_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.13 apply (zenon_L67_); trivial. % 40.94/41.13 apply (zenon_L290_); trivial. % 40.94/41.13 (* end of lemma zenon_L291_ *) % 40.94/41.13 assert (zenon_L292_ : (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((unit) = (e3)) -> ((op (e3) (e4)) = (e0)) -> False). % 40.94/41.13 do 0 intro. intros zenon_H7b zenon_H42 zenon_H2a zenon_H1c2. % 40.94/41.13 cut (((op (unit) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e4)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H7b. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H42. % 40.94/41.13 cut (((e0) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1c3]. % 40.94/41.13 cut (((op (unit) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H127]. % 40.94/41.13 congruence. % 40.94/41.13 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H7f | zenon_intro zenon_H80 ]. % 40.94/41.13 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (unit) (e0)) = (op (e3) (e0)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H127. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H7f. % 40.94/41.13 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 40.94/41.13 cut (((op (e3) (e0)) = (op (unit) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 40.94/41.13 congruence. % 40.94/41.13 apply (zenon_L171_); trivial. % 40.94/41.13 apply zenon_H80. apply refl_equal. % 40.94/41.13 apply zenon_H80. apply refl_equal. % 40.94/41.13 apply zenon_H1c3. apply sym_equal. exact zenon_H1c2. % 40.94/41.13 (* end of lemma zenon_L292_ *) % 40.94/41.13 assert (zenon_L293_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e3)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.94/41.13 do 0 intro. intros zenon_H3b zenon_Hcc zenon_Hcd zenon_H99 zenon_H91 zenon_H1c2 zenon_H42 zenon_H7b zenon_H20 zenon_H1bf zenon_Hb1. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.13 apply (zenon_L74_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.13 apply (zenon_L75_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.13 apply (zenon_L76_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.13 apply (zenon_L292_); trivial. % 40.94/41.13 apply (zenon_L290_); trivial. % 40.94/41.13 (* end of lemma zenon_L293_ *) % 40.94/41.13 assert (zenon_L294_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e4) (e3)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e3) (e4)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e3) (e4)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.13 do 0 intro. intros zenon_Hd9 zenon_H92 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He8 zenon_Hd3 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H83 zenon_Hc zenon_Hbf zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H7b zenon_H42 zenon_H1c2 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.94/41.13 apply (zenon_L288_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.94/41.13 apply (zenon_L125_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.94/41.13 apply (zenon_L291_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.94/41.13 apply (zenon_L293_); trivial. % 40.94/41.13 exact (zenon_Hda zenon_Hde). % 40.94/41.13 (* end of lemma zenon_L294_ *) % 40.94/41.13 assert (zenon_L295_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e3) (e4)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e3) (e4)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.13 do 0 intro. intros zenon_He0 zenon_H2d zenon_Hb zenon_H49 zenon_H81 zenon_H197 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_Hd9 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He8 zenon_Hd3 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H83 zenon_Hc zenon_Hbf zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H7b zenon_H42 zenon_H1c2 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.13 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.13 apply (zenon_L12_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.13 apply (zenon_L285_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.13 apply (zenon_L286_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.13 exact (zenon_He1 zenon_He5). % 40.94/41.13 apply (zenon_L294_); trivial. % 40.94/41.13 (* end of lemma zenon_L295_ *) % 40.94/41.13 assert (zenon_L296_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.13 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_H116 zenon_H4a zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H1c2 zenon_H42 zenon_H7b zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_Hd9 zenon_He1 zenon_H57 zenon_H58 zenon_H6e zenon_H197 zenon_H81 zenon_H49 zenon_Hb zenon_H2d zenon_He0 zenon_Hc3. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.13 apply (zenon_L277_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.13 apply (zenon_L278_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.13 apply (zenon_L279_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.13 apply (zenon_L295_); trivial. % 40.94/41.13 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.13 (* end of lemma zenon_L296_ *) % 40.94/41.13 assert (zenon_L297_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e3) (e4)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.13 do 0 intro. intros zenon_H19a zenon_H168 zenon_Hba zenon_Hbb zenon_H18e zenon_Hc3 zenon_He0 zenon_H2d zenon_Hb zenon_H49 zenon_H81 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_Hd9 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He8 zenon_Hd3 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H83 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H7b zenon_H42 zenon_H1c2 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H4a zenon_H116 zenon_Ha1 zenon_Hc2 zenon_H146. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.13 apply (zenon_L262_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.13 apply (zenon_L178_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.13 apply (zenon_L266_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.13 apply (zenon_L296_); trivial. % 40.94/41.13 exact (zenon_H146 zenon_H144). % 40.94/41.13 (* end of lemma zenon_L297_ *) % 40.94/41.13 assert (zenon_L298_ : (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e0))) -> False). % 40.94/41.13 do 0 intro. intros zenon_H1c4 zenon_H165 zenon_H1a9 zenon_H146 zenon_Hc2 zenon_Ha1 zenon_H116 zenon_H4a zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H42 zenon_H7b zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_Hd9 zenon_He1 zenon_H57 zenon_H58 zenon_H6e zenon_H81 zenon_H49 zenon_Hb zenon_H2d zenon_He0 zenon_Hc3 zenon_H18e zenon_Hbb zenon_Hba zenon_H168 zenon_H19a zenon_H13e. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H166 | zenon_intro zenon_H1c5 ]. % 40.94/41.13 apply (zenon_L242_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1c6 ]. % 40.94/41.13 apply (zenon_L275_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1c7 ]. % 40.94/41.13 apply (zenon_L276_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H142 ]. % 40.94/41.13 apply (zenon_L297_); trivial. % 40.94/41.13 exact (zenon_H13e zenon_H142). % 40.94/41.13 (* end of lemma zenon_L298_ *) % 40.94/41.13 assert (zenon_L299_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e0))) -> False). % 40.94/41.13 do 0 intro. intros zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H88 zenon_H87 zenon_H77 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hee zenon_H1c9 zenon_Hb9 zenon_H73 zenon_H9f zenon_H1c4 zenon_H165 zenon_H1a9 zenon_H146 zenon_Hc2 zenon_Ha1 zenon_H116 zenon_H4a zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H42 zenon_H7b zenon_H20 zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_Hd9 zenon_He1 zenon_H57 zenon_H58 zenon_H6e zenon_H81 zenon_H49 zenon_Hb zenon_H2d zenon_He0 zenon_Hc3 zenon_H18e zenon_Hbb zenon_Hba zenon_H168 zenon_H19a zenon_H13e. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.13 apply (zenon_L272_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.13 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.13 apply (zenon_L273_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.13 apply (zenon_L274_); trivial. % 40.94/41.13 apply (zenon_L298_); trivial. % 40.94/41.13 (* end of lemma zenon_L299_ *) % 40.94/41.13 assert (zenon_L300_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e1) (e4)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.13 do 0 intro. intros zenon_H3b zenon_H113 zenon_H2c zenon_H112 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H20 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.13 apply (zenon_L164_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.13 apply (zenon_L24_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.13 apply (zenon_L42_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.13 apply (zenon_L26_); trivial. % 40.94/41.13 apply (zenon_L44_); trivial. % 40.94/41.13 (* end of lemma zenon_L300_ *) % 40.94/41.13 assert (zenon_L301_ : (~((op (op (e0) (e2)) (e0)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> False). % 40.94/41.13 do 0 intro. intros zenon_H1ce zenon_Hba zenon_H1cf. % 40.94/41.13 cut (((op (e2) (e0)) = (e2)) = ((op (op (e0) (e2)) (e0)) = (e2))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H1ce. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_Hba. % 40.94/41.13 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 40.94/41.13 cut (((op (e2) (e0)) = (op (op (e0) (e2)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d0]. % 40.94/41.13 congruence. % 40.94/41.13 elim (classic ((op (op (e0) (e2)) (e0)) = (op (op (e0) (e2)) (e0)))); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H1d2 ]. % 40.94/41.13 cut (((op (op (e0) (e2)) (e0)) = (op (op (e0) (e2)) (e0))) = ((op (e2) (e0)) = (op (op (e0) (e2)) (e0)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H1d0. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H1d1. % 40.94/41.13 cut (((op (op (e0) (e2)) (e0)) = (op (op (e0) (e2)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d2]. % 40.94/41.13 cut (((op (op (e0) (e2)) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d3]. % 40.94/41.13 congruence. % 40.94/41.13 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 40.94/41.13 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1d4]. % 40.94/41.13 congruence. % 40.94/41.13 exact (zenon_H1d4 zenon_H1cf). % 40.94/41.13 apply zenon_H3f. apply refl_equal. % 40.94/41.13 apply zenon_H1d2. apply refl_equal. % 40.94/41.13 apply zenon_H1d2. apply refl_equal. % 40.94/41.13 apply zenon_H7. apply refl_equal. % 40.94/41.13 (* end of lemma zenon_L301_ *) % 40.94/41.13 assert (zenon_L302_ : (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (op (e0) (e2)) (e0)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (unit) (e1)) = (e1)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.94/41.13 do 0 intro. intros zenon_Ha1 zenon_Hd3 zenon_Hb zenon_H1ce zenon_Hba zenon_H136 zenon_H16 zenon_H3b zenon_H10b zenon_H17 zenon_H22 zenon_H1f zenon_H50 zenon_H91 zenon_Hc zenon_H92 zenon_H1d5 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H20 zenon_H1bf zenon_Hb1. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H10c | zenon_intro zenon_H1d6 ]. % 40.94/41.13 apply (zenon_L149_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H175 | zenon_intro zenon_H1d7 ]. % 40.94/41.13 apply (zenon_L253_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1cf | zenon_intro zenon_H1d8 ]. % 40.94/41.13 apply (zenon_L301_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1da | zenon_intro zenon_H1d9 ]. % 40.94/41.13 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 40.94/41.13 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e2)) = (op (e0) (e3)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_Hb. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H52. % 40.94/41.13 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 40.94/41.13 cut (((op (e0) (e3)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10e]. % 40.94/41.13 congruence. % 40.94/41.13 cut (((op (unit) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e0) (e2)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H10e. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H20. % 40.94/41.13 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 40.94/41.13 cut (((op (unit) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 40.94/41.13 congruence. % 40.94/41.13 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 40.94/41.13 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (unit) (e3)) = (op (e0) (e3)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H195. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H52. % 40.94/41.13 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 40.94/41.13 cut (((op (e0) (e3)) = (op (unit) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 40.94/41.13 congruence. % 40.94/41.13 apply (zenon_L267_); trivial. % 40.94/41.13 apply zenon_H53. apply refl_equal. % 40.94/41.13 apply zenon_H53. apply refl_equal. % 40.94/41.13 apply zenon_H1db. apply sym_equal. exact zenon_H1da. % 40.94/41.13 apply zenon_H53. apply refl_equal. % 40.94/41.13 apply zenon_H53. apply refl_equal. % 40.94/41.13 elim (classic ((op (e0) (e4)) = (op (e0) (e4)))); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H1b8 ]. % 40.94/41.13 cut (((op (e0) (e4)) = (op (e0) (e4))) = ((op (e0) (e2)) = (op (e0) (e4)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_Ha1. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H1b7. % 40.94/41.13 cut (((op (e0) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 40.94/41.13 cut (((op (e0) (e4)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1dc]. % 40.94/41.13 congruence. % 40.94/41.13 cut (((op (unit) (e4)) = (e4)) = ((op (e0) (e4)) = (op (e0) (e2)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H1dc. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_Hd3. % 40.94/41.13 cut (((e4) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1dd]. % 40.94/41.13 cut (((op (unit) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 40.94/41.13 congruence. % 40.94/41.13 elim (classic ((op (e0) (e4)) = (op (e0) (e4)))); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H1b8 ]. % 40.94/41.13 cut (((op (e0) (e4)) = (op (e0) (e4))) = ((op (unit) (e4)) = (op (e0) (e4)))). % 40.94/41.13 intro zenon_D_pnotp. % 40.94/41.13 apply zenon_H1b6. % 40.94/41.13 rewrite <- zenon_D_pnotp. % 40.94/41.13 exact zenon_H1b7. % 40.94/41.13 cut (((op (e0) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 40.94/41.13 cut (((op (e0) (e4)) = (op (unit) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 40.94/41.13 congruence. % 40.94/41.13 apply (zenon_L282_); trivial. % 40.94/41.13 apply zenon_H1b8. apply refl_equal. % 40.94/41.13 apply zenon_H1b8. apply refl_equal. % 40.94/41.13 apply zenon_H1dd. apply sym_equal. exact zenon_H1d9. % 40.94/41.13 apply zenon_H1b8. apply refl_equal. % 40.94/41.13 apply zenon_H1b8. apply refl_equal. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.13 apply (zenon_L287_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.13 apply (zenon_L84_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.13 apply (zenon_L102_); trivial. % 40.94/41.13 apply (zenon_L290_); trivial. % 40.94/41.13 (* end of lemma zenon_L302_ *) % 40.94/41.13 assert (zenon_L303_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e2)) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (op (e0) (e2)) (e0)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (unit) (e1)) = (e1)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.94/41.13 do 0 intro. intros zenon_He0 zenon_H2c zenon_H2d zenon_H116 zenon_Hab zenon_H34 zenon_H32 zenon_H81 zenon_H197 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_Ha1 zenon_Hd3 zenon_Hb zenon_H1ce zenon_Hba zenon_H136 zenon_H16 zenon_H3b zenon_H10b zenon_H17 zenon_H22 zenon_H1f zenon_H50 zenon_H91 zenon_Hc zenon_H1d5 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H20 zenon_H1bf zenon_Hb1. % 40.94/41.13 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.13 apply (zenon_L12_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.13 apply (zenon_L278_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.13 apply (zenon_L286_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.13 exact (zenon_He1 zenon_He5). % 40.94/41.13 apply (zenon_L302_); trivial. % 40.94/41.13 (* end of lemma zenon_L303_ *) % 40.94/41.13 assert (zenon_L304_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e1)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> False). % 40.94/41.13 do 0 intro. intros zenon_H3b zenon_H9b zenon_H18 zenon_H17 zenon_H32 zenon_H99 zenon_H197 zenon_H16 zenon_H81 zenon_Hd3 zenon_Ha5 zenon_He8. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.13 apply (zenon_L55_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.13 apply (zenon_L6_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.13 apply (zenon_L58_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.13 apply (zenon_L270_); trivial. % 40.94/41.13 apply (zenon_L124_); trivial. % 40.94/41.13 (* end of lemma zenon_L304_ *) % 40.94/41.13 assert (zenon_L305_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e3)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.94/41.13 do 0 intro. intros zenon_H3b zenon_Hcc zenon_Hcd zenon_H99 zenon_H91 zenon_H197 zenon_H16 zenon_H81 zenon_H20 zenon_H1bf zenon_Hb1. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.13 apply (zenon_L74_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.13 apply (zenon_L75_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.13 apply (zenon_L76_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.13 apply (zenon_L270_); trivial. % 40.94/41.13 apply (zenon_L290_); trivial. % 40.94/41.13 (* end of lemma zenon_L305_ *) % 40.94/41.13 assert (zenon_L306_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (op (e0) (e2)) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((e1) = (op (e4) (e2))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e3) (e4)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.13 do 0 intro. intros zenon_Hd9 zenon_H42 zenon_H15f zenon_H1d5 zenon_H50 zenon_H10b zenon_H136 zenon_Hba zenon_H1ce zenon_Hb zenon_Ha1 zenon_He1 zenon_H57 zenon_H58 zenon_H6e zenon_H34 zenon_Hab zenon_H116 zenon_H2d zenon_H2c zenon_He0 zenon_He8 zenon_Hd3 zenon_H17 zenon_H18 zenon_H9b zenon_H92 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H81 zenon_H16 zenon_H197 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.94/41.13 apply (zenon_L303_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.94/41.13 apply (zenon_L304_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.94/41.13 apply (zenon_L73_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.94/41.13 apply (zenon_L305_); trivial. % 40.94/41.13 exact (zenon_Hda zenon_Hde). % 40.94/41.13 (* end of lemma zenon_L306_ *) % 40.94/41.13 assert (zenon_L307_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (op (e0) (e2)) (e0)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (unit)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e4) (e3)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.13 do 0 intro. intros zenon_Hc2 zenon_H197 zenon_H81 zenon_He0 zenon_H2d zenon_H116 zenon_H6e zenon_H57 zenon_He1 zenon_Ha1 zenon_Hb zenon_H1ce zenon_Hba zenon_H136 zenon_H10b zenon_H50 zenon_H1d5 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H1c2 zenon_H42 zenon_H7b zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H92 zenon_Hd9 zenon_Hc3. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.13 apply (zenon_L53_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.13 apply (zenon_L306_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.13 apply (zenon_L279_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.13 apply (zenon_L294_); trivial. % 40.94/41.13 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.13 (* end of lemma zenon_L307_ *) % 40.94/41.13 assert (zenon_L308_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e4) (e3)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e3) (e4)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (op (e0) (e2)) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.13 do 0 intro. intros zenon_H19a zenon_H168 zenon_H18e zenon_Hc3 zenon_Hd9 zenon_H92 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He8 zenon_Hd3 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H83 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H7b zenon_H42 zenon_H1c2 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H1d5 zenon_H50 zenon_H10b zenon_H136 zenon_Hba zenon_H1ce zenon_Hb zenon_Ha1 zenon_He1 zenon_H57 zenon_H6e zenon_H116 zenon_H2d zenon_He0 zenon_H81 zenon_Hc2 zenon_H146. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.13 apply (zenon_L263_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.13 apply (zenon_L300_); trivial. % 40.94/41.13 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.14 apply (zenon_L266_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.14 apply (zenon_L307_); trivial. % 40.94/41.14 exact (zenon_H146 zenon_H144). % 40.94/41.14 (* end of lemma zenon_L308_ *) % 40.94/41.14 assert (zenon_L309_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (op (e0) (e2)) (e0)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (unit)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e0))) -> False). % 40.94/41.14 do 0 intro. intros zenon_Hbb zenon_H49 zenon_H9f zenon_Hb9 zenon_H1c9 zenon_H16d zenon_H41 zenon_H51 zenon_H1c8 zenon_H88 zenon_H87 zenon_H77 zenon_H73 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hee zenon_H1c4 zenon_H165 zenon_H1a9 zenon_H146 zenon_Hc2 zenon_H81 zenon_He0 zenon_H2d zenon_H116 zenon_H6e zenon_H57 zenon_He1 zenon_Ha1 zenon_Hb zenon_H1ce zenon_Hba zenon_H136 zenon_H10b zenon_H50 zenon_H1d5 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H42 zenon_H7b zenon_H20 zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_Hd9 zenon_Hc3 zenon_H18e zenon_H168 zenon_H19a zenon_H13e. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.14 apply (zenon_L272_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.14 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.14 apply (zenon_L273_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.14 apply (zenon_L274_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.14 apply (zenon_L12_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.14 apply (zenon_L299_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.14 apply (zenon_L112_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.14 exact (zenon_He1 zenon_He5). % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H166 | zenon_intro zenon_H1c5 ]. % 40.94/41.14 apply (zenon_L243_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1c6 ]. % 40.94/41.14 apply (zenon_L275_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1c7 ]. % 40.94/41.14 apply (zenon_L276_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H142 ]. % 40.94/41.14 apply (zenon_L308_); trivial. % 40.94/41.14 exact (zenon_H13e zenon_H142). % 40.94/41.14 (* end of lemma zenon_L309_ *) % 40.94/41.14 assert (zenon_L310_ : (~((op (e3) (e4)) = (op (unit) (e4)))) -> ((unit) = (e3)) -> False). % 40.94/41.14 do 0 intro. intros zenon_H1de zenon_H2a. % 40.94/41.14 cut (((e4) = (e4))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 40.94/41.14 cut (((e3) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 40.94/41.14 congruence. % 40.94/41.14 apply zenon_H2b. apply sym_equal. exact zenon_H2a. % 40.94/41.14 apply zenon_H97. apply refl_equal. % 40.94/41.14 (* end of lemma zenon_L310_ *) % 40.94/41.14 assert (zenon_L311_ : ((op (unit) (e4)) = (e4)) -> ((unit) = (e3)) -> ((op (e3) (e0)) = (e4)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> False). % 40.94/41.14 do 0 intro. intros zenon_Hd3 zenon_H2a zenon_H1df zenon_H7b. % 40.94/41.14 elim (classic ((op (e3) (e4)) = (op (e3) (e4)))); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H1e1 ]. % 40.94/41.14 cut (((op (e3) (e4)) = (op (e3) (e4))) = ((op (e3) (e0)) = (op (e3) (e4)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H7b. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H1e0. % 40.94/41.14 cut (((op (e3) (e4)) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 40.94/41.14 cut (((op (e3) (e4)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 40.94/41.14 congruence. % 40.94/41.14 cut (((op (unit) (e4)) = (e4)) = ((op (e3) (e4)) = (op (e3) (e0)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H1e2. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_Hd3. % 40.94/41.14 cut (((e4) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e3]. % 40.94/41.14 cut (((op (unit) (e4)) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1e4]. % 40.94/41.14 congruence. % 40.94/41.14 elim (classic ((op (e3) (e4)) = (op (e3) (e4)))); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H1e1 ]. % 40.94/41.14 cut (((op (e3) (e4)) = (op (e3) (e4))) = ((op (unit) (e4)) = (op (e3) (e4)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H1e4. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H1e0. % 40.94/41.14 cut (((op (e3) (e4)) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 40.94/41.14 cut (((op (e3) (e4)) = (op (unit) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 40.94/41.14 congruence. % 40.94/41.14 apply (zenon_L310_); trivial. % 40.94/41.14 apply zenon_H1e1. apply refl_equal. % 40.94/41.14 apply zenon_H1e1. apply refl_equal. % 40.94/41.14 apply zenon_H1e3. apply sym_equal. exact zenon_H1df. % 40.94/41.14 apply zenon_H1e1. apply refl_equal. % 40.94/41.14 apply zenon_H1e1. apply refl_equal. % 40.94/41.14 (* end of lemma zenon_L311_ *) % 40.94/41.14 assert (zenon_L312_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (e3) (e0)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H3b zenon_H1e5 zenon_H99 zenon_H41 zenon_H16d zenon_H50 zenon_H22 zenon_H20 zenon_H1f zenon_H7b zenon_H1df zenon_Hd3 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.14 elim (classic ((op (e4) (e0)) = (op (e4) (e0)))); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha9 ]. % 40.94/41.14 cut (((op (e4) (e0)) = (op (e4) (e0))) = ((op (e3) (e0)) = (op (e4) (e0)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H1e5. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_Ha8. % 40.94/41.14 cut (((op (e4) (e0)) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 40.94/41.14 cut (((op (e4) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 40.94/41.14 congruence. % 40.94/41.14 cut (((op (e4) (unit)) = (e4)) = ((op (e4) (e0)) = (op (e3) (e0)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H1e6. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H99. % 40.94/41.14 cut (((e4) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e3]. % 40.94/41.14 cut (((op (e4) (unit)) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 40.94/41.14 congruence. % 40.94/41.14 elim (classic ((op (e4) (e0)) = (op (e4) (e0)))); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha9 ]. % 40.94/41.14 cut (((op (e4) (e0)) = (op (e4) (e0))) = ((op (e4) (unit)) = (op (e4) (e0)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_Ha7. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_Ha8. % 40.94/41.14 cut (((op (e4) (e0)) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 40.94/41.14 cut (((op (e4) (e0)) = (op (e4) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 40.94/41.14 congruence. % 40.94/41.14 apply (zenon_L54_); trivial. % 40.94/41.14 apply zenon_Ha9. apply refl_equal. % 40.94/41.14 apply zenon_Ha9. apply refl_equal. % 40.94/41.14 apply zenon_H1e3. apply sym_equal. exact zenon_H1df. % 40.94/41.14 apply zenon_Ha9. apply refl_equal. % 40.94/41.14 apply zenon_Ha9. apply refl_equal. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.14 apply (zenon_L249_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.14 apply (zenon_L8_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.14 apply (zenon_L311_); trivial. % 40.94/41.14 apply (zenon_L11_); trivial. % 40.94/41.14 (* end of lemma zenon_L312_ *) % 40.94/41.14 assert (zenon_L313_ : ((op (unit) (e4)) = (e4)) -> ((unit) = (e3)) -> ((op (e3) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> False). % 40.94/41.14 do 0 intro. intros zenon_Hd3 zenon_H2a zenon_H1e7 zenon_H81. % 40.94/41.14 elim (classic ((op (e3) (e4)) = (op (e3) (e4)))); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H1e1 ]. % 40.94/41.14 cut (((op (e3) (e4)) = (op (e3) (e4))) = ((op (e3) (e1)) = (op (e3) (e4)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H81. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H1e0. % 40.94/41.14 cut (((op (e3) (e4)) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 40.94/41.14 cut (((op (e3) (e4)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 40.94/41.14 congruence. % 40.94/41.14 cut (((op (unit) (e4)) = (e4)) = ((op (e3) (e4)) = (op (e3) (e1)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H1e8. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_Hd3. % 40.94/41.14 cut (((e4) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1e9]. % 40.94/41.14 cut (((op (unit) (e4)) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1e4]. % 40.94/41.14 congruence. % 40.94/41.14 elim (classic ((op (e3) (e4)) = (op (e3) (e4)))); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H1e1 ]. % 40.94/41.14 cut (((op (e3) (e4)) = (op (e3) (e4))) = ((op (unit) (e4)) = (op (e3) (e4)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H1e4. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H1e0. % 40.94/41.14 cut (((op (e3) (e4)) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 40.94/41.14 cut (((op (e3) (e4)) = (op (unit) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 40.94/41.14 congruence. % 40.94/41.14 apply (zenon_L310_); trivial. % 40.94/41.14 apply zenon_H1e1. apply refl_equal. % 40.94/41.14 apply zenon_H1e1. apply refl_equal. % 40.94/41.14 apply zenon_H1e9. apply sym_equal. exact zenon_H1e7. % 40.94/41.14 apply zenon_H1e1. apply refl_equal. % 40.94/41.14 apply zenon_H1e1. apply refl_equal. % 40.94/41.14 (* end of lemma zenon_L313_ *) % 40.94/41.14 assert (zenon_L314_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e1)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H3b zenon_H57 zenon_H59 zenon_H58 zenon_H6e zenon_H22 zenon_H20 zenon_H1f zenon_H81 zenon_H1e7 zenon_Hd3 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.14 apply (zenon_L22_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.14 apply (zenon_L29_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.14 apply (zenon_L8_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.14 apply (zenon_L313_); trivial. % 40.94/41.14 apply (zenon_L11_); trivial. % 40.94/41.14 (* end of lemma zenon_L314_ *) % 40.94/41.14 assert (zenon_L315_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e3) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e4)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.14 do 0 intro. intros zenon_He0 zenon_Hb zenon_H49 zenon_H34 zenon_H32 zenon_Hd3 zenon_H1e7 zenon_H81 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_H3b zenon_H17a zenon_H168 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.14 apply (zenon_L12_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.14 apply (zenon_L262_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.14 apply (zenon_L314_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.14 exact (zenon_He1 zenon_He5). % 40.94/41.14 apply (zenon_L263_); trivial. % 40.94/41.14 (* end of lemma zenon_L315_ *) % 40.94/41.14 assert (zenon_L316_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e1) (e4)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H3b zenon_H112 zenon_H16 zenon_H115 zenon_H22 zenon_H1f zenon_H113 zenon_H2c zenon_H116 zenon_H20 zenon_H1bf zenon_Hb1. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.14 apply (zenon_L164_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.14 apply (zenon_L165_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.14 apply (zenon_L8_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.14 apply (zenon_L166_); trivial. % 40.94/41.14 apply (zenon_L290_); trivial. % 40.94/41.14 (* end of lemma zenon_L316_ *) % 40.94/41.14 assert (zenon_L317_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e4)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H3b zenon_Ha2 zenon_Ha1 zenon_H4a zenon_Hc zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H32 zenon_H16 zenon_H34. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.14 apply (zenon_L52_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.14 apply (zenon_L17_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.14 apply (zenon_L8_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.14 apply (zenon_L10_); trivial. % 40.94/41.14 apply (zenon_L11_); trivial. % 40.94/41.14 (* end of lemma zenon_L317_ *) % 40.94/41.14 assert (zenon_L318_ : (~((op (op (e0) (e3)) (e0)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 40.94/41.14 do 0 intro. intros zenon_H1ea zenon_H60 zenon_H1eb. % 40.94/41.14 cut (((op (e3) (e0)) = (e3)) = ((op (op (e0) (e3)) (e0)) = (e3))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H1ea. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H60. % 40.94/41.14 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 40.94/41.14 cut (((op (e3) (e0)) = (op (op (e0) (e3)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 40.94/41.14 congruence. % 40.94/41.14 elim (classic ((op (op (e0) (e3)) (e0)) = (op (op (e0) (e3)) (e0)))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 40.94/41.14 cut (((op (op (e0) (e3)) (e0)) = (op (op (e0) (e3)) (e0))) = ((op (e3) (e0)) = (op (op (e0) (e3)) (e0)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H1ec. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H1ed. % 40.94/41.14 cut (((op (op (e0) (e3)) (e0)) = (op (op (e0) (e3)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 40.94/41.14 cut (((op (op (e0) (e3)) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 40.94/41.14 congruence. % 40.94/41.14 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 40.94/41.14 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1f0]. % 40.94/41.14 congruence. % 40.94/41.14 exact (zenon_H1f0 zenon_H1eb). % 40.94/41.14 apply zenon_H3f. apply refl_equal. % 40.94/41.14 apply zenon_H1ee. apply refl_equal. % 40.94/41.14 apply zenon_H1ee. apply refl_equal. % 40.94/41.14 apply zenon_H1e. apply refl_equal. % 40.94/41.14 (* end of lemma zenon_L318_ *) % 40.94/41.14 assert (zenon_L319_ : ((op (unit) (e4)) = (e4)) -> ((unit) = (e0)) -> ((op (e0) (e3)) = (e4)) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> False). % 40.94/41.14 do 0 intro. intros zenon_Hd3 zenon_H9 zenon_H1f1 zenon_H169. % 40.94/41.14 elim (classic ((op (e0) (e4)) = (op (e0) (e4)))); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H1b8 ]. % 40.94/41.14 cut (((op (e0) (e4)) = (op (e0) (e4))) = ((op (e0) (e3)) = (op (e0) (e4)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H169. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H1b7. % 40.94/41.14 cut (((op (e0) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 40.94/41.14 cut (((op (e0) (e4)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 40.94/41.14 congruence. % 40.94/41.14 cut (((op (unit) (e4)) = (e4)) = ((op (e0) (e4)) = (op (e0) (e3)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H1f2. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_Hd3. % 40.94/41.14 cut (((e4) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1f3]. % 40.94/41.14 cut (((op (unit) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 40.94/41.14 congruence. % 40.94/41.14 elim (classic ((op (e0) (e4)) = (op (e0) (e4)))); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H1b8 ]. % 40.94/41.14 cut (((op (e0) (e4)) = (op (e0) (e4))) = ((op (unit) (e4)) = (op (e0) (e4)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H1b6. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H1b7. % 40.94/41.14 cut (((op (e0) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 40.94/41.14 cut (((op (e0) (e4)) = (op (unit) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 40.94/41.14 congruence. % 40.94/41.14 apply (zenon_L282_); trivial. % 40.94/41.14 apply zenon_H1b8. apply refl_equal. % 40.94/41.14 apply zenon_H1b8. apply refl_equal. % 40.94/41.14 apply zenon_H1f3. apply sym_equal. exact zenon_H1f1. % 40.94/41.14 apply zenon_H1b8. apply refl_equal. % 40.94/41.14 apply zenon_H1b8. apply refl_equal. % 40.94/41.14 (* end of lemma zenon_L319_ *) % 40.94/41.14 assert (zenon_L320_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> ((op (e4) (e3)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (op (e0) (e3)) (e0)) = (e3))) -> ((op (unit) (e4)) = (e4)) -> ((unit) = (e0)) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H1f4 zenon_H92 zenon_H91 zenon_H2c zenon_H17 zenon_H2d zenon_H1f zenon_H20 zenon_H22 zenon_H18 zenon_H161 zenon_H42 zenon_H3b zenon_H16 zenon_H51 zenon_Hc zenon_Hb zenon_H60 zenon_H1ea zenon_Hd3 zenon_H9 zenon_H169. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_H162 | zenon_intro zenon_H1f5 ]. % 40.94/41.14 apply (zenon_L222_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H178 | zenon_intro zenon_H1f6 ]. % 40.94/41.14 apply (zenon_L257_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hd | zenon_intro zenon_H1f7 ]. % 40.94/41.14 apply (zenon_L3_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1f1 ]. % 40.94/41.14 apply (zenon_L318_); trivial. % 40.94/41.14 apply (zenon_L319_); trivial. % 40.94/41.14 (* end of lemma zenon_L320_ *) % 40.94/41.14 assert (zenon_L321_ : (~((op (e0) (e3)) = (op (e0) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (op (e0) (e3)) (e0)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.14 do 0 intro. intros zenon_H169 zenon_Hd3 zenon_H1ea zenon_H60 zenon_Hb zenon_H51 zenon_H3b zenon_H161 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H1f4 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_H9a zenon_H99 zenon_H197 zenon_H16 zenon_H81 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.14 apply (zenon_L320_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.14 apply (zenon_L287_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.14 apply (zenon_L84_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.14 apply (zenon_L270_); trivial. % 40.94/41.14 apply (zenon_L44_); trivial. % 40.94/41.14 (* end of lemma zenon_L321_ *) % 40.94/41.14 assert (zenon_L322_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e2)) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (op (e0) (e3)) (e0)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.14 do 0 intro. intros zenon_He0 zenon_H116 zenon_Hab zenon_H34 zenon_H32 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_H169 zenon_Hd3 zenon_H1ea zenon_H60 zenon_Hb zenon_H51 zenon_H3b zenon_H161 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H1f4 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_H9a zenon_H99 zenon_H197 zenon_H16 zenon_H81 zenon_H91 zenon_Hc. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.14 apply (zenon_L12_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.14 apply (zenon_L278_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.14 apply (zenon_L286_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.14 exact (zenon_He1 zenon_He5). % 40.94/41.14 apply (zenon_L321_); trivial. % 40.94/41.14 (* end of lemma zenon_L322_ *) % 40.94/41.14 assert (zenon_L323_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (e4)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e1)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H3b zenon_Hb6 zenon_Hb7 zenon_H58 zenon_Hb9 zenon_H22 zenon_H20 zenon_H1f zenon_H81 zenon_H1e7 zenon_Hd3 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.14 apply (zenon_L62_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.14 apply (zenon_L63_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.14 apply (zenon_L8_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.14 apply (zenon_L313_); trivial. % 40.94/41.14 apply (zenon_L11_); trivial. % 40.94/41.14 (* end of lemma zenon_L323_ *) % 40.94/41.14 assert (zenon_L324_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.14 do 0 intro. intros zenon_He0 zenon_H17 zenon_H2d zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H1f zenon_H20 zenon_H68 zenon_H32 zenon_H16 zenon_Hed zenon_He6 zenon_He8 zenon_H9b zenon_Hb1 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H22 zenon_H1ad zenon_Hbf zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.14 apply (zenon_L12_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.14 apply (zenon_L285_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.14 apply (zenon_L112_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.14 exact (zenon_He1 zenon_He5). % 40.94/41.14 apply (zenon_L288_); trivial. % 40.94/41.14 (* end of lemma zenon_L324_ *) % 40.94/41.14 assert (zenon_L325_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (op (e0) (e3)) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e3) (e1)) = (e4)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.14 do 0 intro. intros zenon_Hc2 zenon_H4a zenon_Ha1 zenon_H197 zenon_H1f4 zenon_H161 zenon_H51 zenon_H60 zenon_H1ea zenon_H169 zenon_H116 zenon_H1e7 zenon_Hb9 zenon_Hb6 zenon_Hc zenon_H91 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H22 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_He1 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_Hb1 zenon_H9b zenon_He8 zenon_He6 zenon_Hed zenon_H16 zenon_H32 zenon_H68 zenon_H20 zenon_H1f zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_H49 zenon_Hb zenon_H2d zenon_H17 zenon_He0 zenon_Hc3. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.14 apply (zenon_L317_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.14 apply (zenon_L322_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.14 apply (zenon_L323_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.14 apply (zenon_L324_); trivial. % 40.94/41.14 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.14 (* end of lemma zenon_L325_ *) % 40.94/41.14 assert (zenon_L326_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e4) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (e3) (e1)) = (e4)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (op (e0) (e3)) (e0)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H19a zenon_H168 zenon_H1bf zenon_H18e zenon_Hc3 zenon_He0 zenon_H17 zenon_H2d zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H1f zenon_H20 zenon_H68 zenon_H32 zenon_H16 zenon_Hed zenon_He6 zenon_He8 zenon_H9b zenon_Hb1 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H22 zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc zenon_Hb6 zenon_Hb9 zenon_H1e7 zenon_H116 zenon_H169 zenon_H1ea zenon_H60 zenon_H51 zenon_H161 zenon_H1f4 zenon_Ha1 zenon_H4a zenon_Hc2 zenon_H146. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.14 apply (zenon_L315_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.14 apply (zenon_L316_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.14 apply (zenon_L266_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.14 apply (zenon_L325_); trivial. % 40.94/41.14 exact (zenon_H146 zenon_H144). % 40.94/41.14 (* end of lemma zenon_L326_ *) % 40.94/41.14 assert (zenon_L327_ : ((op (unit) (e4)) = (e4)) -> ((unit) = (e3)) -> ((op (e3) (e2)) = (e4)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> False). % 40.94/41.14 do 0 intro. intros zenon_Hd3 zenon_H2a zenon_H1f8 zenon_H83. % 40.94/41.14 elim (classic ((op (e3) (e4)) = (op (e3) (e4)))); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H1e1 ]. % 40.94/41.14 cut (((op (e3) (e4)) = (op (e3) (e4))) = ((op (e3) (e2)) = (op (e3) (e4)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H83. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H1e0. % 40.94/41.14 cut (((op (e3) (e4)) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 40.94/41.14 cut (((op (e3) (e4)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f9]. % 40.94/41.14 congruence. % 40.94/41.14 cut (((op (unit) (e4)) = (e4)) = ((op (e3) (e4)) = (op (e3) (e2)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H1f9. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_Hd3. % 40.94/41.14 cut (((e4) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1fa]. % 40.94/41.14 cut (((op (unit) (e4)) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1e4]. % 40.94/41.14 congruence. % 40.94/41.14 elim (classic ((op (e3) (e4)) = (op (e3) (e4)))); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H1e1 ]. % 40.94/41.14 cut (((op (e3) (e4)) = (op (e3) (e4))) = ((op (unit) (e4)) = (op (e3) (e4)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H1e4. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H1e0. % 40.94/41.14 cut (((op (e3) (e4)) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 40.94/41.14 cut (((op (e3) (e4)) = (op (unit) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 40.94/41.14 congruence. % 40.94/41.14 apply (zenon_L310_); trivial. % 40.94/41.14 apply zenon_H1e1. apply refl_equal. % 40.94/41.14 apply zenon_H1e1. apply refl_equal. % 40.94/41.14 apply zenon_H1fa. apply sym_equal. exact zenon_H1f8. % 40.94/41.14 apply zenon_H1e1. apply refl_equal. % 40.94/41.14 apply zenon_H1e1. apply refl_equal. % 40.94/41.14 (* end of lemma zenon_L327_ *) % 40.94/41.14 assert (zenon_L328_ : (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (op (e0) (e3)) (e0)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (unit) (e1)) = (e1)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e3) (e2)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.14 do 0 intro. intros zenon_H169 zenon_H1ea zenon_H60 zenon_Hb zenon_H51 zenon_H16 zenon_H3b zenon_H42 zenon_H161 zenon_H18 zenon_H2d zenon_H17 zenon_H2c zenon_H1f4 zenon_Hab zenon_Haa zenon_H22 zenon_H20 zenon_H1f zenon_H83 zenon_H1f8 zenon_Hd3 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.14 apply (zenon_L320_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.14 apply (zenon_L56_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.14 apply (zenon_L8_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.14 apply (zenon_L327_); trivial. % 40.94/41.14 apply (zenon_L44_); trivial. % 40.94/41.14 (* end of lemma zenon_L328_ *) % 40.94/41.14 assert (zenon_L329_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (op (e0) (e3)) (e0)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (unit) (e1)) = (e1)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e3) (e2)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.14 do 0 intro. intros zenon_He0 zenon_H116 zenon_H34 zenon_H32 zenon_H81 zenon_H197 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_H169 zenon_H1ea zenon_H60 zenon_Hb zenon_H51 zenon_H16 zenon_H3b zenon_H42 zenon_H161 zenon_H18 zenon_H2d zenon_H17 zenon_H2c zenon_H1f4 zenon_Hab zenon_Haa zenon_H22 zenon_H20 zenon_H1f zenon_H83 zenon_H1f8 zenon_Hd3 zenon_H91 zenon_Hc. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.14 apply (zenon_L12_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.14 apply (zenon_L278_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.14 apply (zenon_L286_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.14 exact (zenon_He1 zenon_He5). % 40.94/41.14 apply (zenon_L328_); trivial. % 40.94/41.14 (* end of lemma zenon_L329_ *) % 40.94/41.14 assert (zenon_L330_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e2)) = (e4)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (op (e0) (e3)) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.14 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_H91 zenon_H1f8 zenon_Haa zenon_H1f4 zenon_H17 zenon_H2d zenon_H18 zenon_H161 zenon_H42 zenon_H51 zenon_Hb zenon_H60 zenon_H1ea zenon_H169 zenon_He1 zenon_H57 zenon_H6e zenon_H197 zenon_H81 zenon_H116 zenon_He0 zenon_H58 zenon_Hb9 zenon_Hb6 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.14 apply (zenon_L277_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.14 apply (zenon_L329_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.14 apply (zenon_L123_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.14 apply (zenon_L285_); trivial. % 40.94/41.14 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.14 (* end of lemma zenon_L330_ *) % 40.94/41.14 assert (zenon_L331_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (op (e0) (e3)) (e0)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e3) (e2)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H19a zenon_H168 zenon_Hba zenon_Hbb zenon_H18e zenon_Hc3 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H4a zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_Hc zenon_H83 zenon_H32 zenon_H16 zenon_H34 zenon_Hb6 zenon_Hb9 zenon_H58 zenon_He0 zenon_H116 zenon_H81 zenon_H6e zenon_H57 zenon_He1 zenon_H169 zenon_H1ea zenon_H60 zenon_Hb zenon_H51 zenon_H42 zenon_H161 zenon_H18 zenon_H2d zenon_H17 zenon_H1f4 zenon_Haa zenon_H1f8 zenon_H91 zenon_Ha1 zenon_Hc2 zenon_H146. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.14 apply (zenon_L262_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.14 apply (zenon_L178_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.14 apply (zenon_L266_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.14 apply (zenon_L330_); trivial. % 40.94/41.14 exact (zenon_H146 zenon_H144). % 40.94/41.14 (* end of lemma zenon_L331_ *) % 40.94/41.14 assert (zenon_L332_ : (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((unit) = (e0)) -> ((op (e3) (e4)) = (e4)) -> False). % 40.94/41.14 do 0 intro. intros zenon_H1fb zenon_Hd3 zenon_H9 zenon_H1fc. % 40.94/41.14 cut (((op (unit) (e4)) = (e4)) = ((op (e0) (e4)) = (op (e3) (e4)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H1fb. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_Hd3. % 40.94/41.14 cut (((e4) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 40.94/41.14 cut (((op (unit) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 40.94/41.14 congruence. % 40.94/41.14 elim (classic ((op (e0) (e4)) = (op (e0) (e4)))); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H1b8 ]. % 40.94/41.14 cut (((op (e0) (e4)) = (op (e0) (e4))) = ((op (unit) (e4)) = (op (e0) (e4)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H1b6. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H1b7. % 40.94/41.14 cut (((op (e0) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 40.94/41.14 cut (((op (e0) (e4)) = (op (unit) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 40.94/41.14 congruence. % 40.94/41.14 apply (zenon_L282_); trivial. % 40.94/41.14 apply zenon_H1b8. apply refl_equal. % 40.94/41.14 apply zenon_H1b8. apply refl_equal. % 40.94/41.14 apply zenon_H1fd. apply sym_equal. exact zenon_H1fc. % 40.94/41.14 (* end of lemma zenon_L332_ *) % 40.94/41.14 assert (zenon_L333_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (e4)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (e1) (e4)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H3b zenon_H1fc zenon_Hd3 zenon_H1fb zenon_Hab zenon_Hc zenon_Haa zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H20 zenon_H1bf zenon_Hb1. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.14 apply (zenon_L332_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.14 apply (zenon_L56_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.14 apply (zenon_L84_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.14 apply (zenon_L102_); trivial. % 40.94/41.14 apply (zenon_L290_); trivial. % 40.94/41.14 (* end of lemma zenon_L333_ *) % 40.94/41.14 assert (zenon_L334_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (e4)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H3b zenon_H1fc zenon_Hd3 zenon_H1fb zenon_H4a zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_Hbf zenon_Hc zenon_H83 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.14 apply (zenon_L332_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.14 apply (zenon_L17_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.14 apply (zenon_L8_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.14 apply (zenon_L67_); trivial. % 40.94/41.14 apply (zenon_L11_); trivial. % 40.94/41.14 (* end of lemma zenon_L334_ *) % 40.94/41.14 assert (zenon_L335_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e3) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.14 do 0 intro. intros zenon_Hc2 zenon_H2c zenon_H17 zenon_H2d zenon_H18 zenon_Ha1 zenon_Hb1 zenon_H1bf zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_Haa zenon_H58 zenon_Hb9 zenon_Hb6 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1fb zenon_Hd3 zenon_H1fc zenon_H3b zenon_Hc3. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.14 apply (zenon_L277_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.14 apply (zenon_L333_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.14 apply (zenon_L123_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.14 apply (zenon_L334_); trivial. % 40.94/41.14 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.14 (* end of lemma zenon_L335_ *) % 40.94/41.14 assert (zenon_L336_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> ((op (e1) (e1)) = (e0)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (op (e0) (e3)) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e3) (e3)) = (e4))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H1c8 zenon_H1c9 zenon_H9f zenon_H1fe zenon_H50 zenon_H16d zenon_H41 zenon_H1e5 zenon_H15f zenon_Hee zenon_Hd9 zenon_Hd4 zenon_He9 zenon_H9b zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H73 zenon_H77 zenon_H87 zenon_H7b zenon_H88 zenon_H146 zenon_H91 zenon_H1f4 zenon_H161 zenon_H42 zenon_H51 zenon_Hb zenon_H60 zenon_H1ea zenon_H169 zenon_He1 zenon_H57 zenon_H6e zenon_H81 zenon_H116 zenon_He0 zenon_H1b9 zenon_H115 zenon_H11f zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_H18e zenon_Hbb zenon_Hba zenon_H168 zenon_H19a zenon_H1ff zenon_Hc2 zenon_H2c zenon_H17 zenon_H2d zenon_H18 zenon_Ha1 zenon_Hb1 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_Haa zenon_H58 zenon_Hb9 zenon_Hb6 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1fb zenon_Hd3 zenon_H3b zenon_Hc3. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.14 apply (zenon_L272_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.14 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.14 apply (zenon_L273_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.14 apply (zenon_L274_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1df | zenon_intro zenon_H200 ]. % 40.94/41.14 apply (zenon_L312_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H201 ]. % 40.94/41.14 apply (zenon_L326_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H202 ]. % 40.94/41.14 apply (zenon_L331_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H203 | zenon_intro zenon_H1fc ]. % 40.94/41.14 exact (zenon_H1ff zenon_H203). % 40.94/41.14 apply (zenon_L335_); trivial. % 40.94/41.14 (* end of lemma zenon_L336_ *) % 40.94/41.14 assert (zenon_L337_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (op (e0) (e3)) (e0)) = (e3))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H19a zenon_H168 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H18e zenon_H92 zenon_Hc zenon_H91 zenon_H81 zenon_H16 zenon_H99 zenon_H9a zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H1f4 zenon_H2c zenon_H17 zenon_H2d zenon_H1f zenon_H20 zenon_H22 zenon_H161 zenon_H3b zenon_H51 zenon_Hb zenon_H60 zenon_H1ea zenon_Hd3 zenon_H169 zenon_H146. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.14 apply (zenon_L263_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.14 apply (zenon_L300_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.14 apply (zenon_L266_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.14 apply (zenon_L321_); trivial. % 40.94/41.14 exact (zenon_H146 zenon_H144). % 40.94/41.14 (* end of lemma zenon_L337_ *) % 40.94/41.14 assert (zenon_L338_ : (~((op (e4) (e4)) = (e2))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e3) (e3)) = (e4))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (op (e0) (e3)) (e0)) = (e3))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.14 do 0 intro. intros zenon_Hc3 zenon_H1fb zenon_H49 zenon_H83 zenon_Hb6 zenon_Hb9 zenon_Haa zenon_Hb1 zenon_Ha1 zenon_Hc2 zenon_H1ff zenon_Hba zenon_Hbb zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H11f zenon_H115 zenon_H1b9 zenon_He0 zenon_H116 zenon_H6e zenon_H87 zenon_Hed zenon_He6 zenon_He8 zenon_He9 zenon_Hd4 zenon_Hd9 zenon_Hee zenon_H1e5 zenon_H41 zenon_H16d zenon_H50 zenon_H1fe zenon_H1c9 zenon_H1c8 zenon_H34 zenon_H32 zenon_Hcc zenon_H9b zenon_H7b zenon_H89 zenon_H77 zenon_H9f zenon_H73 zenon_H58 zenon_H57 zenon_H88 zenon_He1 zenon_H19a zenon_H168 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H18e zenon_Hc zenon_H91 zenon_H81 zenon_H16 zenon_H99 zenon_H9a zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H1f4 zenon_H2c zenon_H17 zenon_H2d zenon_H1f zenon_H20 zenon_H22 zenon_H161 zenon_H3b zenon_H51 zenon_Hb zenon_H60 zenon_H1ea zenon_Hd3 zenon_H169 zenon_H146. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.14 apply (zenon_L12_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.14 apply (zenon_L336_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.14 apply (zenon_L238_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.14 exact (zenon_He1 zenon_He5). % 40.94/41.14 apply (zenon_L337_); trivial. % 40.94/41.14 (* end of lemma zenon_L338_ *) % 40.94/41.14 assert (zenon_L339_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (op (e0) (e3)) (e0)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e4))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H15b zenon_Hda zenon_H146 zenon_H169 zenon_Hd3 zenon_H1ea zenon_H60 zenon_Hb zenon_H51 zenon_H3b zenon_H161 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H1f4 zenon_H42 zenon_H18 zenon_Hc8 zenon_H9a zenon_H99 zenon_H16 zenon_H81 zenon_H91 zenon_Hc zenon_H18e zenon_H112 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H168 zenon_H19a zenon_He1 zenon_H88 zenon_H57 zenon_H58 zenon_H73 zenon_H9f zenon_H77 zenon_H89 zenon_H7b zenon_H9b zenon_Hcc zenon_H32 zenon_H1c8 zenon_H1c9 zenon_H1fe zenon_H50 zenon_H16d zenon_H41 zenon_H1e5 zenon_Hee zenon_Hd9 zenon_Hd4 zenon_He9 zenon_He8 zenon_He6 zenon_Hed zenon_H87 zenon_H6e zenon_H116 zenon_He0 zenon_H1b9 zenon_H115 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hbb zenon_Hba zenon_H1ff zenon_Hc2 zenon_Ha1 zenon_Hb1 zenon_Haa zenon_Hb9 zenon_Hb6 zenon_H83 zenon_H49 zenon_H1fb zenon_Hc3 zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 40.94/41.14 apply (zenon_L240_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 40.94/41.14 apply (zenon_L338_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 40.94/41.14 apply (zenon_L216_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 40.94/41.14 apply (zenon_L217_); trivial. % 40.94/41.14 apply (zenon_L218_); trivial. % 40.94/41.14 (* end of lemma zenon_L339_ *) % 40.94/41.14 assert (zenon_L340_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.14 do 0 intro. intros zenon_He0 zenon_H2c zenon_H17 zenon_H2d zenon_H18 zenon_Hb zenon_H116 zenon_H34 zenon_H16 zenon_H87 zenon_H20 zenon_H83 zenon_H5f zenon_H81 zenon_H7b zenon_H89 zenon_H57 zenon_H58 zenon_H6e zenon_H22 zenon_H1f zenon_H77 zenon_H73 zenon_H61 zenon_H68 zenon_H88 zenon_He1 zenon_H3b zenon_H9b zenon_Hab zenon_Haa zenon_H32 zenon_Hb1 zenon_Ha5 zenon_H99 zenon_H91 zenon_Hc. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.14 apply (zenon_L12_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.14 apply (zenon_L278_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.14 apply (zenon_L41_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.14 exact (zenon_He1 zenon_He5). % 40.94/41.14 apply (zenon_L61_); trivial. % 40.94/41.14 (* end of lemma zenon_L340_ *) % 40.94/41.14 assert (zenon_L341_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (e4) (e2)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e4)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.14 do 0 intro. intros zenon_He0 zenon_Hb zenon_H49 zenon_He9 zenon_Hc9 zenon_Hd3 zenon_H99 zenon_H83 zenon_H5f zenon_H32 zenon_Hc8 zenon_H89 zenon_H57 zenon_H58 zenon_H6e zenon_H77 zenon_H34 zenon_H73 zenon_H61 zenon_H68 zenon_H88 zenon_He1 zenon_H3b zenon_H17a zenon_H168 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.14 apply (zenon_L12_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.14 apply (zenon_L262_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.14 apply (zenon_L212_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.14 exact (zenon_He1 zenon_He5). % 40.94/41.14 apply (zenon_L263_); trivial. % 40.94/41.14 (* end of lemma zenon_L341_ *) % 40.94/41.14 assert (zenon_L342_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e2)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e4)) = (e2)) -> False). % 40.94/41.14 do 0 intro. intros zenon_H3b zenon_Hc8 zenon_Hc9 zenon_H99 zenon_H32 zenon_H22 zenon_H20 zenon_H1f zenon_H197 zenon_H16 zenon_H81 zenon_He9 zenon_Hc zenon_Hc7. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.14 apply (zenon_L70_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.14 apply (zenon_L71_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.14 apply (zenon_L8_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.14 apply (zenon_L270_); trivial. % 40.94/41.14 apply (zenon_L192_); trivial. % 40.94/41.14 (* end of lemma zenon_L342_ *) % 40.94/41.14 assert (zenon_L343_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((e1) = (op (e4) (e2))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e2)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.14 do 0 intro. intros zenon_Hc2 zenon_H17 zenon_H2d zenon_H18 zenon_Ha1 zenon_H116 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_H34 zenon_H83 zenon_H49 zenon_H4a zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc8 zenon_Hc9 zenon_H99 zenon_H32 zenon_H22 zenon_H20 zenon_H1f zenon_H197 zenon_H16 zenon_H81 zenon_He9 zenon_Hc. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.14 apply (zenon_L277_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.14 apply (zenon_L278_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.14 apply (zenon_L279_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.14 apply (zenon_L285_); trivial. % 40.94/41.14 apply (zenon_L342_); trivial. % 40.94/41.14 (* end of lemma zenon_L343_ *) % 40.94/41.14 assert (zenon_L344_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((e1) = (e3))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e2)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H19a zenon_H91 zenon_H168 zenon_He1 zenon_H88 zenon_H73 zenon_H77 zenon_H6e zenon_H57 zenon_H89 zenon_Hb zenon_He0 zenon_H18e zenon_Hc zenon_He9 zenon_H81 zenon_H16 zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_H99 zenon_Hc9 zenon_Hc8 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H4a zenon_H49 zenon_H83 zenon_H34 zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H116 zenon_Ha1 zenon_H18 zenon_H2d zenon_H17 zenon_Hc2 zenon_H146. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.14 apply (zenon_L341_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.14 apply (zenon_L167_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.14 apply (zenon_L266_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.14 apply (zenon_L343_); trivial. % 40.94/41.14 exact (zenon_H146 zenon_H144). % 40.94/41.14 (* end of lemma zenon_L344_ *) % 40.94/41.14 assert (zenon_L345_ : (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e4) (e2)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.14 do 0 intro. intros zenon_H146 zenon_Hc2 zenon_H17 zenon_H2d zenon_H18 zenon_Ha1 zenon_H116 zenon_H60 zenon_H8e zenon_Hb6 zenon_H49 zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_H18e zenon_He0 zenon_Hb zenon_H89 zenon_H168 zenon_H19a zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_H16 zenon_H34 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H3b zenon_Hc8 zenon_H32 zenon_H22 zenon_H20 zenon_H1f zenon_Hc9 zenon_H99 zenon_H91 zenon_Hc. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.14 apply (zenon_L12_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.14 apply (zenon_L344_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.14 apply (zenon_L112_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.14 exact (zenon_He1 zenon_He5). % 40.94/41.14 apply (zenon_L73_); trivial. % 40.94/41.14 (* end of lemma zenon_L345_ *) % 40.94/41.14 assert (zenon_L346_ : (~((op (e1) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (op (e0) (e3)) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((e1) = (e3))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e3) (e4)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H157 zenon_H152 zenon_H14d zenon_Hc3 zenon_H1fb zenon_Hb9 zenon_H1ff zenon_Hbb zenon_H1e5 zenon_H41 zenon_H16d zenon_H50 zenon_H1fe zenon_H1c9 zenon_H1c8 zenon_H9f zenon_H1f4 zenon_H161 zenon_H51 zenon_H1ea zenon_H169 zenon_H15b zenon_Haa zenon_Hab zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_He1 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_Hd3 zenon_H9b zenon_He8 zenon_He6 zenon_Hed zenon_H34 zenon_H16 zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H88 zenon_H19a zenon_H168 zenon_H89 zenon_Hb zenon_He0 zenon_H18e zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H49 zenon_Hb6 zenon_H8e zenon_H60 zenon_H116 zenon_Ha1 zenon_H18 zenon_H2d zenon_H17 zenon_Hc2 zenon_H146 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H7b zenon_H42 zenon_H1c2 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.94/41.14 apply (zenon_L339_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.94/41.14 apply (zenon_L340_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.94/41.14 apply (zenon_L345_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.94/41.14 apply (zenon_L293_); trivial. % 40.94/41.14 exact (zenon_Hda zenon_Hde). % 40.94/41.14 (* end of lemma zenon_L346_ *) % 40.94/41.14 assert (zenon_L347_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e3) (e4)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e3) (e4)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.14 do 0 intro. intros zenon_He0 zenon_H2d zenon_Hb zenon_H49 zenon_H88 zenon_H81 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hee zenon_He1 zenon_Hd9 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He8 zenon_Hd3 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H83 zenon_Hc zenon_Hbf zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H7b zenon_H42 zenon_H1c2 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.14 apply (zenon_L12_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.14 apply (zenon_L285_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.14 apply (zenon_L112_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.14 exact (zenon_He1 zenon_He5). % 40.94/41.14 apply (zenon_L294_); trivial. % 40.94/41.14 (* end of lemma zenon_L347_ *) % 40.94/41.14 assert (zenon_L348_ : (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (op (e0) (e3)) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e4) (e4)) = (e0))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H1c4 zenon_H165 zenon_H1a9 zenon_Hc3 zenon_He0 zenon_H2d zenon_Hb zenon_H49 zenon_H88 zenon_H81 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hee zenon_He1 zenon_Hd9 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He8 zenon_Hd3 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H83 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H20 zenon_H7b zenon_H42 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda zenon_Hb6 zenon_H8e zenon_H60 zenon_H157 zenon_H152 zenon_H14d zenon_H1fb zenon_Hb9 zenon_H1ff zenon_Hbb zenon_H1e5 zenon_H41 zenon_H16d zenon_H50 zenon_H1fe zenon_H1c9 zenon_H1c8 zenon_H9f zenon_H1f4 zenon_H161 zenon_H51 zenon_H1ea zenon_H169 zenon_H15b zenon_Haa zenon_H19a zenon_H168 zenon_H89 zenon_H18e zenon_H116 zenon_Ha1 zenon_Hc2 zenon_H146 zenon_H13e. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.14 apply (zenon_L272_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.14 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.14 apply (zenon_L273_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.14 apply (zenon_L274_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H166 | zenon_intro zenon_H1c5 ]. % 40.94/41.14 apply (zenon_L234_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1c6 ]. % 40.94/41.14 apply (zenon_L275_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1c7 ]. % 40.94/41.14 apply (zenon_L276_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H142 ]. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.14 apply (zenon_L277_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.14 apply (zenon_L346_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.14 apply (zenon_L279_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.14 apply (zenon_L347_); trivial. % 40.94/41.14 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.14 exact (zenon_H13e zenon_H142). % 40.94/41.14 (* end of lemma zenon_L348_ *) % 40.94/41.14 assert (zenon_L349_ : (~((op (op (e0) (e4)) (e0)) = (e4))) -> ((op (e4) (e0)) = (e4)) -> ((op (e0) (e4)) = (e4)) -> False). % 40.94/41.14 do 0 intro. intros zenon_H204 zenon_H9a zenon_H205. % 40.94/41.14 cut (((op (e4) (e0)) = (e4)) = ((op (op (e0) (e4)) (e0)) = (e4))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H204. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H9a. % 40.94/41.14 cut (((e4) = (e4))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 40.94/41.14 cut (((op (e4) (e0)) = (op (op (e0) (e4)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 40.94/41.14 congruence. % 40.94/41.14 elim (classic ((op (op (e0) (e4)) (e0)) = (op (op (e0) (e4)) (e0)))); [ zenon_intro zenon_H207 | zenon_intro zenon_H208 ]. % 40.94/41.14 cut (((op (op (e0) (e4)) (e0)) = (op (op (e0) (e4)) (e0))) = ((op (e4) (e0)) = (op (op (e0) (e4)) (e0)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H206. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H207. % 40.94/41.14 cut (((op (op (e0) (e4)) (e0)) = (op (op (e0) (e4)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H208]. % 40.94/41.14 cut (((op (op (e0) (e4)) (e0)) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H209]. % 40.94/41.14 congruence. % 40.94/41.14 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 40.94/41.14 cut (((op (e0) (e4)) = (e4))); [idtac | apply NNPP; zenon_intro zenon_H20a]. % 40.94/41.14 congruence. % 40.94/41.14 exact (zenon_H20a zenon_H205). % 40.94/41.14 apply zenon_H3f. apply refl_equal. % 40.94/41.14 apply zenon_H208. apply refl_equal. % 40.94/41.14 apply zenon_H208. apply refl_equal. % 40.94/41.14 apply zenon_H97. apply refl_equal. % 40.94/41.14 (* end of lemma zenon_L349_ *) % 40.94/41.14 assert (zenon_L350_ : ((op (e0) (unit)) = (e0)) -> ((unit) = (e3)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H50 zenon_H2a zenon_H16d zenon_H161. % 40.94/41.14 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 40.94/41.14 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e0)) = (op (e0) (e3)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H161. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H52. % 40.94/41.14 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 40.94/41.14 cut (((op (e0) (e3)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H20b]. % 40.94/41.14 congruence. % 40.94/41.14 cut (((op (e0) (unit)) = (e0)) = ((op (e0) (e3)) = (op (e0) (e0)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H20b. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H50. % 40.94/41.14 cut (((e0) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 40.94/41.14 cut (((op (e0) (unit)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 40.94/41.14 congruence. % 40.94/41.14 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 40.94/41.14 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (unit)) = (op (e0) (e3)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H55. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H52. % 40.94/41.14 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 40.94/41.14 cut (((op (e0) (e3)) = (op (e0) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 40.94/41.14 congruence. % 40.94/41.14 apply (zenon_L18_); trivial. % 40.94/41.14 apply zenon_H53. apply refl_equal. % 40.94/41.14 apply zenon_H53. apply refl_equal. % 40.94/41.14 apply zenon_H171. apply sym_equal. exact zenon_H16d. % 40.94/41.14 apply zenon_H53. apply refl_equal. % 40.94/41.14 apply zenon_H53. apply refl_equal. % 40.94/41.14 (* end of lemma zenon_L350_ *) % 40.94/41.14 assert (zenon_L351_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e1) (e4)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.14 do 0 intro. intros zenon_H3b zenon_H1b4 zenon_Hd3 zenon_H1b3 zenon_H41 zenon_H22 zenon_H20 zenon_H1f zenon_H161 zenon_H16d zenon_H50 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.14 apply (zenon_L283_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.14 apply (zenon_L249_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.14 apply (zenon_L8_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.14 apply (zenon_L350_); trivial. % 40.94/41.14 apply (zenon_L44_); trivial. % 40.94/41.14 (* end of lemma zenon_L351_ *) % 40.94/41.14 assert (zenon_L352_ : (~((op (e0) (e4)) = (op (e2) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((unit) = (e0)) -> ((op (e2) (e4)) = (e4)) -> False). % 40.94/41.14 do 0 intro. intros zenon_H20c zenon_Hd3 zenon_H9 zenon_H20d. % 40.94/41.14 cut (((op (unit) (e4)) = (e4)) = ((op (e0) (e4)) = (op (e2) (e4)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H20c. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_Hd3. % 40.94/41.14 cut (((e4) = (op (e2) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 40.94/41.14 cut (((op (unit) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 40.94/41.14 congruence. % 40.94/41.14 elim (classic ((op (e0) (e4)) = (op (e0) (e4)))); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H1b8 ]. % 40.94/41.14 cut (((op (e0) (e4)) = (op (e0) (e4))) = ((op (unit) (e4)) = (op (e0) (e4)))). % 40.94/41.14 intro zenon_D_pnotp. % 40.94/41.14 apply zenon_H1b6. % 40.94/41.14 rewrite <- zenon_D_pnotp. % 40.94/41.14 exact zenon_H1b7. % 40.94/41.14 cut (((op (e0) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 40.94/41.14 cut (((op (e0) (e4)) = (op (unit) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 40.94/41.14 congruence. % 40.94/41.14 apply (zenon_L282_); trivial. % 40.94/41.14 apply zenon_H1b8. apply refl_equal. % 40.94/41.14 apply zenon_H1b8. apply refl_equal. % 40.94/41.14 apply zenon_H20e. apply sym_equal. exact zenon_H20d. % 40.94/41.14 (* end of lemma zenon_L352_ *) % 40.94/41.14 assert (zenon_L353_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e2) (e4)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.14 do 0 intro. intros zenon_H3b zenon_H20d zenon_Hd3 zenon_H20c zenon_H41 zenon_H22 zenon_H20 zenon_H1f zenon_H161 zenon_H16d zenon_H50 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.14 apply (zenon_L352_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.14 apply (zenon_L249_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.14 apply (zenon_L8_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.14 apply (zenon_L350_); trivial. % 40.94/41.14 apply (zenon_L44_); trivial. % 40.94/41.14 (* end of lemma zenon_L353_ *) % 40.94/41.14 assert (zenon_L354_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (e4)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.14 do 0 intro. intros zenon_H3b zenon_H1fc zenon_Hd3 zenon_H1fb zenon_H41 zenon_H16d zenon_H50 zenon_H22 zenon_H20 zenon_H1f zenon_H197 zenon_H16 zenon_H81 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.14 apply (zenon_L332_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.14 apply (zenon_L249_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.14 apply (zenon_L8_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.14 apply (zenon_L270_); trivial. % 40.94/41.14 apply (zenon_L44_); trivial. % 40.94/41.14 (* end of lemma zenon_L354_ *) % 40.94/41.14 assert (zenon_L355_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e3) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H19a zenon_H17 zenon_H2d zenon_H18 zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_H92 zenon_Hc zenon_H91 zenon_H81 zenon_H16 zenon_H1f zenon_H20 zenon_H22 zenon_H50 zenon_H16d zenon_H41 zenon_H1fb zenon_Hd3 zenon_H1fc zenon_H3b zenon_H146. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.14 apply (zenon_L263_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.14 apply (zenon_L300_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.14 apply (zenon_L266_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.14 apply (zenon_L354_); trivial. % 40.94/41.14 exact (zenon_H146 zenon_H144). % 40.94/41.14 (* end of lemma zenon_L355_ *) % 40.94/41.14 assert (zenon_L356_ : (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e4) (e0)) = (e4)) -> (~((op (op (e0) (e4)) (e0)) = (e4))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.14 do 0 intro. intros zenon_H20f zenon_H9a zenon_H204 zenon_H1b3 zenon_H161 zenon_H20c zenon_H146 zenon_H3b zenon_Hd3 zenon_H1fb zenon_H41 zenon_H16d zenon_H50 zenon_H22 zenon_H20 zenon_H1f zenon_H16 zenon_H81 zenon_H91 zenon_Hc zenon_H92 zenon_H18e zenon_H2c zenon_H112 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H168 zenon_H18 zenon_H2d zenon_H17 zenon_H19a zenon_Hda. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H205 | zenon_intro zenon_H210 ]. % 40.94/41.14 apply (zenon_L349_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H211 ]. % 40.94/41.14 apply (zenon_L351_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H20d | zenon_intro zenon_H212 ]. % 40.94/41.14 apply (zenon_L353_); trivial. % 40.94/41.14 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H1fc | zenon_intro zenon_Hde ]. % 40.94/41.14 apply (zenon_L355_); trivial. % 40.94/41.14 exact (zenon_Hda zenon_Hde). % 40.94/41.14 (* end of lemma zenon_L356_ *) % 40.94/41.14 assert (zenon_L357_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e2)) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e4) (e0)) = (e4)) -> (~((op (op (e0) (e4)) (e0)) = (e4))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.14 do 0 intro. intros zenon_He0 zenon_Hb zenon_H116 zenon_Hab zenon_H34 zenon_H32 zenon_H197 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_H20f zenon_H9a zenon_H204 zenon_H1b3 zenon_H161 zenon_H20c zenon_H146 zenon_H3b zenon_Hd3 zenon_H1fb zenon_H41 zenon_H16d zenon_H50 zenon_H22 zenon_H20 zenon_H1f zenon_H16 zenon_H81 zenon_H91 zenon_Hc zenon_H18e zenon_H2c zenon_H112 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H168 zenon_H18 zenon_H2d zenon_H17 zenon_H19a zenon_Hda. % 40.94/41.15 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.15 apply (zenon_L12_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.15 apply (zenon_L278_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.15 apply (zenon_L286_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.15 exact (zenon_He1 zenon_He5). % 40.94/41.15 apply (zenon_L356_); trivial. % 40.94/41.15 (* end of lemma zenon_L357_ *) % 40.94/41.15 assert (zenon_L358_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (op (e0) (e4)) (e0)) = (e4))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((e1) = (op (e4) (e2))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e3) (e4)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.15 do 0 intro. intros zenon_Hd9 zenon_H19a zenon_H2d zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_H50 zenon_H16d zenon_H41 zenon_H1fb zenon_H146 zenon_H20c zenon_H161 zenon_H1b3 zenon_H204 zenon_H20f zenon_He1 zenon_H57 zenon_H58 zenon_H6e zenon_H34 zenon_Hab zenon_H116 zenon_Hb zenon_He0 zenon_He8 zenon_Hd3 zenon_H17 zenon_H18 zenon_H9b zenon_H92 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H81 zenon_H16 zenon_H197 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.94/41.15 apply (zenon_L357_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.94/41.15 apply (zenon_L304_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.94/41.15 apply (zenon_L73_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.94/41.15 apply (zenon_L305_); trivial. % 40.94/41.15 exact (zenon_Hda zenon_Hde). % 40.94/41.15 (* end of lemma zenon_L358_ *) % 40.94/41.15 assert (zenon_L359_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (op (e0) (e4)) (e0)) = (e4))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e4) (e3)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.15 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_H197 zenon_H81 zenon_He0 zenon_Hb zenon_H116 zenon_H6e zenon_H57 zenon_He1 zenon_H20f zenon_H204 zenon_H161 zenon_H20c zenon_H146 zenon_H1fb zenon_H41 zenon_H16d zenon_H50 zenon_H18e zenon_H168 zenon_H2d zenon_H19a zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H1c2 zenon_H42 zenon_H7b zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H92 zenon_Hd9 zenon_Hc3. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.15 apply (zenon_L53_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.15 apply (zenon_L358_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.15 apply (zenon_L279_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.15 apply (zenon_L294_); trivial. % 40.94/41.15 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.15 (* end of lemma zenon_L359_ *) % 40.94/41.15 assert (zenon_L360_ : (~((op (e4) (e4)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e4) (e3)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e3) (e4)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((e1) = (e3))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (op (e0) (e4)) (e0)) = (e4))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.15 do 0 intro. intros zenon_Hc3 zenon_Hd9 zenon_H92 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He8 zenon_Hd3 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H83 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H7b zenon_H42 zenon_H1c2 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H19a zenon_H2d zenon_H168 zenon_H18e zenon_H50 zenon_H16d zenon_H41 zenon_H1fb zenon_H20c zenon_H161 zenon_H204 zenon_H20f zenon_He1 zenon_H57 zenon_H6e zenon_H116 zenon_Hb zenon_He0 zenon_H81 zenon_Ha1 zenon_Hc2 zenon_H146. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.15 apply (zenon_L263_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.15 apply (zenon_L300_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.15 apply (zenon_L266_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.15 apply (zenon_L359_); trivial. % 40.94/41.15 exact (zenon_H146 zenon_H144). % 40.94/41.15 (* end of lemma zenon_L360_ *) % 40.94/41.15 assert (zenon_L361_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (op (e0) (e4)) (e0)) = (e4))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e4) (e4)) = (e0))) -> False). % 40.94/41.15 do 0 intro. intros zenon_Hbb zenon_H49 zenon_H9f zenon_Hb9 zenon_H1c9 zenon_H51 zenon_H1c8 zenon_H88 zenon_H87 zenon_H77 zenon_H73 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hee zenon_H1c4 zenon_H165 zenon_H1a9 zenon_H146 zenon_Hc2 zenon_Ha1 zenon_H81 zenon_He0 zenon_Hb zenon_H116 zenon_H6e zenon_H57 zenon_He1 zenon_H20f zenon_H204 zenon_H161 zenon_H20c zenon_H1fb zenon_H41 zenon_H16d zenon_H50 zenon_H18e zenon_H168 zenon_H2d zenon_H19a zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H42 zenon_H7b zenon_H20 zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_Hd9 zenon_Hc3 zenon_H13e. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.15 apply (zenon_L272_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.15 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.15 apply (zenon_L273_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.15 apply (zenon_L274_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.15 apply (zenon_L12_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.15 apply (zenon_L299_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.15 apply (zenon_L112_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.15 exact (zenon_He1 zenon_He5). % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H166 | zenon_intro zenon_H1c5 ]. % 40.94/41.15 apply (zenon_L243_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1c6 ]. % 40.94/41.15 apply (zenon_L275_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1c7 ]. % 40.94/41.15 apply (zenon_L276_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H142 ]. % 40.94/41.15 apply (zenon_L360_); trivial. % 40.94/41.15 exact (zenon_H13e zenon_H142). % 40.94/41.15 (* end of lemma zenon_L361_ *) % 40.94/41.15 assert (zenon_L362_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.94/41.15 do 0 intro. intros zenon_H3b zenon_H17 zenon_H16 zenon_H213 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H20 zenon_H1bf zenon_Hb1. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.15 cut (((op (unit) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e1) (e0)))). % 40.94/41.15 intro zenon_D_pnotp. % 40.94/41.15 apply zenon_H213. % 40.94/41.15 rewrite <- zenon_D_pnotp. % 40.94/41.15 exact zenon_H16. % 40.94/41.15 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 40.94/41.15 cut (((op (unit) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 40.94/41.15 congruence. % 40.94/41.15 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 40.94/41.15 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (unit) (e1)) = (op (e0) (e1)))). % 40.94/41.15 intro zenon_D_pnotp. % 40.94/41.15 apply zenon_H177. % 40.94/41.15 rewrite <- zenon_D_pnotp. % 40.94/41.15 exact zenon_H138. % 40.94/41.15 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 40.94/41.15 cut (((op (e0) (e1)) = (op (unit) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H174]. % 40.94/41.15 congruence. % 40.94/41.15 apply (zenon_L252_); trivial. % 40.94/41.15 apply zenon_H139. apply refl_equal. % 40.94/41.15 apply zenon_H139. apply refl_equal. % 40.94/41.15 apply zenon_H1c. apply sym_equal. exact zenon_H17. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.15 apply (zenon_L287_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.15 apply (zenon_L84_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.15 apply (zenon_L102_); trivial. % 40.94/41.15 apply (zenon_L290_); trivial. % 40.94/41.15 (* end of lemma zenon_L362_ *) % 40.94/41.15 assert (zenon_L363_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (e3))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.94/41.15 do 0 intro. intros zenon_H1c8 zenon_H146 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H1f zenon_H81 zenon_H18e zenon_H112 zenon_H115 zenon_H2c zenon_H116 zenon_He0 zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H57 zenon_H58 zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H168 zenon_H2d zenon_H91 zenon_Hc zenon_H19a zenon_H1c9 zenon_H22 zenon_Hb9 zenon_H34 zenon_H32 zenon_H73 zenon_H5f zenon_H9f zenon_H9b zenon_H61 zenon_H3b zenon_H17 zenon_H16 zenon_H213 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H20 zenon_Hb1. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.15 apply (zenon_L272_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.15 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.15 apply (zenon_L273_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.15 apply (zenon_L51_); trivial. % 40.94/41.15 apply (zenon_L362_); trivial. % 40.94/41.15 (* end of lemma zenon_L363_ *) % 40.94/41.15 assert (zenon_L364_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e0)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 40.94/41.15 do 0 intro. intros zenon_H15b zenon_Hb1 zenon_H20 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H213 zenon_H16 zenon_H17 zenon_H3b zenon_H61 zenon_H9b zenon_H9f zenon_H5f zenon_H73 zenon_H32 zenon_Hb9 zenon_H22 zenon_H1c9 zenon_H19a zenon_Hc zenon_H91 zenon_H2d zenon_H168 zenon_He1 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_Hd3 zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H58 zenon_H57 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H7b zenon_H88 zenon_H49 zenon_Hb zenon_He0 zenon_H116 zenon_H2c zenon_H115 zenon_H112 zenon_H18e zenon_H81 zenon_H1f zenon_H50 zenon_H16d zenon_H41 zenon_H51 zenon_H146 zenon_H1c8 zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 40.94/41.15 apply (zenon_L250_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 40.94/41.15 apply (zenon_L363_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 40.94/41.15 apply (zenon_L216_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 40.94/41.15 apply (zenon_L217_); trivial. % 40.94/41.15 apply (zenon_L218_); trivial. % 40.94/41.15 (* end of lemma zenon_L364_ *) % 40.94/41.15 assert (zenon_L365_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e3) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e1)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> False). % 40.94/41.15 do 0 intro. intros zenon_H3b zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_H32 zenon_H99 zenon_H1c2 zenon_H42 zenon_H7b zenon_Hd3 zenon_Ha5 zenon_He8. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.15 apply (zenon_L55_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.15 apply (zenon_L6_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.15 apply (zenon_L58_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.15 apply (zenon_L292_); trivial. % 40.94/41.15 apply (zenon_L124_); trivial. % 40.94/41.15 (* end of lemma zenon_L365_ *) % 40.94/41.15 assert (zenon_L366_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e1) (e4)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e3)) = (e4)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> False). % 40.94/41.15 do 0 intro. intros zenon_H3b zenon_Hcc zenon_Hab zenon_Hc zenon_Haa zenon_H99 zenon_H91 zenon_H1c2 zenon_H42 zenon_H7b zenon_Hd3 zenon_Hcd zenon_Hd4. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.15 apply (zenon_L74_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.15 apply (zenon_L56_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.15 apply (zenon_L76_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.15 apply (zenon_L292_); trivial. % 40.94/41.15 apply (zenon_L80_); trivial. % 40.94/41.15 (* end of lemma zenon_L366_ *) % 40.94/41.15 assert (zenon_L367_ : (~((op (e1) (e1)) = (op (e4) (e1)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e0)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e3) (e4)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e1) (e4)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.15 do 0 intro. intros zenon_H157 zenon_H34 zenon_H11f zenon_H152 zenon_H14d zenon_H1c8 zenon_H146 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H81 zenon_H18e zenon_H112 zenon_H115 zenon_H2c zenon_H116 zenon_He0 zenon_Hb zenon_H49 zenon_H88 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H57 zenon_H58 zenon_H68 zenon_Hed zenon_He6 zenon_He9 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H168 zenon_H2d zenon_H19a zenon_H1c9 zenon_Hb9 zenon_H73 zenon_H5f zenon_H9f zenon_H61 zenon_H213 zenon_Hb1 zenon_H15b zenon_He8 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H92 zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_Hc8 zenon_Hd4 zenon_Hd3 zenon_H7b zenon_H42 zenon_H1c2 zenon_H91 zenon_H99 zenon_Haa zenon_Hc zenon_Hab zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.94/41.15 apply (zenon_L364_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.94/41.15 apply (zenon_L365_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.94/41.15 apply (zenon_L73_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.94/41.15 apply (zenon_L366_); trivial. % 40.94/41.15 exact (zenon_Hda zenon_Hde). % 40.94/41.15 (* end of lemma zenon_L367_ *) % 40.94/41.15 assert (zenon_L368_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e0) (e1)) = (op (e1) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e4) (e3)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.15 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_Haa zenon_Hd4 zenon_H15b zenon_H213 zenon_H9f zenon_H73 zenon_Hb9 zenon_H1c9 zenon_H19a zenon_H2d zenon_H168 zenon_He1 zenon_Hee zenon_Hba zenon_He9 zenon_He6 zenon_Hed zenon_H57 zenon_H6e zenon_H77 zenon_H87 zenon_H88 zenon_H49 zenon_Hb zenon_He0 zenon_H116 zenon_H18e zenon_H81 zenon_H50 zenon_H16d zenon_H41 zenon_H51 zenon_H146 zenon_H1c8 zenon_H14d zenon_H152 zenon_H157 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H1c2 zenon_H42 zenon_H7b zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H92 zenon_Hd9 zenon_Hc3. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.15 apply (zenon_L53_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.15 apply (zenon_L367_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.15 apply (zenon_L279_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.15 apply (zenon_L294_); trivial. % 40.94/41.15 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.15 (* end of lemma zenon_L368_ *) % 40.94/41.15 assert (zenon_L369_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e0))) -> False). % 40.94/41.15 do 0 intro. intros zenon_Hbb zenon_H1c4 zenon_H165 zenon_H1a9 zenon_Hc3 zenon_Hd9 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He8 zenon_Hd3 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H83 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H20 zenon_H7b zenon_H42 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H157 zenon_H152 zenon_H14d zenon_H1c8 zenon_H146 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H81 zenon_H18e zenon_H116 zenon_He0 zenon_Hb zenon_H49 zenon_H88 zenon_H87 zenon_H77 zenon_H6e zenon_H57 zenon_Hed zenon_He6 zenon_He9 zenon_Hba zenon_Hee zenon_He1 zenon_H168 zenon_H2d zenon_H19a zenon_H1c9 zenon_Hb9 zenon_H73 zenon_H9f zenon_H213 zenon_H15b zenon_Hd4 zenon_Haa zenon_Ha1 zenon_Hc2 zenon_H13e. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.15 apply (zenon_L272_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.15 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.15 apply (zenon_L273_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.15 apply (zenon_L274_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.15 apply (zenon_L12_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.15 apply (zenon_L298_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.15 apply (zenon_L112_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.15 exact (zenon_He1 zenon_He5). % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H166 | zenon_intro zenon_H1c5 ]. % 40.94/41.15 apply (zenon_L243_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1c6 ]. % 40.94/41.15 apply (zenon_L275_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1c7 ]. % 40.94/41.15 apply (zenon_L276_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H142 ]. % 40.94/41.15 apply (zenon_L368_); trivial. % 40.94/41.15 exact (zenon_H13e zenon_H142). % 40.94/41.15 (* end of lemma zenon_L369_ *) % 40.94/41.15 assert (zenon_L370_ : ((~((op (e1) (e1)) = (op (e1) (e1))))/\(((op (op (e1) (e1)) (e1)) = (e1))/\(~((op (op (e1) (e1)) (e1)) = (e1))))) -> False). % 40.94/41.15 do 0 intro. intros zenon_H214. % 40.94/41.15 apply (zenon_and_s _ _ zenon_H214). zenon_intro zenon_H1a. zenon_intro zenon_H215. % 40.94/41.15 apply zenon_H1a. apply refl_equal. % 40.94/41.15 (* end of lemma zenon_L370_ *) % 40.94/41.15 assert (zenon_L371_ : ((op (e3) (unit)) = (e3)) -> ((unit) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 40.94/41.15 do 0 intro. intros zenon_H5f zenon_H9 zenon_H216 zenon_H217. % 40.94/41.15 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H7f | zenon_intro zenon_H80 ]. % 40.94/41.15 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e1) (e0)) = (op (e3) (e0)))). % 40.94/41.15 intro zenon_D_pnotp. % 40.94/41.15 apply zenon_H217. % 40.94/41.15 rewrite <- zenon_D_pnotp. % 40.94/41.15 exact zenon_H7f. % 40.94/41.15 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 40.94/41.15 cut (((op (e3) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 40.94/41.15 congruence. % 40.94/41.15 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e0)) = (op (e1) (e0)))). % 40.94/41.15 intro zenon_D_pnotp. % 40.94/41.15 apply zenon_H218. % 40.94/41.15 rewrite <- zenon_D_pnotp. % 40.94/41.15 exact zenon_H5f. % 40.94/41.15 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 40.94/41.15 cut (((op (e3) (unit)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 40.94/41.15 congruence. % 40.94/41.15 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H7f | zenon_intro zenon_H80 ]. % 40.94/41.15 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e3) (unit)) = (op (e3) (e0)))). % 40.94/41.15 intro zenon_D_pnotp. % 40.94/41.15 apply zenon_H7e. % 40.94/41.15 rewrite <- zenon_D_pnotp. % 40.94/41.15 exact zenon_H7f. % 40.94/41.15 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 40.94/41.15 cut (((op (e3) (e0)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 40.94/41.15 congruence. % 40.94/41.15 apply (zenon_L34_); trivial. % 40.94/41.15 apply zenon_H80. apply refl_equal. % 40.94/41.15 apply zenon_H80. apply refl_equal. % 40.94/41.15 apply zenon_H219. apply sym_equal. exact zenon_H216. % 40.94/41.15 apply zenon_H80. apply refl_equal. % 40.94/41.15 apply zenon_H80. apply refl_equal. % 40.94/41.15 (* end of lemma zenon_L371_ *) % 40.94/41.15 assert (zenon_L372_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.15 do 0 intro. intros zenon_H3b zenon_H217 zenon_H216 zenon_H5f zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.15 apply (zenon_L371_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.15 apply (zenon_L287_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.15 apply (zenon_L84_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.15 apply (zenon_L102_); trivial. % 40.94/41.15 apply (zenon_L44_); trivial. % 40.94/41.15 (* end of lemma zenon_L372_ *) % 40.94/41.15 assert (zenon_L373_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e3)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.15 do 0 intro. intros zenon_H3b zenon_Hcc zenon_Hb1 zenon_Hcd zenon_H99 zenon_H197 zenon_H16 zenon_H81 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.15 apply (zenon_L74_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.15 apply (zenon_L75_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.15 apply (zenon_L76_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.15 apply (zenon_L270_); trivial. % 40.94/41.15 apply (zenon_L44_); trivial. % 40.94/41.15 (* end of lemma zenon_L373_ *) % 40.94/41.15 assert (zenon_L374_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (unit)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e3) (e4)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e3) (e4)) = (e1)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.15 do 0 intro. intros zenon_Hd9 zenon_H15f zenon_H5f zenon_H216 zenon_H217 zenon_He8 zenon_Hd3 zenon_H7b zenon_H42 zenon_H1c2 zenon_H17 zenon_H18 zenon_H9b zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_Hc8 zenon_H92 zenon_Hc zenon_H91 zenon_H81 zenon_H16 zenon_H197 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.94/41.15 apply (zenon_L372_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.94/41.15 apply (zenon_L365_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.94/41.15 apply (zenon_L73_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.94/41.15 apply (zenon_L373_); trivial. % 40.94/41.15 exact (zenon_Hda zenon_Hde). % 40.94/41.15 (* end of lemma zenon_L374_ *) % 40.94/41.15 assert (zenon_L375_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.15 do 0 intro. intros zenon_H19a zenon_H2d zenon_H168 zenon_H60 zenon_H68 zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_Hda zenon_H3b zenon_Hcc zenon_Hb1 zenon_H99 zenon_H16 zenon_H81 zenon_H91 zenon_Hc zenon_H92 zenon_Hc8 zenon_H32 zenon_H22 zenon_H20 zenon_H1f zenon_H9b zenon_H18 zenon_H17 zenon_H1c2 zenon_H42 zenon_H7b zenon_Hd3 zenon_He8 zenon_H217 zenon_H216 zenon_H5f zenon_H15f zenon_Hd9 zenon_H146. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.15 apply (zenon_L263_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.15 apply (zenon_L300_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.15 apply (zenon_L266_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.15 apply (zenon_L374_); trivial. % 40.94/41.15 exact (zenon_H146 zenon_H144). % 40.94/41.15 (* end of lemma zenon_L375_ *) % 40.94/41.15 assert (zenon_L376_ : (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (unit)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e0))) -> False). % 40.94/41.15 do 0 intro. intros zenon_H1c4 zenon_H165 zenon_H115 zenon_H34 zenon_H11f zenon_H1a9 zenon_H146 zenon_Hd9 zenon_H15f zenon_H5f zenon_H216 zenon_H217 zenon_He8 zenon_Hd3 zenon_H7b zenon_H42 zenon_H17 zenon_H18 zenon_H9b zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_Hc8 zenon_H92 zenon_Hc zenon_H91 zenon_H81 zenon_H16 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda zenon_H18e zenon_H2c zenon_H112 zenon_H61 zenon_H8e zenon_H68 zenon_H60 zenon_H168 zenon_H2d zenon_H19a zenon_H13e. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H166 | zenon_intro zenon_H1c5 ]. % 40.94/41.15 apply (zenon_L243_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1c6 ]. % 40.94/41.15 apply (zenon_L275_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1c7 ]. % 40.94/41.15 apply (zenon_L276_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H142 ]. % 40.94/41.15 apply (zenon_L375_); trivial. % 40.94/41.15 exact (zenon_H13e zenon_H142). % 40.94/41.15 (* end of lemma zenon_L376_ *) % 40.94/41.15 assert (zenon_L377_ : (~((op (e3) (e2)) = (op (e4) (e2)))) -> ((op (op (e1) (e2)) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.15 do 0 intro. intros zenon_H21a zenon_H21b zenon_H21c zenon_H34. % 40.94/41.15 cut (((op (op (e1) (e2)) (e2)) = (e1)) = ((op (e3) (e2)) = (op (e4) (e2)))). % 40.94/41.15 intro zenon_D_pnotp. % 40.94/41.15 apply zenon_H21a. % 40.94/41.15 rewrite <- zenon_D_pnotp. % 40.94/41.15 exact zenon_H21b. % 40.94/41.15 cut (((e1) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 40.94/41.15 cut (((op (op (e1) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 40.94/41.15 congruence. % 40.94/41.15 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 40.94/41.15 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (op (e1) (e2)) (e2)) = (op (e3) (e2)))). % 40.94/41.15 intro zenon_D_pnotp. % 40.94/41.15 apply zenon_H21d. % 40.94/41.15 rewrite <- zenon_D_pnotp. % 40.94/41.15 exact zenon_H85. % 40.94/41.15 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 40.94/41.15 cut (((op (e3) (e2)) = (op (op (e1) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 40.94/41.15 congruence. % 40.94/41.15 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 40.94/41.15 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 40.94/41.15 congruence. % 40.94/41.15 apply zenon_H21f. apply sym_equal. exact zenon_H21c. % 40.94/41.15 apply zenon_H7. apply refl_equal. % 40.94/41.15 apply zenon_H86. apply refl_equal. % 40.94/41.15 apply zenon_H86. apply refl_equal. % 40.94/41.15 exact (zenon_H35 zenon_H34). % 40.94/41.15 (* end of lemma zenon_L377_ *) % 40.94/41.15 assert (zenon_L378_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (unit) (e3)) = (e3)) -> ((unit) = (e0)) -> ((op (e1) (e3)) = (e3)) -> False). % 40.94/41.15 do 0 intro. intros zenon_H220 zenon_H20 zenon_H9 zenon_H221. % 40.94/41.15 cut (((op (unit) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 40.94/41.15 intro zenon_D_pnotp. % 40.94/41.15 apply zenon_H220. % 40.94/41.15 rewrite <- zenon_D_pnotp. % 40.94/41.15 exact zenon_H20. % 40.94/41.15 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H222]. % 40.94/41.15 cut (((op (unit) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 40.94/41.15 congruence. % 40.94/41.15 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 40.94/41.15 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (unit) (e3)) = (op (e0) (e3)))). % 40.94/41.15 intro zenon_D_pnotp. % 40.94/41.15 apply zenon_H195. % 40.94/41.15 rewrite <- zenon_D_pnotp. % 40.94/41.15 exact zenon_H52. % 40.94/41.15 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 40.94/41.15 cut (((op (e0) (e3)) = (op (unit) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 40.94/41.15 congruence. % 40.94/41.15 apply (zenon_L267_); trivial. % 40.94/41.15 apply zenon_H53. apply refl_equal. % 40.94/41.15 apply zenon_H53. apply refl_equal. % 40.94/41.15 apply zenon_H222. apply sym_equal. exact zenon_H221. % 40.94/41.15 (* end of lemma zenon_L378_ *) % 40.94/41.15 assert (zenon_L379_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.15 do 0 intro. intros zenon_H3b zenon_H221 zenon_H220 zenon_H41 zenon_H22 zenon_H20 zenon_H1f zenon_H161 zenon_H16d zenon_H50 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.15 apply (zenon_L378_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.15 apply (zenon_L249_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.15 apply (zenon_L8_); trivial. % 40.94/41.15 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.15 apply (zenon_L350_); trivial. % 40.94/41.15 apply (zenon_L11_); trivial. % 40.94/41.15 (* end of lemma zenon_L379_ *) % 40.94/41.15 assert (zenon_L380_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (~((op (e4) (e4)) = (e0))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (unit)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((e0) = (e3))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> ((op (op (e1) (e2)) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> False). % 40.94/41.16 do 0 intro. intros zenon_H223 zenon_H13e zenon_H19a zenon_H2d zenon_H168 zenon_H60 zenon_H68 zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_Hda zenon_Hcc zenon_Hb1 zenon_H99 zenon_H81 zenon_H91 zenon_Hc zenon_Hc8 zenon_H9b zenon_H18 zenon_H17 zenon_H42 zenon_H7b zenon_Hd3 zenon_He8 zenon_H217 zenon_H5f zenon_H15f zenon_Hd9 zenon_H146 zenon_H1a9 zenon_H11f zenon_H115 zenon_H165 zenon_H1c4 zenon_He1 zenon_H88 zenon_H73 zenon_H77 zenon_H6e zenon_H58 zenon_H57 zenon_H89 zenon_H83 zenon_H87 zenon_H1c8 zenon_H51 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hee zenon_Hb9 zenon_H9f zenon_Hc2 zenon_Ha1 zenon_H116 zenon_Hb6 zenon_H1b3 zenon_H1ad zenon_H1b9 zenon_H49 zenon_Hb zenon_He0 zenon_Hc3 zenon_Hbb zenon_Hba zenon_H1c9 zenon_H21b zenon_H21a zenon_H34 zenon_H16 zenon_H32 zenon_H50 zenon_H16d zenon_H161 zenon_H1f zenon_H20 zenon_H41 zenon_H220 zenon_H3b zenon_H1ae zenon_H22. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H216 | zenon_intro zenon_H224 ]. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.16 apply (zenon_L12_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.16 apply (zenon_L299_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.16 apply (zenon_L41_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.16 exact (zenon_He1 zenon_He5). % 40.94/41.16 apply (zenon_L376_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1cc | zenon_intro zenon_H225 ]. % 40.94/41.16 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.16 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H21c | zenon_intro zenon_H226 ]. % 40.94/41.16 apply (zenon_L377_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H221 | zenon_intro zenon_H1af ]. % 40.94/41.16 apply (zenon_L379_); trivial. % 40.94/41.16 apply (zenon_L281_); trivial. % 40.94/41.16 (* end of lemma zenon_L380_ *) % 40.94/41.16 assert (zenon_L381_ : ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (e3)) = (e0)) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 40.94/41.16 do 0 intro. intros zenon_H11f zenon_H227 zenon_H34 zenon_H111. % 40.94/41.16 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 40.94/41.16 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e1)) = (op (e1) (e3)))). % 40.94/41.16 intro zenon_D_pnotp. % 40.94/41.16 apply zenon_H111. % 40.94/41.16 rewrite <- zenon_D_pnotp. % 40.94/41.16 exact zenon_H2e. % 40.94/41.16 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 40.94/41.16 cut (((op (e1) (e3)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 40.94/41.16 congruence. % 40.94/41.16 cut (((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) = ((op (e1) (e3)) = (op (e1) (e1)))). % 40.94/41.16 intro zenon_D_pnotp. % 40.94/41.16 apply zenon_H135. % 40.94/41.16 rewrite <- zenon_D_pnotp. % 40.94/41.16 exact zenon_H11f. % 40.94/41.16 cut (((op (op (e4) (e2)) (op (e4) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 40.94/41.16 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H228]. % 40.94/41.16 congruence. % 40.94/41.16 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 40.94/41.16 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((e0) = (op (e1) (e3)))). % 40.94/41.16 intro zenon_D_pnotp. % 40.94/41.16 apply zenon_H228. % 40.94/41.16 rewrite <- zenon_D_pnotp. % 40.94/41.16 exact zenon_H2e. % 40.94/41.16 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 40.94/41.16 cut (((op (e1) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H229]. % 40.94/41.16 congruence. % 40.94/41.16 exact (zenon_H229 zenon_H227). % 40.94/41.16 apply zenon_H2f. apply refl_equal. % 40.94/41.16 apply zenon_H2f. apply refl_equal. % 40.94/41.16 apply (zenon_L169_); trivial. % 40.94/41.16 apply zenon_H2f. apply refl_equal. % 40.94/41.16 apply zenon_H2f. apply refl_equal. % 40.94/41.16 (* end of lemma zenon_L381_ *) % 40.94/41.16 assert (zenon_L382_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.16 do 0 intro. intros zenon_Hf6 zenon_Hc zenon_H91 zenon_H2c zenon_H17 zenon_H2d zenon_H18 zenon_H51 zenon_H178 zenon_He1 zenon_Hee zenon_Hd9 zenon_Hd4 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_He8 zenon_He6 zenon_Hed zenon_H87 zenon_H83 zenon_H81 zenon_H49 zenon_Hb zenon_He0 zenon_H6e zenon_Hbb zenon_Hf7 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H9b zenon_H7b zenon_H89 zenon_H77 zenon_H9f zenon_H73 zenon_H57 zenon_H22 zenon_H1f zenon_H88 zenon_H3b zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H20 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hba | zenon_intro zenon_Hf8 ]. % 40.94/41.16 apply (zenon_L260_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf9 ]. % 40.94/41.16 apply (zenon_L121_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hfa ]. % 40.94/41.16 exact (zenon_Hf7 zenon_Hfb). % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H59 | zenon_intro zenon_Hb7 ]. % 40.94/41.16 apply (zenon_L238_); trivial. % 40.94/41.16 apply (zenon_L279_); trivial. % 40.94/41.16 (* end of lemma zenon_L382_ *) % 40.94/41.16 assert (zenon_L383_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.16 do 0 intro. intros zenon_H3b zenon_H10f zenon_H18 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H32 zenon_H16 zenon_H34. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.16 apply (zenon_L156_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.16 apply (zenon_L6_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.16 apply (zenon_L8_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.16 apply (zenon_L10_); trivial. % 40.94/41.16 apply (zenon_L11_); trivial. % 40.94/41.16 (* end of lemma zenon_L383_ *) % 40.94/41.16 assert (zenon_L384_ : ((op (op (e1) (e3)) (e3)) = (e1)) -> ((op (e1) (e3)) = (e4)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> False). % 40.94/41.16 do 0 intro. intros zenon_H22a zenon_H22b zenon_H22c zenon_H22d. % 40.94/41.16 elim (classic ((op (e4) (e3)) = (op (e4) (e3)))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ]. % 40.94/41.16 cut (((op (e4) (e3)) = (op (e4) (e3))) = ((op (e2) (e3)) = (op (e4) (e3)))). % 40.94/41.16 intro zenon_D_pnotp. % 40.94/41.16 apply zenon_H22d. % 40.94/41.16 rewrite <- zenon_D_pnotp. % 40.94/41.16 exact zenon_Hb2. % 40.94/41.16 cut (((op (e4) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 40.94/41.16 cut (((op (e4) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H22e]. % 40.94/41.16 congruence. % 40.94/41.16 cut (((op (op (e1) (e3)) (e3)) = (e1)) = ((op (e4) (e3)) = (op (e2) (e3)))). % 40.94/41.16 intro zenon_D_pnotp. % 40.94/41.16 apply zenon_H22e. % 40.94/41.16 rewrite <- zenon_D_pnotp. % 40.94/41.16 exact zenon_H22a. % 40.94/41.16 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H22f]. % 40.94/41.16 cut (((op (op (e1) (e3)) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H230]. % 40.94/41.16 congruence. % 40.94/41.16 elim (classic ((op (e4) (e3)) = (op (e4) (e3)))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ]. % 40.94/41.16 cut (((op (e4) (e3)) = (op (e4) (e3))) = ((op (op (e1) (e3)) (e3)) = (op (e4) (e3)))). % 40.94/41.16 intro zenon_D_pnotp. % 40.94/41.16 apply zenon_H230. % 40.94/41.16 rewrite <- zenon_D_pnotp. % 40.94/41.16 exact zenon_Hb2. % 40.94/41.16 cut (((op (e4) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 40.94/41.16 cut (((op (e4) (e3)) = (op (op (e1) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H231]. % 40.94/41.16 congruence. % 40.94/41.16 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 40.94/41.16 cut (((e4) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H232]. % 40.94/41.16 congruence. % 40.94/41.16 apply zenon_H232. apply sym_equal. exact zenon_H22b. % 40.94/41.16 apply zenon_H1e. apply refl_equal. % 40.94/41.16 apply zenon_Hb3. apply refl_equal. % 40.94/41.16 apply zenon_Hb3. apply refl_equal. % 40.94/41.16 apply zenon_H22f. apply sym_equal. exact zenon_H22c. % 40.94/41.16 apply zenon_Hb3. apply refl_equal. % 40.94/41.16 apply zenon_Hb3. apply refl_equal. % 40.94/41.16 (* end of lemma zenon_L384_ *) % 40.94/41.16 assert (zenon_L385_ : ((e1) = (op (e4) (e2))) -> ((op (e4) (e3)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> False). % 40.94/41.16 do 0 intro. intros zenon_H34 zenon_H233 zenon_H91. % 40.94/41.16 elim (classic ((op (e4) (e3)) = (op (e4) (e3)))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ]. % 40.94/41.16 cut (((op (e4) (e3)) = (op (e4) (e3))) = ((op (e4) (e2)) = (op (e4) (e3)))). % 40.94/41.16 intro zenon_D_pnotp. % 40.94/41.16 apply zenon_H91. % 40.94/41.16 rewrite <- zenon_D_pnotp. % 40.94/41.16 exact zenon_Hb2. % 40.94/41.16 cut (((op (e4) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 40.94/41.16 cut (((op (e4) (e3)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 40.94/41.16 congruence. % 40.94/41.16 cut (((e1) = (op (e4) (e2))) = ((op (e4) (e3)) = (op (e4) (e2)))). % 40.94/41.16 intro zenon_D_pnotp. % 40.94/41.16 apply zenon_Hcb. % 40.94/41.16 rewrite <- zenon_D_pnotp. % 40.94/41.16 exact zenon_H34. % 40.94/41.16 cut (((op (e4) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 40.94/41.16 cut (((e1) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H234]. % 40.94/41.16 congruence. % 40.94/41.16 elim (classic ((op (e4) (e3)) = (op (e4) (e3)))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ]. % 40.94/41.16 cut (((op (e4) (e3)) = (op (e4) (e3))) = ((e1) = (op (e4) (e3)))). % 40.94/41.16 intro zenon_D_pnotp. % 40.94/41.16 apply zenon_H234. % 40.94/41.16 rewrite <- zenon_D_pnotp. % 40.94/41.16 exact zenon_Hb2. % 40.94/41.16 cut (((op (e4) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 40.94/41.16 cut (((op (e4) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H235]. % 40.94/41.16 congruence. % 40.94/41.16 exact (zenon_H235 zenon_H233). % 40.94/41.16 apply zenon_Hb3. apply refl_equal. % 40.94/41.16 apply zenon_Hb3. apply refl_equal. % 40.94/41.16 apply zenon_H96. apply refl_equal. % 40.94/41.16 apply zenon_Hb3. apply refl_equal. % 40.94/41.16 apply zenon_Hb3. apply refl_equal. % 40.94/41.16 (* end of lemma zenon_L385_ *) % 40.94/41.16 assert (zenon_L386_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> ((op (e1) (e3)) = (e4)) -> ((op (op (e1) (e3)) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> False). % 40.94/41.16 do 0 intro. intros zenon_H236 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_H88 zenon_H57 zenon_H73 zenon_H9f zenon_H77 zenon_H89 zenon_H7b zenon_H9b zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_Hf7 zenon_Hbb zenon_H6e zenon_He0 zenon_Hb zenon_H49 zenon_H81 zenon_H83 zenon_H87 zenon_Hed zenon_He6 zenon_He8 zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hd9 zenon_Hee zenon_He1 zenon_H51 zenon_Hc zenon_Hf6 zenon_H16 zenon_H32 zenon_H2c zenon_H17 zenon_H2d zenon_H1f zenon_H20 zenon_H22 zenon_H18 zenon_H3b zenon_H22d zenon_H22b zenon_H22a zenon_H237 zenon_H34 zenon_H91. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H178 | zenon_intro zenon_H238 ]. % 40.94/41.16 apply (zenon_L382_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H10f | zenon_intro zenon_H239 ]. % 40.94/41.16 apply (zenon_L383_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H22c | zenon_intro zenon_H23a ]. % 40.94/41.16 apply (zenon_L384_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H23b | zenon_intro zenon_H233 ]. % 40.94/41.16 exact (zenon_H237 zenon_H23b). % 40.94/41.16 apply (zenon_L385_); trivial. % 40.94/41.16 (* end of lemma zenon_L386_ *) % 40.94/41.16 assert (zenon_L387_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((unit) = (e0)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e2)) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> ((op (op (e1) (e3)) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> False). % 40.94/41.16 do 0 intro. intros zenon_H23c zenon_H111 zenon_H11f zenon_H9 zenon_H116 zenon_Hab zenon_H50 zenon_H16d zenon_H161 zenon_H41 zenon_H220 zenon_H236 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_H88 zenon_H57 zenon_H73 zenon_H9f zenon_H77 zenon_H89 zenon_H7b zenon_H9b zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_Hf7 zenon_Hbb zenon_H6e zenon_He0 zenon_Hb zenon_H49 zenon_H81 zenon_H83 zenon_H87 zenon_Hed zenon_He6 zenon_He8 zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hd9 zenon_Hee zenon_He1 zenon_H51 zenon_Hc zenon_Hf6 zenon_H16 zenon_H32 zenon_H2c zenon_H17 zenon_H2d zenon_H1f zenon_H20 zenon_H22 zenon_H18 zenon_H3b zenon_H22d zenon_H22a zenon_H237 zenon_H34 zenon_H91. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H227 | zenon_intro zenon_H23d ]. % 40.94/41.16 apply (zenon_L381_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H10f | zenon_intro zenon_H23e ]. % 40.94/41.16 apply (zenon_L156_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H4a | zenon_intro zenon_H23f ]. % 40.94/41.16 apply (zenon_L278_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H221 | zenon_intro zenon_H22b ]. % 40.94/41.16 apply (zenon_L379_); trivial. % 40.94/41.16 apply (zenon_L386_); trivial. % 40.94/41.16 (* end of lemma zenon_L387_ *) % 40.94/41.16 assert (zenon_L388_ : ((e1) = (op (e4) (e2))) -> (~((op (e3) (e3)) = (e1))) -> ((op (op (e1) (e3)) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((op (e1) (e4)) = (e2)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.16 do 0 intro. intros zenon_H34 zenon_H237 zenon_H22a zenon_H22d zenon_H3b zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H32 zenon_Hf6 zenon_H51 zenon_He1 zenon_Hee zenon_Hd9 zenon_Hd4 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_He8 zenon_He6 zenon_Hed zenon_H87 zenon_H83 zenon_H49 zenon_Hb zenon_He0 zenon_H6e zenon_Hbb zenon_Hf7 zenon_Hcc zenon_H9b zenon_H7b zenon_H89 zenon_H77 zenon_H9f zenon_H73 zenon_H57 zenon_H88 zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H236 zenon_H220 zenon_H41 zenon_H161 zenon_H16d zenon_H50 zenon_Hab zenon_H116 zenon_H11f zenon_H111 zenon_H23c zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_H9a zenon_H99 zenon_H197 zenon_H16 zenon_H81 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.16 apply (zenon_L387_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.16 apply (zenon_L287_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.16 apply (zenon_L84_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.16 apply (zenon_L270_); trivial. % 40.94/41.16 apply (zenon_L44_); trivial. % 40.94/41.16 (* end of lemma zenon_L388_ *) % 40.94/41.16 assert (zenon_L389_ : ((e1) = (op (e4) (e2))) -> (~((op (e3) (e3)) = (e1))) -> ((op (op (e1) (e3)) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((op (e1) (e4)) = (e2)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.16 do 0 intro. intros zenon_H34 zenon_H237 zenon_H22a zenon_H22d zenon_H3b zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H32 zenon_Hf6 zenon_H51 zenon_He1 zenon_Hee zenon_Hd9 zenon_Hd4 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_He8 zenon_He6 zenon_Hed zenon_H87 zenon_H83 zenon_H49 zenon_Hb zenon_He0 zenon_H6e zenon_Hbb zenon_Hf7 zenon_Hcc zenon_H9b zenon_H7b zenon_H89 zenon_H77 zenon_H9f zenon_H73 zenon_H57 zenon_H88 zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H236 zenon_H220 zenon_H41 zenon_H161 zenon_H16d zenon_H50 zenon_Hab zenon_H116 zenon_H11f zenon_H111 zenon_H23c zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_H9a zenon_H99 zenon_H197 zenon_H16 zenon_H81 zenon_H91 zenon_Hc. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.16 apply (zenon_L12_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.16 apply (zenon_L278_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.16 apply (zenon_L286_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.16 exact (zenon_He1 zenon_He5). % 40.94/41.16 apply (zenon_L388_); trivial. % 40.94/41.16 (* end of lemma zenon_L389_ *) % 40.94/41.16 assert (zenon_L390_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> ((op (op (e1) (e3)) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.16 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_H197 zenon_H23c zenon_H111 zenon_H116 zenon_H50 zenon_H16d zenon_H161 zenon_H41 zenon_H220 zenon_H236 zenon_H60 zenon_H8e zenon_H9f zenon_H89 zenon_Hf7 zenon_Hbb zenon_H51 zenon_Hf6 zenon_H22d zenon_H22a zenon_H237 zenon_Hb9 zenon_Hb6 zenon_Hc zenon_H91 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H22 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_He1 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_Hb1 zenon_H9b zenon_He8 zenon_He6 zenon_Hed zenon_H16 zenon_H32 zenon_H68 zenon_H20 zenon_H1f zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_H49 zenon_Hb zenon_H2d zenon_H17 zenon_He0 zenon_Hc3. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.16 apply (zenon_L277_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.16 apply (zenon_L389_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.16 apply (zenon_L123_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.16 apply (zenon_L324_); trivial. % 40.94/41.16 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.16 (* end of lemma zenon_L390_ *) % 40.94/41.16 assert (zenon_L391_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e3)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.16 do 0 intro. intros zenon_H3b zenon_Hcc zenon_Hb1 zenon_Hcd zenon_H99 zenon_H68 zenon_H60 zenon_H20 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.16 apply (zenon_L74_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.16 apply (zenon_L75_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.16 apply (zenon_L76_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.16 apply (zenon_L26_); trivial. % 40.94/41.16 apply (zenon_L44_); trivial. % 40.94/41.16 (* end of lemma zenon_L391_ *) % 40.94/41.16 assert (zenon_L392_ : (~((op (e4) (e4)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (op (e1) (e3)) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e3) (e4)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.16 do 0 intro. intros zenon_Hc3 zenon_He0 zenon_H2d zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H42 zenon_Hb6 zenon_Hb9 zenon_H237 zenon_H22a zenon_H22d zenon_Hf6 zenon_H51 zenon_Hbb zenon_Hf7 zenon_H89 zenon_H9f zenon_H8e zenon_H236 zenon_H220 zenon_H41 zenon_H161 zenon_H16d zenon_H50 zenon_H116 zenon_H111 zenon_H23c zenon_Ha1 zenon_Hc2 zenon_He8 zenon_Hd3 zenon_H81 zenon_H16 zenon_H197 zenon_H17 zenon_H18 zenon_H9b zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_H92 zenon_Hc zenon_H91 zenon_H20 zenon_H60 zenon_H68 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.94/41.16 apply (zenon_L390_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.94/41.16 apply (zenon_L304_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.94/41.16 apply (zenon_L73_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.94/41.16 apply (zenon_L391_); trivial. % 40.94/41.16 exact (zenon_Hda zenon_Hde). % 40.94/41.16 (* end of lemma zenon_L392_ *) % 40.94/41.16 assert (zenon_L393_ : (~((op (e4) (e4)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> ((op (op (e1) (e3)) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.16 do 0 intro. intros zenon_H13e zenon_H1a9 zenon_H165 zenon_H1c4 zenon_H1c9 zenon_H1c8 zenon_H19a zenon_H168 zenon_H18e zenon_Hda zenon_H3b zenon_Hcc zenon_Hb1 zenon_H99 zenon_H68 zenon_H60 zenon_H20 zenon_H91 zenon_Hc zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_H81 zenon_Hd3 zenon_He8 zenon_Hc2 zenon_Ha1 zenon_H23c zenon_H111 zenon_H116 zenon_H50 zenon_H16d zenon_H161 zenon_H41 zenon_H220 zenon_H236 zenon_H8e zenon_H9f zenon_H89 zenon_Hf7 zenon_Hbb zenon_H51 zenon_Hf6 zenon_H22d zenon_H22a zenon_H237 zenon_Hb9 zenon_Hb6 zenon_H42 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He1 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_He6 zenon_Hed zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H7b zenon_H88 zenon_H49 zenon_Hb zenon_H2d zenon_He0 zenon_Hc3 zenon_H146. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.16 apply (zenon_L12_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.16 apply (zenon_L299_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.16 apply (zenon_L41_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.16 exact (zenon_He1 zenon_He5). % 40.94/41.16 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.16 apply (zenon_L263_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.16 apply (zenon_L300_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.16 apply (zenon_L266_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.16 apply (zenon_L392_); trivial. % 40.94/41.16 exact (zenon_H146 zenon_H144). % 40.94/41.16 (* end of lemma zenon_L393_ *) % 40.94/41.16 assert (zenon_L394_ : (~((op (e2) (e4)) = (op (e3) (e4)))) -> ((op (op (e1) (e4)) (e4)) = (e1)) -> ((op (e1) (e4)) = (e2)) -> ((op (e3) (e4)) = (e1)) -> False). % 40.94/41.16 do 0 intro. intros zenon_H240 zenon_H241 zenon_Hab zenon_H197. % 40.94/41.16 cut (((op (op (e1) (e4)) (e4)) = (e1)) = ((op (e2) (e4)) = (op (e3) (e4)))). % 40.94/41.16 intro zenon_D_pnotp. % 40.94/41.16 apply zenon_H240. % 40.94/41.16 rewrite <- zenon_D_pnotp. % 40.94/41.16 exact zenon_H241. % 40.94/41.16 cut (((e1) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 40.94/41.16 cut (((op (op (e1) (e4)) (e4)) = (op (e2) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H242]. % 40.94/41.16 congruence. % 40.94/41.16 elim (classic ((op (e2) (e4)) = (op (e2) (e4)))); [ zenon_intro zenon_H243 | zenon_intro zenon_H19f ]. % 40.94/41.16 cut (((op (e2) (e4)) = (op (e2) (e4))) = ((op (op (e1) (e4)) (e4)) = (op (e2) (e4)))). % 40.94/41.16 intro zenon_D_pnotp. % 40.94/41.16 apply zenon_H242. % 40.94/41.16 rewrite <- zenon_D_pnotp. % 40.94/41.16 exact zenon_H243. % 40.94/41.16 cut (((op (e2) (e4)) = (op (e2) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 40.94/41.16 cut (((op (e2) (e4)) = (op (op (e1) (e4)) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H244]. % 40.94/41.16 congruence. % 40.94/41.16 cut (((e4) = (e4))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 40.94/41.16 cut (((e2) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 40.94/41.16 congruence. % 40.94/41.16 apply zenon_Hac. apply sym_equal. exact zenon_Hab. % 40.94/41.16 apply zenon_H97. apply refl_equal. % 40.94/41.16 apply zenon_H19f. apply refl_equal. % 40.94/41.16 apply zenon_H19f. apply refl_equal. % 40.94/41.16 apply zenon_H198. apply sym_equal. exact zenon_H197. % 40.94/41.16 (* end of lemma zenon_L394_ *) % 40.94/41.16 assert (zenon_L395_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (e3) (e4)) = (e1)) -> ((op (op (e1) (e4)) (e4)) = (e1)) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.16 do 0 intro. intros zenon_Hc2 zenon_H17 zenon_H2d zenon_H18 zenon_Ha1 zenon_H197 zenon_H241 zenon_H240 zenon_H58 zenon_Hb9 zenon_Hb6 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.16 apply (zenon_L277_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.16 apply (zenon_L394_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.16 apply (zenon_L123_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.16 apply (zenon_L285_); trivial. % 40.94/41.16 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.16 (* end of lemma zenon_L395_ *) % 40.94/41.16 assert (zenon_L396_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> ((op (op (e1) (e4)) (e4)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.16 do 0 intro. intros zenon_H19a zenon_H91 zenon_H168 zenon_He1 zenon_Hee zenon_Hd9 zenon_Hd4 zenon_He9 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H81 zenon_H7b zenon_H88 zenon_Hb zenon_He0 zenon_Hba zenon_H57 zenon_Hbb zenon_H18e zenon_Hc3 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H4a zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_Hc zenon_H83 zenon_H32 zenon_H16 zenon_H34 zenon_Hb6 zenon_Hb9 zenon_H58 zenon_H240 zenon_H241 zenon_Ha1 zenon_H18 zenon_H2d zenon_H17 zenon_Hc2 zenon_H146. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.16 apply (zenon_L264_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.16 apply (zenon_L178_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.16 apply (zenon_L266_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.16 apply (zenon_L395_); trivial. % 40.94/41.16 exact (zenon_H146 zenon_H144). % 40.94/41.16 (* end of lemma zenon_L396_ *) % 40.94/41.16 assert (zenon_L397_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (e3) (e4)) = (e1)) -> ((op (op (e1) (e4)) (e4)) = (e1)) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e4) (e3)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.16 do 0 intro. intros zenon_Hc2 zenon_H2d zenon_Ha1 zenon_H197 zenon_H241 zenon_H240 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H1c2 zenon_H42 zenon_H7b zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H92 zenon_Hd9 zenon_Hc3. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.16 apply (zenon_L53_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.16 apply (zenon_L394_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.16 apply (zenon_L279_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.16 apply (zenon_L294_); trivial. % 40.94/41.16 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.16 (* end of lemma zenon_L397_ *) % 40.94/41.16 assert (zenon_L398_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e4) (e3)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e3) (e4)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> ((op (op (e1) (e4)) (e4)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.16 do 0 intro. intros zenon_H19a zenon_H168 zenon_H18e zenon_Hc3 zenon_Hd9 zenon_H92 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He8 zenon_Hd3 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H83 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H7b zenon_H42 zenon_H1c2 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H240 zenon_H241 zenon_Ha1 zenon_H2d zenon_Hc2 zenon_H146. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.16 apply (zenon_L263_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.16 apply (zenon_L300_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.16 apply (zenon_L266_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.16 apply (zenon_L397_); trivial. % 40.94/41.16 exact (zenon_H146 zenon_H144). % 40.94/41.16 (* end of lemma zenon_L398_ *) % 40.94/41.16 assert (zenon_L399_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (op (e1) (e4)) (e4)) = (e1)) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e0))) -> False). % 40.94/41.16 do 0 intro. intros zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H116 zenon_H1c9 zenon_H9f zenon_Hb9 zenon_H49 zenon_Hbb zenon_Hba zenon_He0 zenon_Hb zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hee zenon_H87 zenon_H81 zenon_H89 zenon_H57 zenon_H6e zenon_H77 zenon_H73 zenon_H88 zenon_He1 zenon_H1c4 zenon_H165 zenon_H1a9 zenon_H146 zenon_Hc2 zenon_H2d zenon_Ha1 zenon_H241 zenon_H240 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H42 zenon_H7b zenon_H20 zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_Hd9 zenon_Hc3 zenon_H18e zenon_H168 zenon_H19a zenon_H13e. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.16 apply (zenon_L272_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.16 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.16 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.16 apply (zenon_L273_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.16 apply (zenon_L274_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.16 apply (zenon_L12_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.16 apply (zenon_L396_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.16 apply (zenon_L41_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.16 exact (zenon_He1 zenon_He5). % 40.94/41.16 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H166 | zenon_intro zenon_H1c5 ]. % 40.94/41.16 apply (zenon_L243_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1c6 ]. % 40.94/41.16 apply (zenon_L275_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1c7 ]. % 40.94/41.16 apply (zenon_L276_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H142 ]. % 40.94/41.16 apply (zenon_L398_); trivial. % 40.94/41.16 exact (zenon_H13e zenon_H142). % 40.94/41.16 (* end of lemma zenon_L399_ *) % 40.94/41.16 assert (zenon_L400_ : (~((op (e0) (e2)) = (op (e2) (e0)))) -> ((op (unit) (e2)) = (e2)) -> ((unit) = (e0)) -> ((op (e2) (e0)) = (e2)) -> False). % 40.94/41.16 do 0 intro. intros zenon_H245 zenon_Hc zenon_H9 zenon_Hba. % 40.94/41.16 cut (((op (unit) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e2) (e0)))). % 40.94/41.16 intro zenon_D_pnotp. % 40.94/41.16 apply zenon_H245. % 40.94/41.16 rewrite <- zenon_D_pnotp. % 40.94/41.16 exact zenon_Hc. % 40.94/41.16 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 40.94/41.16 cut (((op (unit) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 40.94/41.16 congruence. % 40.94/41.16 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H10 | zenon_intro zenon_H11 ]. % 40.94/41.16 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (unit) (e2)) = (op (e0) (e2)))). % 40.94/41.16 intro zenon_D_pnotp. % 40.94/41.16 apply zenon_Hf. % 40.94/41.16 rewrite <- zenon_D_pnotp. % 40.94/41.16 exact zenon_H10. % 40.94/41.16 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 40.94/41.16 cut (((op (e0) (e2)) = (op (unit) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H8]. % 40.94/41.16 congruence. % 40.94/41.16 apply (zenon_L2_); trivial. % 40.94/41.16 apply zenon_H11. apply refl_equal. % 40.94/41.16 apply zenon_H11. apply refl_equal. % 40.94/41.16 apply zenon_Hbd. apply sym_equal. exact zenon_Hba. % 40.94/41.16 (* end of lemma zenon_L400_ *) % 40.94/41.16 assert (zenon_L401_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e0)))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.94/41.16 do 0 intro. intros zenon_H3b zenon_Hba zenon_H245 zenon_H4a zenon_Hc zenon_H49 zenon_Hc8 zenon_H9a zenon_H99 zenon_H197 zenon_H16 zenon_H81 zenon_H20 zenon_H1bf zenon_Hb1. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.16 apply (zenon_L400_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.16 apply (zenon_L17_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.16 apply (zenon_L84_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.16 apply (zenon_L270_); trivial. % 40.94/41.16 apply (zenon_L290_); trivial. % 40.94/41.16 (* end of lemma zenon_L401_ *) % 40.94/41.16 assert (zenon_L402_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.16 do 0 intro. intros zenon_H3b zenon_Hba zenon_H245 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_H9a zenon_H99 zenon_H197 zenon_H16 zenon_H81 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.16 apply (zenon_L400_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.16 apply (zenon_L287_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.16 apply (zenon_L84_); trivial. % 40.94/41.16 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.16 apply (zenon_L270_); trivial. % 40.94/41.16 apply (zenon_L44_); trivial. % 40.94/41.16 (* end of lemma zenon_L402_ *) % 40.94/41.16 assert (zenon_L403_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((e3) = (op (e2) (e4))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H19a zenon_H17 zenon_H2d zenon_H1f zenon_H168 zenon_H20 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_H22 zenon_H92 zenon_Hc zenon_H91 zenon_H81 zenon_H16 zenon_H99 zenon_H9a zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H245 zenon_Hba zenon_H3b zenon_H146. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.17 apply (zenon_L263_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.17 apply (zenon_L300_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.17 apply (zenon_L266_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.17 apply (zenon_L402_); trivial. % 40.94/41.17 exact (zenon_H146 zenon_H144). % 40.94/41.17 (* end of lemma zenon_L403_ *) % 40.94/41.17 assert (zenon_L404_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (e3) (e4)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.17 do 0 intro. intros zenon_He0 zenon_Hb zenon_H1bf zenon_H197 zenon_H49 zenon_H88 zenon_H7b zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H32 zenon_H34 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hd9 zenon_Hee zenon_He1 zenon_H19a zenon_H17 zenon_H2d zenon_H1f zenon_H168 zenon_H20 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_H22 zenon_Hc zenon_H91 zenon_H81 zenon_H16 zenon_H99 zenon_H9a zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H245 zenon_Hba zenon_H3b zenon_H146. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.17 apply (zenon_L12_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.17 apply (zenon_L401_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.17 apply (zenon_L112_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.17 exact (zenon_He1 zenon_He5). % 40.94/41.17 apply (zenon_L403_); trivial. % 40.94/41.17 (* end of lemma zenon_L404_ *) % 40.94/41.17 assert (zenon_L405_ : (~((op (e4) (e4)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> ((e1) = (op (e4) (e2))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e3) (e4)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H146 zenon_Hba zenon_H245 zenon_H15f zenon_H42 zenon_H18e zenon_H2c zenon_H112 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H168 zenon_H2d zenon_H19a zenon_He1 zenon_Hee zenon_Hd9 zenon_Hd4 zenon_He9 zenon_He6 zenon_Hed zenon_H34 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H7b zenon_H88 zenon_H49 zenon_Hb zenon_He0 zenon_He8 zenon_Hd3 zenon_H17 zenon_H18 zenon_H9b zenon_H92 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H81 zenon_H16 zenon_H197 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.94/41.17 apply (zenon_L404_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.94/41.17 apply (zenon_L304_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.94/41.17 apply (zenon_L73_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.94/41.17 apply (zenon_L305_); trivial. % 40.94/41.17 exact (zenon_Hda zenon_Hde). % 40.94/41.17 (* end of lemma zenon_L405_ *) % 40.94/41.17 assert (zenon_L406_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e4) (e4)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> ((e1) = (op (e4) (e2))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H1c9 zenon_Hb9 zenon_H9f zenon_H13e zenon_Hbb zenon_Hc3 zenon_H1b9 zenon_H115 zenon_H11f zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hb6 zenon_H116 zenon_Ha1 zenon_Hc2 zenon_H1a9 zenon_H165 zenon_H1c4 zenon_H89 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H16 zenon_H81 zenon_H20 zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H9b zenon_H18 zenon_H17 zenon_Hd3 zenon_He8 zenon_He0 zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H34 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hd9 zenon_Hee zenon_He1 zenon_H19a zenon_H2d zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_H42 zenon_H15f zenon_H245 zenon_Hba zenon_H146. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.17 apply (zenon_L272_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.17 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.17 apply (zenon_L273_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.17 apply (zenon_L274_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.17 apply (zenon_L12_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.17 apply (zenon_L298_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.17 apply (zenon_L41_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.17 exact (zenon_He1 zenon_He5). % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.17 apply (zenon_L263_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.17 apply (zenon_L300_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.17 apply (zenon_L266_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.17 apply (zenon_L405_); trivial. % 40.94/41.17 exact (zenon_H146 zenon_H144). % 40.94/41.17 (* end of lemma zenon_L406_ *) % 40.94/41.17 assert (zenon_L407_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((unit) = (e0)) -> ((op (e2) (e1)) = (e1)) -> False). % 40.94/41.17 do 0 intro. intros zenon_H246 zenon_H16 zenon_H9 zenon_H247. % 40.94/41.17 cut (((op (unit) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H246. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H16. % 40.94/41.17 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H248]. % 40.94/41.17 cut (((op (unit) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 40.94/41.17 congruence. % 40.94/41.17 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 40.94/41.17 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (unit) (e1)) = (op (e0) (e1)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H177. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H138. % 40.94/41.17 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 40.94/41.17 cut (((op (e0) (e1)) = (op (unit) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H174]. % 40.94/41.17 congruence. % 40.94/41.17 apply (zenon_L252_); trivial. % 40.94/41.17 apply zenon_H139. apply refl_equal. % 40.94/41.17 apply zenon_H139. apply refl_equal. % 40.94/41.17 apply zenon_H248. apply sym_equal. exact zenon_H247. % 40.94/41.17 (* end of lemma zenon_L407_ *) % 40.94/41.17 assert (zenon_L408_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H3b zenon_Hbb zenon_Hba zenon_H22 zenon_H20 zenon_H1f zenon_H6e zenon_Hf2 zenon_H58 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.17 apply (zenon_L119_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.17 apply (zenon_L65_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.17 apply (zenon_L8_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.17 apply (zenon_L120_); trivial. % 40.94/41.17 apply (zenon_L11_); trivial. % 40.94/41.17 (* end of lemma zenon_L408_ *) % 40.94/41.17 assert (zenon_L409_ : ((e1) = (op (e4) (e2))) -> ((op (e2) (e1)) = (e4)) -> (~((op (op (e2) (e1)) (e2)) = (e1))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H34 zenon_H249 zenon_H24a. % 40.94/41.17 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12 ]. % 40.94/41.17 cut (((e1) = (e1)) = ((op (op (e2) (e1)) (e2)) = (e1))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H24a. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H12a. % 40.94/41.17 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 40.94/41.17 cut (((e1) = (op (op (e2) (e1)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H24b]. % 40.94/41.17 congruence. % 40.94/41.17 cut (((e1) = (op (e4) (e2))) = ((e1) = (op (op (e2) (e1)) (e2)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H24b. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H34. % 40.94/41.17 cut (((op (e4) (e2)) = (op (op (e2) (e1)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H24c]. % 40.94/41.17 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 40.94/41.17 congruence. % 40.94/41.17 apply zenon_H12. apply refl_equal. % 40.94/41.17 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 40.94/41.17 cut (((e4) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H24d]. % 40.94/41.17 congruence. % 40.94/41.17 apply zenon_H24d. apply sym_equal. exact zenon_H249. % 40.94/41.17 apply zenon_H7. apply refl_equal. % 40.94/41.17 apply zenon_H12. apply refl_equal. % 40.94/41.17 apply zenon_H12. apply refl_equal. % 40.94/41.17 (* end of lemma zenon_L409_ *) % 40.94/41.17 assert (zenon_L410_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((unit) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (op (e2) (e1)) (e2)) = (e1))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H24e zenon_H14d zenon_H11f zenon_H9 zenon_H246 zenon_H16 zenon_H32 zenon_H58 zenon_H6e zenon_H1f zenon_H20 zenon_Hba zenon_Hbb zenon_H3b zenon_H22 zenon_Hb9 zenon_H34 zenon_H24a. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H14c | zenon_intro zenon_H24f ]. % 40.94/41.17 apply (zenon_L216_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H247 | zenon_intro zenon_H250 ]. % 40.94/41.17 apply (zenon_L407_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H251 ]. % 40.94/41.17 apply (zenon_L408_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H19e | zenon_intro zenon_H249 ]. % 40.94/41.17 apply (zenon_L273_); trivial. % 40.94/41.17 apply (zenon_L409_); trivial. % 40.94/41.17 (* end of lemma zenon_L410_ *) % 40.94/41.17 assert (zenon_L411_ : (~((op (op (e2) (e1)) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H24a zenon_Hb9 zenon_H3b zenon_Hbb zenon_Hba zenon_H6e zenon_H58 zenon_H246 zenon_H11f zenon_H14d zenon_H24e zenon_H4a zenon_Hc zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_H197 zenon_H81 zenon_H32 zenon_H16 zenon_H34. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.17 apply (zenon_L410_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.17 apply (zenon_L17_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.17 apply (zenon_L8_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.17 apply (zenon_L270_); trivial. % 40.94/41.17 apply (zenon_L11_); trivial. % 40.94/41.17 (* end of lemma zenon_L411_ *) % 40.94/41.17 assert (zenon_L412_ : (~((op (op (e2) (e1)) (e2)) = (e1))) -> ((e1) = (op (e4) (e2))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.17 do 0 intro. intros zenon_H24a zenon_H34 zenon_Hb9 zenon_H3b zenon_Hbb zenon_Hba zenon_H6e zenon_H58 zenon_H32 zenon_H246 zenon_H11f zenon_H14d zenon_H24e zenon_Hab zenon_Haa zenon_H22 zenon_H20 zenon_H1f zenon_H197 zenon_H16 zenon_H81 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.17 apply (zenon_L410_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.17 apply (zenon_L56_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.17 apply (zenon_L8_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.17 apply (zenon_L270_); trivial. % 40.94/41.17 apply (zenon_L44_); trivial. % 40.94/41.17 (* end of lemma zenon_L412_ *) % 40.94/41.17 assert (zenon_L413_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (op (e2) (e1)) (e2)) = (e1))) -> ((e1) = (op (e4) (e2))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.17 do 0 intro. intros zenon_He0 zenon_H2c zenon_H17 zenon_H2d zenon_H18 zenon_Hb zenon_H49 zenon_H57 zenon_He1 zenon_H24a zenon_H34 zenon_Hb9 zenon_H3b zenon_Hbb zenon_Hba zenon_H6e zenon_H58 zenon_H32 zenon_H246 zenon_H11f zenon_H14d zenon_H24e zenon_Hab zenon_Haa zenon_H22 zenon_H20 zenon_H1f zenon_H197 zenon_H16 zenon_H81 zenon_H91 zenon_Hc. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.17 apply (zenon_L12_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.17 apply (zenon_L411_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.17 apply (zenon_L286_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.17 exact (zenon_He1 zenon_He5). % 40.94/41.17 apply (zenon_L412_); trivial. % 40.94/41.17 (* end of lemma zenon_L413_ *) % 40.94/41.17 assert (zenon_L414_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (op (e2) (e1)) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e4) (e3)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.17 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_H81 zenon_H197 zenon_Haa zenon_H24e zenon_H14d zenon_H246 zenon_H6e zenon_Hba zenon_Hbb zenon_Hb9 zenon_H24a zenon_He1 zenon_H57 zenon_H49 zenon_Hb zenon_H2d zenon_He0 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H1c2 zenon_H42 zenon_H7b zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H92 zenon_Hd9 zenon_Hc3. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.17 apply (zenon_L53_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.17 apply (zenon_L413_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.17 apply (zenon_L279_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.17 apply (zenon_L294_); trivial. % 40.94/41.17 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.17 (* end of lemma zenon_L414_ *) % 40.94/41.17 assert (zenon_L415_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e4) (e3)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e3) (e4)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (op (e2) (e1)) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H19a zenon_H168 zenon_H18e zenon_Hc3 zenon_Hd9 zenon_H92 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He8 zenon_Hd3 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H83 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H7b zenon_H42 zenon_H1c2 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_He0 zenon_H2d zenon_Hb zenon_H49 zenon_H57 zenon_He1 zenon_H24a zenon_Hb9 zenon_Hbb zenon_Hba zenon_H6e zenon_H246 zenon_H14d zenon_H24e zenon_Haa zenon_H81 zenon_Ha1 zenon_Hc2 zenon_H146. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.17 apply (zenon_L263_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.17 apply (zenon_L300_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.17 apply (zenon_L266_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.17 apply (zenon_L414_); trivial. % 40.94/41.17 exact (zenon_H146 zenon_H144). % 40.94/41.17 (* end of lemma zenon_L415_ *) % 40.94/41.17 assert (zenon_L416_ : (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (op (e2) (e1)) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e0))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H116 zenon_H9f zenon_H1c9 zenon_H50 zenon_H16d zenon_H41 zenon_H51 zenon_H1c8 zenon_H88 zenon_H87 zenon_H77 zenon_H73 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hee zenon_H1c4 zenon_H165 zenon_H1a9 zenon_H146 zenon_Hc2 zenon_Ha1 zenon_H81 zenon_Haa zenon_H24e zenon_H14d zenon_H246 zenon_H6e zenon_Hba zenon_Hbb zenon_Hb9 zenon_H24a zenon_He1 zenon_H57 zenon_H49 zenon_Hb zenon_H2d zenon_He0 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H42 zenon_H7b zenon_H20 zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_Hd9 zenon_Hc3 zenon_H18e zenon_H168 zenon_H19a zenon_H13e. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.17 apply (zenon_L272_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.17 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.17 apply (zenon_L273_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.17 apply (zenon_L274_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.17 apply (zenon_L12_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.17 apply (zenon_L299_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.17 apply (zenon_L112_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.17 exact (zenon_He1 zenon_He5). % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H166 | zenon_intro zenon_H1c5 ]. % 40.94/41.17 apply (zenon_L243_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1c6 ]. % 40.94/41.17 apply (zenon_L275_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1c7 ]. % 40.94/41.17 apply (zenon_L276_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H142 ]. % 40.94/41.17 apply (zenon_L415_); trivial. % 40.94/41.17 exact (zenon_H13e zenon_H142). % 40.94/41.17 (* end of lemma zenon_L416_ *) % 40.94/41.17 assert (zenon_L417_ : ((~((op (e2) (e2)) = (op (e2) (e2))))/\(((op (op (e2) (e2)) (e2)) = (e2))/\(~((op (op (e2) (e2)) (e2)) = (e2))))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H252. % 40.94/41.17 apply (zenon_and_s _ _ zenon_H252). zenon_intro zenon_H254. zenon_intro zenon_H253. % 40.94/41.17 apply zenon_H254. apply refl_equal. % 40.94/41.17 (* end of lemma zenon_L417_ *) % 40.94/41.17 assert (zenon_L418_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.17 do 0 intro. intros zenon_He0 zenon_Hb zenon_H49 zenon_H34 zenon_H32 zenon_H87 zenon_H83 zenon_H5f zenon_H81 zenon_H7b zenon_H89 zenon_H57 zenon_H58 zenon_H6e zenon_H77 zenon_H73 zenon_H61 zenon_H68 zenon_H88 zenon_He1 zenon_H3b zenon_H178 zenon_H51 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.17 apply (zenon_L12_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.17 apply (zenon_L258_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.17 apply (zenon_L41_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.17 exact (zenon_He1 zenon_He5). % 40.94/41.17 apply (zenon_L259_); trivial. % 40.94/41.17 (* end of lemma zenon_L418_ *) % 40.94/41.17 assert (zenon_L419_ : (~((op (e1) (e3)) = (op (op (e2) (e3)) (e3)))) -> ((op (e2) (e3)) = (e1)) -> False). % 40.94/41.17 do 0 intro. intros zenon_H255 zenon_H22c. % 40.94/41.17 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 40.94/41.17 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H22f]. % 40.94/41.17 congruence. % 40.94/41.17 apply zenon_H22f. apply sym_equal. exact zenon_H22c. % 40.94/41.17 apply zenon_H1e. apply refl_equal. % 40.94/41.17 (* end of lemma zenon_L419_ *) % 40.94/41.17 assert (zenon_L420_ : (~((op (e1) (e3)) = (op (e4) (e3)))) -> ((op (op (e2) (e3)) (e3)) = (e2)) -> ((op (e2) (e3)) = (e1)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.17 do 0 intro. intros zenon_H256 zenon_H257 zenon_H22c zenon_H92. % 40.94/41.17 cut (((op (op (e2) (e3)) (e3)) = (e2)) = ((op (e1) (e3)) = (op (e4) (e3)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H256. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H257. % 40.94/41.17 cut (((e2) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H93]. % 40.94/41.17 cut (((op (op (e2) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H258]. % 40.94/41.17 congruence. % 40.94/41.17 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 40.94/41.17 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (op (e2) (e3)) (e3)) = (op (e1) (e3)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H258. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H2e. % 40.94/41.17 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 40.94/41.17 cut (((op (e1) (e3)) = (op (op (e2) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H255]. % 40.94/41.17 congruence. % 40.94/41.17 apply (zenon_L419_); trivial. % 40.94/41.17 apply zenon_H2f. apply refl_equal. % 40.94/41.17 apply zenon_H2f. apply refl_equal. % 40.94/41.17 apply zenon_H93. apply sym_equal. exact zenon_H92. % 40.94/41.17 (* end of lemma zenon_L420_ *) % 40.94/41.17 assert (zenon_L421_ : (~((op (e4) (e4)) = (e0))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e4) (e3)))) -> ((op (op (e2) (e3)) (e3)) = (e2)) -> ((op (e2) (e3)) = (e1)) -> False). % 40.94/41.17 do 0 intro. intros zenon_H13e zenon_H19a zenon_H168 zenon_Hbb zenon_H18e zenon_Hc3 zenon_He0 zenon_H2d zenon_Hb zenon_H49 zenon_H15f zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_H17 zenon_H18 zenon_Hc zenon_H42 zenon_Hda zenon_Hb6 zenon_H8e zenon_H60 zenon_H116 zenon_Ha1 zenon_Hc2 zenon_H146 zenon_H1a9 zenon_H165 zenon_H1c4 zenon_H9f zenon_Hb9 zenon_H1c9 zenon_H50 zenon_H16d zenon_H41 zenon_H51 zenon_H1c8 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H1f zenon_H20 zenon_H22 zenon_H68 zenon_H32 zenon_H16 zenon_H34 zenon_H3b zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_H91 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H256 zenon_H257 zenon_H22c. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.17 apply (zenon_L12_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.17 apply (zenon_L299_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.17 apply (zenon_L112_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.17 exact (zenon_He1 zenon_He5). % 40.94/41.17 apply (zenon_L420_); trivial. % 40.94/41.17 (* end of lemma zenon_L421_ *) % 40.94/41.17 assert (zenon_L422_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (op (e2) (e3)) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e4) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> ((op (unit) (e0)) = (e0)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H236 zenon_H89 zenon_H257 zenon_H256 zenon_He1 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H3b zenon_H16 zenon_H32 zenon_H68 zenon_H22 zenon_H20 zenon_H1f zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H1c9 zenon_Hb9 zenon_H9f zenon_H1c4 zenon_H165 zenon_H1a9 zenon_H146 zenon_Hc2 zenon_Ha1 zenon_H116 zenon_H60 zenon_H8e zenon_Hb6 zenon_Hda zenon_H42 zenon_Hc zenon_H18 zenon_H17 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H15f zenon_H49 zenon_Hb zenon_H2d zenon_He0 zenon_Hc3 zenon_H18e zenon_Hbb zenon_H168 zenon_H19a zenon_H13e zenon_H237 zenon_H34 zenon_H91. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H178 | zenon_intro zenon_H238 ]. % 40.94/41.17 apply (zenon_L418_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H10f | zenon_intro zenon_H239 ]. % 40.94/41.17 apply (zenon_L157_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H22c | zenon_intro zenon_H23a ]. % 40.94/41.17 apply (zenon_L421_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H23b | zenon_intro zenon_H233 ]. % 40.94/41.17 exact (zenon_H237 zenon_H23b). % 40.94/41.17 apply (zenon_L385_); trivial. % 40.94/41.17 (* end of lemma zenon_L422_ *) % 40.94/41.17 assert (zenon_L423_ : ((op (op (e2) (e4)) (e4)) = (e2)) -> ((e3) = (op (e2) (e4))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H259 zenon_H22 zenon_Hab zenon_H1ad. % 40.94/41.17 elim (classic ((op (e3) (e4)) = (op (e3) (e4)))); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H1e1 ]. % 40.94/41.17 cut (((op (e3) (e4)) = (op (e3) (e4))) = ((op (e1) (e4)) = (op (e3) (e4)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H1ad. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H1e0. % 40.94/41.17 cut (((op (e3) (e4)) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 40.94/41.17 cut (((op (e3) (e4)) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H25a]. % 40.94/41.17 congruence. % 40.94/41.17 cut (((op (op (e2) (e4)) (e4)) = (e2)) = ((op (e3) (e4)) = (op (e1) (e4)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H25a. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H259. % 40.94/41.17 cut (((e2) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 40.94/41.17 cut (((op (op (e2) (e4)) (e4)) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H25b]. % 40.94/41.17 congruence. % 40.94/41.17 elim (classic ((op (e3) (e4)) = (op (e3) (e4)))); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H1e1 ]. % 40.94/41.17 cut (((op (e3) (e4)) = (op (e3) (e4))) = ((op (op (e2) (e4)) (e4)) = (op (e3) (e4)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H25b. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H1e0. % 40.94/41.17 cut (((op (e3) (e4)) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 40.94/41.17 cut (((op (e3) (e4)) = (op (op (e2) (e4)) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H25c]. % 40.94/41.17 congruence. % 40.94/41.17 cut (((e4) = (e4))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 40.94/41.17 cut (((e3) = (op (e2) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 40.94/41.17 congruence. % 40.94/41.17 exact (zenon_H23 zenon_H22). % 40.94/41.17 apply zenon_H97. apply refl_equal. % 40.94/41.17 apply zenon_H1e1. apply refl_equal. % 40.94/41.17 apply zenon_H1e1. apply refl_equal. % 40.94/41.17 apply zenon_Hac. apply sym_equal. exact zenon_Hab. % 40.94/41.17 apply zenon_H1e1. apply refl_equal. % 40.94/41.17 apply zenon_H1e1. apply refl_equal. % 40.94/41.17 (* end of lemma zenon_L423_ *) % 40.94/41.17 assert (zenon_L424_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (op (e2) (e4)) (e4)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.17 do 0 intro. intros zenon_Hc2 zenon_H17 zenon_H2d zenon_H18 zenon_Ha1 zenon_H259 zenon_H58 zenon_Hb9 zenon_Hb6 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.17 apply (zenon_L277_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.17 apply (zenon_L423_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.17 apply (zenon_L123_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.17 apply (zenon_L285_); trivial. % 40.94/41.17 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.17 (* end of lemma zenon_L424_ *) % 40.94/41.17 assert (zenon_L425_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (op (e2) (e4)) (e4)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e4) (e3)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.17 do 0 intro. intros zenon_Hc2 zenon_H2d zenon_Ha1 zenon_H259 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H1c2 zenon_H42 zenon_H7b zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H92 zenon_Hd9 zenon_Hc3. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.17 apply (zenon_L53_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.17 apply (zenon_L423_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.17 apply (zenon_L279_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.17 apply (zenon_L294_); trivial. % 40.94/41.17 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.17 (* end of lemma zenon_L425_ *) % 40.94/41.17 assert (zenon_L426_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (op (e2) (e4)) (e4)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e0))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H1c8 zenon_H146 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H18e zenon_H116 zenon_H168 zenon_H19a zenon_H1c9 zenon_H9f zenon_He0 zenon_Hb zenon_H49 zenon_Hb9 zenon_H88 zenon_H81 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hee zenon_He1 zenon_H1c4 zenon_H165 zenon_H1a9 zenon_Hc3 zenon_Hd9 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He8 zenon_Hd3 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H83 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H20 zenon_H7b zenon_H42 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H259 zenon_Ha1 zenon_H2d zenon_Hc2 zenon_H13e. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.17 apply (zenon_L272_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.17 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.17 apply (zenon_L273_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.17 apply (zenon_L274_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.17 apply (zenon_L12_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.17 apply (zenon_L424_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.17 apply (zenon_L112_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.17 exact (zenon_He1 zenon_He5). % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H166 | zenon_intro zenon_H1c5 ]. % 40.94/41.17 apply (zenon_L243_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1c6 ]. % 40.94/41.17 apply (zenon_L275_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1c7 ]. % 40.94/41.17 apply (zenon_L276_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H142 ]. % 40.94/41.17 apply (zenon_L425_); trivial. % 40.94/41.17 exact (zenon_H13e zenon_H142). % 40.94/41.17 (* end of lemma zenon_L426_ *) % 40.94/41.17 assert (zenon_L427_ : (~((op (e0) (e3)) = (op (e3) (e0)))) -> ((op (unit) (e3)) = (e3)) -> ((unit) = (e0)) -> ((op (e3) (e0)) = (e3)) -> False). % 40.94/41.17 do 0 intro. intros zenon_H25d zenon_H20 zenon_H9 zenon_H60. % 40.94/41.17 cut (((op (unit) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e3) (e0)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H25d. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H20. % 40.94/41.17 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 40.94/41.17 cut (((op (unit) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 40.94/41.17 congruence. % 40.94/41.17 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 40.94/41.17 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (unit) (e3)) = (op (e0) (e3)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H195. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H52. % 40.94/41.17 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 40.94/41.17 cut (((op (e0) (e3)) = (op (unit) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 40.94/41.17 congruence. % 40.94/41.17 apply (zenon_L267_); trivial. % 40.94/41.17 apply zenon_H53. apply refl_equal. % 40.94/41.17 apply zenon_H53. apply refl_equal. % 40.94/41.17 apply zenon_H65. apply sym_equal. exact zenon_H60. % 40.94/41.17 (* end of lemma zenon_L427_ *) % 40.94/41.17 assert (zenon_L428_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e0)))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.17 do 0 intro. intros zenon_H3b zenon_H60 zenon_H25d zenon_Hab zenon_Haa zenon_H22 zenon_H20 zenon_H1f zenon_H197 zenon_H16 zenon_H81 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.17 apply (zenon_L427_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.17 apply (zenon_L56_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.17 apply (zenon_L8_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.17 apply (zenon_L270_); trivial. % 40.94/41.17 apply (zenon_L44_); trivial. % 40.94/41.17 (* end of lemma zenon_L428_ *) % 40.94/41.17 assert (zenon_L429_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H19a zenon_H17 zenon_H2d zenon_H18 zenon_H168 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_H92 zenon_Hc zenon_H91 zenon_H81 zenon_H16 zenon_H1f zenon_H20 zenon_H22 zenon_Haa zenon_Hab zenon_H25d zenon_H60 zenon_H3b zenon_H146. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.17 apply (zenon_L263_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.17 apply (zenon_L300_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.17 apply (zenon_L266_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.17 apply (zenon_L428_); trivial. % 40.94/41.17 exact (zenon_H146 zenon_H144). % 40.94/41.17 (* end of lemma zenon_L429_ *) % 40.94/41.17 assert (zenon_L430_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.17 do 0 intro. intros zenon_He0 zenon_Hb zenon_H116 zenon_H34 zenon_H32 zenon_H197 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_H19a zenon_H17 zenon_H2d zenon_H18 zenon_H168 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_Hc zenon_H91 zenon_H81 zenon_H16 zenon_H1f zenon_H20 zenon_H22 zenon_Haa zenon_Hab zenon_H25d zenon_H60 zenon_H3b zenon_H146. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.17 apply (zenon_L12_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.17 apply (zenon_L278_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.17 apply (zenon_L286_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.17 exact (zenon_He1 zenon_He5). % 40.94/41.17 apply (zenon_L429_); trivial. % 40.94/41.17 (* end of lemma zenon_L430_ *) % 40.94/41.17 assert (zenon_L431_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.17 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_H146 zenon_H25d zenon_Haa zenon_H81 zenon_H91 zenon_H18e zenon_H168 zenon_H18 zenon_H2d zenon_H17 zenon_H19a zenon_He1 zenon_H57 zenon_H6e zenon_H197 zenon_H116 zenon_Hb zenon_He0 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.17 apply (zenon_L277_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.17 apply (zenon_L430_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.17 apply (zenon_L279_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.17 apply (zenon_L285_); trivial. % 40.94/41.17 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.17 (* end of lemma zenon_L431_ *) % 40.94/41.17 assert (zenon_L432_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((e1) = (e3))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e3)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.17 do 0 intro. intros zenon_Hee zenon_Hd9 zenon_Hd4 zenon_He9 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H73 zenon_H77 zenon_H87 zenon_H7b zenon_H88 zenon_Hba zenon_Hbb zenon_Hc3 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H4a zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_Hc zenon_H83 zenon_H32 zenon_H16 zenon_H34 zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_He0 zenon_Hb zenon_H116 zenon_H6e zenon_H57 zenon_He1 zenon_H19a zenon_H17 zenon_H2d zenon_H18 zenon_H168 zenon_H18e zenon_H91 zenon_H81 zenon_Haa zenon_H25d zenon_Ha1 zenon_Hc2 zenon_H146. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.17 apply (zenon_L264_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.17 apply (zenon_L178_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.17 apply (zenon_L266_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.17 apply (zenon_L431_); trivial. % 40.94/41.17 exact (zenon_H146 zenon_H144). % 40.94/41.17 (* end of lemma zenon_L432_ *) % 40.94/41.17 assert (zenon_L433_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (e4) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e3)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.17 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_H92 zenon_Haa zenon_H25d zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H1c2 zenon_H42 zenon_H7b zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_Hd9 zenon_He1 zenon_H57 zenon_H58 zenon_H6e zenon_H197 zenon_H81 zenon_H49 zenon_Hb zenon_H2d zenon_He0 zenon_Hc3. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.17 apply (zenon_L53_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.17 apply (zenon_L428_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.17 apply (zenon_L279_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.17 apply (zenon_L295_); trivial. % 40.94/41.17 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.17 (* end of lemma zenon_L433_ *) % 40.94/41.17 assert (zenon_L434_ : (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (e4) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e3)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e0))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H1c4 zenon_H165 zenon_H1a9 zenon_H146 zenon_Hc2 zenon_Ha1 zenon_H92 zenon_Haa zenon_H25d zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H42 zenon_H7b zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_Hd9 zenon_He1 zenon_H57 zenon_H58 zenon_H6e zenon_H81 zenon_H49 zenon_Hb zenon_H2d zenon_He0 zenon_Hc3 zenon_H18e zenon_H168 zenon_H19a zenon_H13e. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H166 | zenon_intro zenon_H1c5 ]. % 40.94/41.17 apply (zenon_L243_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1c6 ]. % 40.94/41.17 apply (zenon_L275_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1c7 ]. % 40.94/41.17 apply (zenon_L276_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H142 ]. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.17 apply (zenon_L263_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.17 apply (zenon_L300_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.17 apply (zenon_L266_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.17 apply (zenon_L433_); trivial. % 40.94/41.17 exact (zenon_H146 zenon_H144). % 40.94/41.17 exact (zenon_H13e zenon_H142). % 40.94/41.17 (* end of lemma zenon_L434_ *) % 40.94/41.17 assert (zenon_L435_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e3)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e0))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H1c9 zenon_Hb9 zenon_H9f zenon_H116 zenon_Hbb zenon_H88 zenon_H87 zenon_H77 zenon_H73 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hee zenon_H1c4 zenon_H165 zenon_H1a9 zenon_H146 zenon_Hc2 zenon_Ha1 zenon_Haa zenon_H25d zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H42 zenon_H7b zenon_H20 zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_Hd9 zenon_He1 zenon_H57 zenon_H58 zenon_H6e zenon_H81 zenon_H49 zenon_Hb zenon_H2d zenon_He0 zenon_Hc3 zenon_H18e zenon_H168 zenon_H19a zenon_H13e. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.17 apply (zenon_L272_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.17 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.17 apply (zenon_L273_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.17 apply (zenon_L274_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.17 apply (zenon_L12_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.17 apply (zenon_L432_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.17 apply (zenon_L112_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.17 exact (zenon_He1 zenon_He5). % 40.94/41.17 apply (zenon_L434_); trivial. % 40.94/41.17 (* end of lemma zenon_L435_ *) % 40.94/41.17 assert (zenon_L436_ : ((op (unit) (e2)) = (e2)) -> ((unit) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 40.94/41.17 do 0 intro. intros zenon_Hc zenon_H2a zenon_H25e zenon_H8e. % 40.94/41.17 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 40.94/41.17 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e0)) = (op (e3) (e2)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H8e. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H85. % 40.94/41.17 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 40.94/41.17 cut (((op (e3) (e2)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 40.94/41.17 congruence. % 40.94/41.17 cut (((op (unit) (e2)) = (e2)) = ((op (e3) (e2)) = (op (e3) (e0)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H8f. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_Hc. % 40.94/41.17 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H25f]. % 40.94/41.17 cut (((op (unit) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 40.94/41.17 congruence. % 40.94/41.17 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 40.94/41.17 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (unit) (e2)) = (op (e3) (e2)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_Hc1. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H85. % 40.94/41.17 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 40.94/41.17 cut (((op (e3) (e2)) = (op (unit) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 40.94/41.17 congruence. % 40.94/41.17 apply (zenon_L66_); trivial. % 40.94/41.17 apply zenon_H86. apply refl_equal. % 40.94/41.17 apply zenon_H86. apply refl_equal. % 40.94/41.17 apply zenon_H25f. apply sym_equal. exact zenon_H25e. % 40.94/41.17 apply zenon_H86. apply refl_equal. % 40.94/41.17 apply zenon_H86. apply refl_equal. % 40.94/41.17 (* end of lemma zenon_L436_ *) % 40.94/41.17 assert (zenon_L437_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H3b zenon_H58 zenon_H260 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_H9a zenon_H99 zenon_H8e zenon_H25e zenon_Hc zenon_H20 zenon_H1bf zenon_Hb1. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.17 cut (((op (e2) (unit)) = (e2)) = ((op (e2) (e0)) = (op (e3) (e0)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H260. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H58. % 40.94/41.17 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H25f]. % 40.94/41.17 cut (((op (e2) (unit)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 40.94/41.17 congruence. % 40.94/41.17 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 40.94/41.17 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e2) (unit)) = (op (e2) (e0)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H5b. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H5c. % 40.94/41.17 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 40.94/41.17 cut (((op (e2) (e0)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 40.94/41.17 congruence. % 40.94/41.17 apply (zenon_L21_); trivial. % 40.94/41.17 apply zenon_H5d. apply refl_equal. % 40.94/41.17 apply zenon_H5d. apply refl_equal. % 40.94/41.17 apply zenon_H25f. apply sym_equal. exact zenon_H25e. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.17 apply (zenon_L287_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.17 apply (zenon_L84_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.17 apply (zenon_L436_); trivial. % 40.94/41.17 apply (zenon_L290_); trivial. % 40.94/41.17 (* end of lemma zenon_L437_ *) % 40.94/41.17 assert (zenon_L438_ : (~((op (e2) (e1)) = (op (e4) (e1)))) -> ((op (op (e3) (e1)) (e1)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> ((op (e4) (e1)) = (e3)) -> False). % 40.94/41.17 do 0 intro. intros zenon_H261 zenon_H262 zenon_H263 zenon_H1bf. % 40.94/41.17 cut (((op (op (e3) (e1)) (e1)) = (e3)) = ((op (e2) (e1)) = (op (e4) (e1)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H261. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H262. % 40.94/41.17 cut (((e3) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 40.94/41.17 cut (((op (op (e3) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 40.94/41.17 congruence. % 40.94/41.17 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H70 | zenon_intro zenon_H71 ]. % 40.94/41.17 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (op (e3) (e1)) (e1)) = (op (e2) (e1)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H264. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H70. % 40.94/41.17 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 40.94/41.17 cut (((op (e2) (e1)) = (op (op (e3) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H265]. % 40.94/41.17 congruence. % 40.94/41.17 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 40.94/41.17 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H266]. % 40.94/41.17 congruence. % 40.94/41.17 apply zenon_H266. apply sym_equal. exact zenon_H263. % 40.94/41.17 apply zenon_H12. apply refl_equal. % 40.94/41.17 apply zenon_H71. apply refl_equal. % 40.94/41.17 apply zenon_H71. apply refl_equal. % 40.94/41.17 apply zenon_H1c0. apply sym_equal. exact zenon_H1bf. % 40.94/41.17 (* end of lemma zenon_L438_ *) % 40.94/41.17 assert (zenon_L439_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (unit) (e2)) = (e2)) -> ((unit) = (e0)) -> ((op (e3) (e2)) = (e2)) -> False). % 40.94/41.17 do 0 intro. intros zenon_H267 zenon_Hc zenon_H9 zenon_H268. % 40.94/41.17 cut (((op (unit) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_H267. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_Hc. % 40.94/41.17 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H269]. % 40.94/41.17 cut (((op (unit) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 40.94/41.17 congruence. % 40.94/41.17 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H10 | zenon_intro zenon_H11 ]. % 40.94/41.17 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (unit) (e2)) = (op (e0) (e2)))). % 40.94/41.17 intro zenon_D_pnotp. % 40.94/41.17 apply zenon_Hf. % 40.94/41.17 rewrite <- zenon_D_pnotp. % 40.94/41.17 exact zenon_H10. % 40.94/41.17 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 40.94/41.17 cut (((op (e0) (e2)) = (op (unit) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H8]. % 40.94/41.17 congruence. % 40.94/41.17 apply (zenon_L2_); trivial. % 40.94/41.17 apply zenon_H11. apply refl_equal. % 40.94/41.17 apply zenon_H11. apply refl_equal. % 40.94/41.17 apply zenon_H269. apply sym_equal. exact zenon_H268. % 40.94/41.17 (* end of lemma zenon_L439_ *) % 40.94/41.17 assert (zenon_L440_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (e2)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H3b zenon_H268 zenon_Hc zenon_H267 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H20 zenon_H1bf zenon_Hb1. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.17 apply (zenon_L439_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.17 apply (zenon_L287_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.17 apply (zenon_L84_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.17 apply (zenon_L102_); trivial. % 40.94/41.17 apply (zenon_L290_); trivial. % 40.94/41.17 (* end of lemma zenon_L440_ *) % 40.94/41.17 assert (zenon_L441_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.17 do 0 intro. intros zenon_He0 zenon_H17 zenon_H2d zenon_Hb zenon_H83 zenon_H49 zenon_H16 zenon_H32 zenon_H81 zenon_H197 zenon_H1f zenon_H20 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H22 zenon_H1ad zenon_Hbf zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.17 apply (zenon_L12_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.17 apply (zenon_L285_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.17 apply (zenon_L286_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.17 exact (zenon_He1 zenon_He5). % 40.94/41.17 apply (zenon_L288_); trivial. % 40.94/41.17 (* end of lemma zenon_L441_ *) % 40.94/41.17 assert (zenon_L442_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (op (e3) (e1)) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.17 do 0 intro. intros zenon_H26a zenon_H8e zenon_H260 zenon_H262 zenon_H261 zenon_Hb1 zenon_H1bf zenon_H267 zenon_He0 zenon_H17 zenon_H2d zenon_Hb zenon_H83 zenon_H49 zenon_H16 zenon_H32 zenon_H81 zenon_H197 zenon_H1f zenon_H20 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H22 zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H25e | zenon_intro zenon_H26b ]. % 40.94/41.17 apply (zenon_L437_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H263 | zenon_intro zenon_H26c ]. % 40.94/41.17 apply (zenon_L438_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H268 | zenon_intro zenon_H26d ]. % 40.94/41.17 apply (zenon_L440_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_He5 | zenon_intro zenon_Hbf ]. % 40.94/41.17 exact (zenon_He1 zenon_He5). % 40.94/41.17 apply (zenon_L441_); trivial. % 40.94/41.17 (* end of lemma zenon_L442_ *) % 40.94/41.17 assert (zenon_L443_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> ((op (op (e3) (e1)) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e3) (e4)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.17 do 0 intro. intros zenon_Hd9 zenon_H42 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He1 zenon_H57 zenon_H58 zenon_H6e zenon_H49 zenon_H83 zenon_Hb zenon_H2d zenon_He0 zenon_H267 zenon_H261 zenon_H262 zenon_H260 zenon_H8e zenon_H26a zenon_He8 zenon_Hd3 zenon_H17 zenon_H18 zenon_H9b zenon_H92 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H81 zenon_H16 zenon_H197 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.94/41.17 apply (zenon_L442_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.94/41.17 apply (zenon_L304_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.94/41.17 apply (zenon_L73_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.94/41.17 apply (zenon_L305_); trivial. % 40.94/41.17 exact (zenon_Hda zenon_Hde). % 40.94/41.17 (* end of lemma zenon_L443_ *) % 40.94/41.17 assert (zenon_L444_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (op (e3) (e1)) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H19a zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H61 zenon_H18e zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H16 zenon_H81 zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H92 zenon_H9b zenon_H18 zenon_H17 zenon_Hd3 zenon_He8 zenon_H26a zenon_H8e zenon_H260 zenon_H262 zenon_H261 zenon_H267 zenon_He0 zenon_H2d zenon_Hb zenon_H83 zenon_H49 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H42 zenon_Hd9 zenon_H146. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.17 apply (zenon_L263_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.17 apply (zenon_L300_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.17 apply (zenon_L266_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.17 apply (zenon_L443_); trivial. % 40.94/41.17 exact (zenon_H146 zenon_H144). % 40.94/41.17 (* end of lemma zenon_L444_ *) % 40.94/41.17 assert (zenon_L445_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (op (e3) (e1)) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.17 do 0 intro. intros zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H1c9 zenon_Hb9 zenon_H9f zenon_H116 zenon_Hab zenon_H88 zenon_H7b zenon_H87 zenon_H77 zenon_H73 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hee zenon_H19a zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H61 zenon_H18e zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H16 zenon_H81 zenon_H20 zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H9b zenon_H18 zenon_H17 zenon_Hd3 zenon_He8 zenon_H26a zenon_H8e zenon_H260 zenon_H262 zenon_H261 zenon_H267 zenon_He0 zenon_H2d zenon_Hb zenon_H83 zenon_H49 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H42 zenon_Hd9 zenon_H146. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.17 apply (zenon_L272_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.17 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.17 apply (zenon_L273_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.17 apply (zenon_L274_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.17 apply (zenon_L12_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.17 apply (zenon_L278_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.17 apply (zenon_L112_); trivial. % 40.94/41.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.17 exact (zenon_He1 zenon_He5). % 40.94/41.17 apply (zenon_L444_); trivial. % 40.94/41.17 (* end of lemma zenon_L445_ *) % 40.94/41.17 assert (zenon_L446_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> ((op (op (e3) (e1)) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.18 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_H146 zenon_H267 zenon_H261 zenon_H262 zenon_H260 zenon_H26a zenon_H18e zenon_H168 zenon_H19a zenon_Hee zenon_Hba zenon_Hd4 zenon_He9 zenon_He6 zenon_Hed zenon_H73 zenon_H77 zenon_H87 zenon_H88 zenon_H116 zenon_H9f zenon_Hb9 zenon_H1c9 zenon_H50 zenon_H16d zenon_H41 zenon_H51 zenon_H1c8 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H1c2 zenon_H42 zenon_H7b zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_Hd9 zenon_He1 zenon_H57 zenon_H58 zenon_H6e zenon_H197 zenon_H81 zenon_H49 zenon_Hb zenon_H2d zenon_He0 zenon_Hc3. % 40.94/41.18 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.18 apply (zenon_L277_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.18 apply (zenon_L445_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.18 apply (zenon_L279_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.18 apply (zenon_L295_); trivial. % 40.94/41.18 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.18 (* end of lemma zenon_L446_ *) % 40.94/41.18 assert (zenon_L447_ : ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e3) (e4)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (op (e3) (e1)) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.18 do 0 intro. intros zenon_H4a zenon_Hbb zenon_Hc3 zenon_He0 zenon_H2d zenon_Hb zenon_H49 zenon_H81 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_Hd9 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He8 zenon_Hd3 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H83 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H7b zenon_H42 zenon_H1c2 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H1c9 zenon_Hb9 zenon_H9f zenon_H116 zenon_H88 zenon_H87 zenon_H77 zenon_H73 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hee zenon_H19a zenon_H168 zenon_H18e zenon_H26a zenon_H260 zenon_H262 zenon_H261 zenon_H267 zenon_Ha1 zenon_Hc2 zenon_H146. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.18 apply (zenon_L262_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.18 apply (zenon_L178_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.18 apply (zenon_L266_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.18 apply (zenon_L446_); trivial. % 40.94/41.18 exact (zenon_H146 zenon_H144). % 40.94/41.18 (* end of lemma zenon_L447_ *) % 40.94/41.18 assert (zenon_L448_ : (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> ((op (op (e3) (e1)) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e4) (e4)) = (e0))) -> False). % 40.94/41.18 do 0 intro. intros zenon_H1c4 zenon_H169 zenon_H165 zenon_H1a9 zenon_H146 zenon_Hc2 zenon_Ha1 zenon_H267 zenon_H261 zenon_H262 zenon_H260 zenon_H26a zenon_H18e zenon_H168 zenon_H19a zenon_Hee zenon_Hba zenon_Hd4 zenon_He9 zenon_He6 zenon_Hed zenon_H73 zenon_H77 zenon_H87 zenon_H88 zenon_H116 zenon_H9f zenon_Hb9 zenon_H1c9 zenon_H50 zenon_H16d zenon_H41 zenon_H51 zenon_H1c8 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H42 zenon_H7b zenon_H20 zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_Hd9 zenon_He1 zenon_H57 zenon_H58 zenon_H6e zenon_H81 zenon_H49 zenon_Hb zenon_H2d zenon_He0 zenon_Hc3 zenon_Hbb zenon_H4a zenon_H13e. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.18 apply (zenon_L272_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.18 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.18 apply (zenon_L273_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.18 apply (zenon_L274_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H166 | zenon_intro zenon_H1c5 ]. % 40.94/41.18 apply (zenon_L234_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1c6 ]. % 40.94/41.18 apply (zenon_L275_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1c7 ]. % 40.94/41.18 apply (zenon_L276_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H142 ]. % 40.94/41.18 apply (zenon_L447_); trivial. % 40.94/41.18 exact (zenon_H13e zenon_H142). % 40.94/41.18 (* end of lemma zenon_L448_ *) % 40.94/41.18 assert (zenon_L449_ : (~((op (e4) (e4)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (op (e3) (e1)) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.18 do 0 intro. intros zenon_H13e zenon_Hbb zenon_Hc3 zenon_Hb6 zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H1c9 zenon_Hb9 zenon_H9f zenon_H116 zenon_Ha1 zenon_Hc2 zenon_H1a9 zenon_H165 zenon_H169 zenon_H1c4 zenon_H88 zenon_H7b zenon_H87 zenon_H77 zenon_H73 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hee zenon_H19a zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H61 zenon_H18e zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H16 zenon_H81 zenon_H20 zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H9b zenon_H18 zenon_H17 zenon_Hd3 zenon_He8 zenon_H26a zenon_H8e zenon_H260 zenon_H262 zenon_H261 zenon_H267 zenon_He0 zenon_H2d zenon_Hb zenon_H83 zenon_H49 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H42 zenon_Hd9 zenon_H146. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.18 apply (zenon_L272_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.18 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.18 apply (zenon_L273_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.18 apply (zenon_L274_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.18 apply (zenon_L12_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.18 apply (zenon_L448_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.18 apply (zenon_L112_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.18 exact (zenon_He1 zenon_He5). % 40.94/41.18 apply (zenon_L444_); trivial. % 40.94/41.18 (* end of lemma zenon_L449_ *) % 40.94/41.18 assert (zenon_L450_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (unit)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e0))) -> False). % 40.94/41.18 do 0 intro. intros zenon_He0 zenon_Hb zenon_H116 zenon_Hab zenon_H88 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hee zenon_He1 zenon_H1c4 zenon_H165 zenon_H115 zenon_H34 zenon_H11f zenon_H1a9 zenon_H146 zenon_Hd9 zenon_H15f zenon_H5f zenon_H216 zenon_H217 zenon_He8 zenon_Hd3 zenon_H7b zenon_H42 zenon_H17 zenon_H18 zenon_H9b zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_Hc8 zenon_Hc zenon_H91 zenon_H81 zenon_H16 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda zenon_H18e zenon_H2c zenon_H112 zenon_H61 zenon_H8e zenon_H68 zenon_H60 zenon_H168 zenon_H2d zenon_H19a zenon_H13e. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.18 apply (zenon_L12_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.18 apply (zenon_L278_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.18 apply (zenon_L112_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.18 exact (zenon_He1 zenon_He5). % 40.94/41.18 apply (zenon_L376_); trivial. % 40.94/41.18 (* end of lemma zenon_L450_ *) % 40.94/41.18 assert (zenon_L451_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.94/41.18 do 0 intro. intros zenon_H3b zenon_H217 zenon_H216 zenon_H5f zenon_H4a zenon_Hc zenon_H49 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H20 zenon_H1bf zenon_Hb1. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.18 apply (zenon_L371_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.18 apply (zenon_L17_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.18 apply (zenon_L84_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.18 apply (zenon_L102_); trivial. % 40.94/41.18 apply (zenon_L290_); trivial. % 40.94/41.18 (* end of lemma zenon_L451_ *) % 40.94/41.18 assert (zenon_L452_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 40.94/41.18 do 0 intro. intros zenon_H1c8 zenon_H146 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H18e zenon_H112 zenon_H115 zenon_H116 zenon_H168 zenon_H19a zenon_H1c9 zenon_Hb9 zenon_H9f zenon_He0 zenon_H2c zenon_H17 zenon_H2d zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H1f zenon_H20 zenon_H22 zenon_H68 zenon_H32 zenon_H16 zenon_H34 zenon_Hed zenon_He6 zenon_He8 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H3b zenon_H217 zenon_H216 zenon_H5f zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.18 apply (zenon_L272_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.18 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.18 apply (zenon_L273_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.18 apply (zenon_L51_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.18 apply (zenon_L12_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.18 apply (zenon_L451_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.18 apply (zenon_L112_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.18 exact (zenon_He1 zenon_He5). % 40.94/41.18 apply (zenon_L372_); trivial. % 40.94/41.18 (* end of lemma zenon_L452_ *) % 40.94/41.18 assert (zenon_L453_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (op (e3) (e2)) (e2)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> False). % 40.94/41.18 do 0 intro. intros zenon_H26e zenon_H26f zenon_H125 zenon_H21c. % 40.94/41.18 cut (((op (op (e3) (e2)) (e2)) = (e3)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 40.94/41.18 intro zenon_D_pnotp. % 40.94/41.18 apply zenon_H26e. % 40.94/41.18 rewrite <- zenon_D_pnotp. % 40.94/41.18 exact zenon_H26f. % 40.94/41.18 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 40.94/41.18 cut (((op (op (e3) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H270]. % 40.94/41.18 congruence. % 40.94/41.18 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H10 | zenon_intro zenon_H11 ]. % 40.94/41.18 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (op (e3) (e2)) (e2)) = (op (e0) (e2)))). % 40.94/41.18 intro zenon_D_pnotp. % 40.94/41.18 apply zenon_H270. % 40.94/41.18 rewrite <- zenon_D_pnotp. % 40.94/41.18 exact zenon_H10. % 40.94/41.18 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 40.94/41.18 cut (((op (e0) (e2)) = (op (op (e3) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H271]. % 40.94/41.18 congruence. % 40.94/41.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 40.94/41.18 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H126]. % 40.94/41.18 congruence. % 40.94/41.18 apply zenon_H126. apply sym_equal. exact zenon_H125. % 40.94/41.18 apply zenon_H7. apply refl_equal. % 40.94/41.18 apply zenon_H11. apply refl_equal. % 40.94/41.18 apply zenon_H11. apply refl_equal. % 40.94/41.18 apply zenon_H21f. apply sym_equal. exact zenon_H21c. % 40.94/41.18 (* end of lemma zenon_L453_ *) % 40.94/41.18 assert (zenon_L454_ : (~((op (e3) (e2)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> ((op (e3) (e2)) = (e1)) -> False). % 40.94/41.18 do 0 intro. intros zenon_H21a zenon_H34 zenon_H272. % 40.94/41.18 cut (((e1) = (op (e4) (e2))) = ((op (e3) (e2)) = (op (e4) (e2)))). % 40.94/41.18 intro zenon_D_pnotp. % 40.94/41.18 apply zenon_H21a. % 40.94/41.18 rewrite <- zenon_D_pnotp. % 40.94/41.18 exact zenon_H34. % 40.94/41.18 cut (((op (e4) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 40.94/41.18 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H273]. % 40.94/41.18 congruence. % 40.94/41.18 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 40.94/41.18 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((e1) = (op (e3) (e2)))). % 40.94/41.18 intro zenon_D_pnotp. % 40.94/41.18 apply zenon_H273. % 40.94/41.18 rewrite <- zenon_D_pnotp. % 40.94/41.18 exact zenon_H85. % 40.94/41.18 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 40.94/41.18 cut (((op (e3) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H274]. % 40.94/41.18 congruence. % 40.94/41.18 exact (zenon_H274 zenon_H272). % 40.94/41.18 apply zenon_H86. apply refl_equal. % 40.94/41.18 apply zenon_H86. apply refl_equal. % 40.94/41.18 apply zenon_H96. apply refl_equal. % 40.94/41.18 (* end of lemma zenon_L454_ *) % 40.94/41.18 assert (zenon_L455_ : ((op (op (e3) (e2)) (e2)) = (e3)) -> ((op (e3) (e2)) = (e4)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> False). % 40.94/41.18 do 0 intro. intros zenon_H26f zenon_H1f8 zenon_H21c zenon_H275. % 40.94/41.18 elim (classic ((op (e4) (e2)) = (op (e4) (e2)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 40.94/41.18 cut (((op (e4) (e2)) = (op (e4) (e2))) = ((op (e1) (e2)) = (op (e4) (e2)))). % 40.94/41.18 intro zenon_D_pnotp. % 40.94/41.18 apply zenon_H275. % 40.94/41.18 rewrite <- zenon_D_pnotp. % 40.94/41.18 exact zenon_H95. % 40.94/41.18 cut (((op (e4) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 40.94/41.18 cut (((op (e4) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H276]. % 40.94/41.18 congruence. % 40.94/41.18 cut (((op (op (e3) (e2)) (e2)) = (e3)) = ((op (e4) (e2)) = (op (e1) (e2)))). % 40.94/41.18 intro zenon_D_pnotp. % 40.94/41.18 apply zenon_H276. % 40.94/41.18 rewrite <- zenon_D_pnotp. % 40.94/41.18 exact zenon_H26f. % 40.94/41.18 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 40.94/41.18 cut (((op (op (e3) (e2)) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H277]. % 40.94/41.18 congruence. % 40.94/41.18 elim (classic ((op (e4) (e2)) = (op (e4) (e2)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 40.94/41.18 cut (((op (e4) (e2)) = (op (e4) (e2))) = ((op (op (e3) (e2)) (e2)) = (op (e4) (e2)))). % 40.94/41.18 intro zenon_D_pnotp. % 40.94/41.18 apply zenon_H277. % 40.94/41.18 rewrite <- zenon_D_pnotp. % 40.94/41.18 exact zenon_H95. % 40.94/41.18 cut (((op (e4) (e2)) = (op (e4) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 40.94/41.18 cut (((op (e4) (e2)) = (op (op (e3) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 40.94/41.18 congruence. % 40.94/41.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 40.94/41.18 cut (((e4) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1fa]. % 40.94/41.18 congruence. % 40.94/41.18 apply zenon_H1fa. apply sym_equal. exact zenon_H1f8. % 40.94/41.18 apply zenon_H7. apply refl_equal. % 40.94/41.18 apply zenon_H96. apply refl_equal. % 40.94/41.18 apply zenon_H96. apply refl_equal. % 40.94/41.18 apply zenon_H21f. apply sym_equal. exact zenon_H21c. % 40.94/41.18 apply zenon_H96. apply refl_equal. % 40.94/41.18 apply zenon_H96. apply refl_equal. % 40.94/41.18 (* end of lemma zenon_L455_ *) % 40.94/41.18 assert (zenon_L456_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (op (e3) (e2)) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> False). % 40.94/41.18 do 0 intro. intros zenon_H223 zenon_H217 zenon_Hb1 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H279 zenon_H26e zenon_H21a zenon_Hc zenon_H267 zenon_H5f zenon_H8e zenon_H26f zenon_H275 zenon_H61 zenon_H60 zenon_H9f zenon_H73 zenon_Hb9 zenon_H1c9 zenon_H19a zenon_H91 zenon_H17 zenon_H2d zenon_H168 zenon_He1 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_Hd3 zenon_H9b zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H58 zenon_H57 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H7b zenon_H88 zenon_H49 zenon_Hb zenon_He0 zenon_H116 zenon_H2c zenon_H115 zenon_H112 zenon_H18e zenon_H81 zenon_H51 zenon_H146 zenon_H1c8 zenon_H34 zenon_H16 zenon_H32 zenon_H50 zenon_H16d zenon_H161 zenon_H1f zenon_H20 zenon_H41 zenon_H220 zenon_H3b zenon_H1ae zenon_H22. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H216 | zenon_intro zenon_H224 ]. % 40.94/41.18 apply (zenon_L452_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1cc | zenon_intro zenon_H225 ]. % 40.94/41.18 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.18 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H21c | zenon_intro zenon_H226 ]. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.18 apply (zenon_L272_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.18 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.18 apply (zenon_L273_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.18 apply (zenon_L274_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H125 | zenon_intro zenon_H27a ]. % 40.94/41.18 apply (zenon_L453_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H272 | zenon_intro zenon_H27b ]. % 40.94/41.18 apply (zenon_L454_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H268 | zenon_intro zenon_H27c ]. % 40.94/41.18 apply (zenon_L439_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H76 | zenon_intro zenon_H1f8 ]. % 40.94/41.18 apply (zenon_L83_); trivial. % 40.94/41.18 apply (zenon_L455_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.18 apply (zenon_L287_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.18 apply (zenon_L84_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.18 apply (zenon_L102_); trivial. % 40.94/41.18 apply (zenon_L290_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H221 | zenon_intro zenon_H1af ]. % 40.94/41.18 apply (zenon_L379_); trivial. % 40.94/41.18 apply (zenon_L281_); trivial. % 40.94/41.18 (* end of lemma zenon_L456_ *) % 40.94/41.18 assert (zenon_L457_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> ((op (op (e3) (e2)) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (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) (e4)) = (e3)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 40.94/41.18 do 0 intro. intros zenon_H15b zenon_H89 zenon_Hc2 zenon_Ha1 zenon_Haa zenon_Hb6 zenon_Hda zenon_Hc3 zenon_Hbb zenon_H22 zenon_H1ae zenon_H3b zenon_H220 zenon_H41 zenon_H20 zenon_H1f zenon_H161 zenon_H16d zenon_H50 zenon_H32 zenon_H16 zenon_H1c8 zenon_H146 zenon_H51 zenon_H81 zenon_H18e zenon_H112 zenon_H115 zenon_H2c zenon_H116 zenon_He0 zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H57 zenon_H58 zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_H9b zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H168 zenon_H2d zenon_H17 zenon_H91 zenon_H19a zenon_H1c9 zenon_Hb9 zenon_H73 zenon_H9f zenon_H60 zenon_H61 zenon_H275 zenon_H26f zenon_H8e zenon_H5f zenon_H267 zenon_Hc zenon_H21a zenon_H26e zenon_H279 zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_Hb1 zenon_H217 zenon_H223 zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 40.94/41.18 apply (zenon_L240_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 40.94/41.18 apply (zenon_L456_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 40.94/41.18 apply (zenon_L216_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 40.94/41.18 apply (zenon_L217_); trivial. % 40.94/41.18 apply (zenon_L218_); trivial. % 40.94/41.18 (* end of lemma zenon_L457_ *) % 40.94/41.18 assert (zenon_L458_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e4) (e2)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e1)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.18 do 0 intro. intros zenon_H3b zenon_Hc9 zenon_H99 zenon_Hc8 zenon_Hab zenon_Haa zenon_H22 zenon_H20 zenon_H1f zenon_H81 zenon_H1e7 zenon_Hd3 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.18 apply (zenon_L70_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.18 apply (zenon_L56_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.18 apply (zenon_L8_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.18 apply (zenon_L313_); trivial. % 40.94/41.18 apply (zenon_L44_); trivial. % 40.94/41.18 (* end of lemma zenon_L458_ *) % 40.94/41.18 assert (zenon_L459_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e3)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e1)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.18 do 0 intro. intros zenon_H3b zenon_Hcc zenon_Hb1 zenon_Hcd zenon_H99 zenon_H81 zenon_H1e7 zenon_Hd3 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.18 apply (zenon_L74_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.18 apply (zenon_L75_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.18 apply (zenon_L76_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.18 apply (zenon_L313_); trivial. % 40.94/41.18 apply (zenon_L44_); trivial. % 40.94/41.18 (* end of lemma zenon_L459_ *) % 40.94/41.18 assert (zenon_L460_ : (~((op (e1) (e1)) = (op (e4) (e1)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (op (e3) (e2)) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> ((op (unit) (e1)) = (e1)) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e3) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.18 do 0 intro. intros zenon_H157 zenon_H34 zenon_H11f zenon_H152 zenon_H14d zenon_H223 zenon_H217 zenon_H18 zenon_H42 zenon_H279 zenon_H26e zenon_H21a zenon_H267 zenon_H5f zenon_H8e zenon_H26f zenon_H275 zenon_H61 zenon_H60 zenon_H9f zenon_H73 zenon_Hb9 zenon_H1c9 zenon_H19a zenon_H17 zenon_H2d zenon_H168 zenon_He1 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H58 zenon_H57 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H7b zenon_H88 zenon_H49 zenon_Hb zenon_He0 zenon_H116 zenon_H2c zenon_H115 zenon_H112 zenon_H18e zenon_H51 zenon_H146 zenon_H1c8 zenon_H16 zenon_H50 zenon_H16d zenon_H161 zenon_H41 zenon_H220 zenon_H1ae zenon_Hbb zenon_Hc3 zenon_Hb6 zenon_Ha1 zenon_Hc2 zenon_H89 zenon_H15b zenon_H32 zenon_H9b zenon_H1f zenon_H20 zenon_H22 zenon_Haa zenon_Hab zenon_Hc8 zenon_H92 zenon_Hc zenon_H91 zenon_Hd3 zenon_H1e7 zenon_H81 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.18 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.94/41.18 apply (zenon_L457_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.94/41.18 apply (zenon_L61_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.94/41.18 apply (zenon_L458_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.94/41.18 apply (zenon_L459_); trivial. % 40.94/41.18 exact (zenon_Hda zenon_Hde). % 40.94/41.18 (* end of lemma zenon_L460_ *) % 40.94/41.18 assert (zenon_L461_ : (~((op (e4) (e4)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e4) (e4)) = (e1))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e3) (e3)) = (e4))) -> ((op (op (e3) (e2)) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (unit) (e0)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> False). % 40.94/41.18 do 0 intro. intros zenon_H13e zenon_H15f zenon_H1a9 zenon_H165 zenon_H1c4 zenon_H146 zenon_Hd3 zenon_H1fb zenon_H81 zenon_H91 zenon_Hc zenon_H18e zenon_H2c zenon_H112 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H168 zenon_H18 zenon_H2d zenon_H17 zenon_H19a zenon_H1ff zenon_H26f zenon_H275 zenon_H157 zenon_H11f zenon_H152 zenon_H14d zenon_H223 zenon_H217 zenon_H42 zenon_H279 zenon_H26e zenon_H21a zenon_H267 zenon_H9f zenon_H73 zenon_Hb9 zenon_H1c9 zenon_He1 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_He8 zenon_He6 zenon_Hed zenon_H58 zenon_H57 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H7b zenon_H88 zenon_H49 zenon_Hb zenon_He0 zenon_H116 zenon_H115 zenon_H51 zenon_H1c8 zenon_Hbb zenon_Hc3 zenon_Hb6 zenon_Ha1 zenon_Hc2 zenon_H89 zenon_H15b zenon_H9b zenon_Haa zenon_Hab zenon_Hc8 zenon_H99 zenon_Hb1 zenon_Hcc zenon_Hda zenon_H1e5 zenon_H1fe zenon_H34 zenon_H16 zenon_H32 zenon_H50 zenon_H16d zenon_H161 zenon_H1f zenon_H20 zenon_H41 zenon_H220 zenon_H3b zenon_H1ae zenon_H22. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H216 | zenon_intro zenon_H224 ]. % 40.94/41.18 apply (zenon_L450_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1cc | zenon_intro zenon_H225 ]. % 40.94/41.18 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.18 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H21c | zenon_intro zenon_H226 ]. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.18 apply (zenon_L12_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.18 apply (zenon_L278_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.18 apply (zenon_L112_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.18 exact (zenon_He1 zenon_He5). % 40.94/41.18 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1df | zenon_intro zenon_H200 ]. % 40.94/41.18 apply (zenon_L312_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H201 ]. % 40.94/41.18 apply (zenon_L460_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H202 ]. % 40.94/41.18 apply (zenon_L455_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H203 | zenon_intro zenon_H1fc ]. % 40.94/41.18 exact (zenon_H1ff zenon_H203). % 40.94/41.18 apply (zenon_L355_); trivial. % 40.94/41.18 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H221 | zenon_intro zenon_H1af ]. % 40.94/41.18 apply (zenon_L379_); trivial. % 40.94/41.18 apply (zenon_L281_); trivial. % 40.94/41.18 (* end of lemma zenon_L461_ *) % 40.94/41.18 assert (zenon_L462_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> ((op (op (e3) (e2)) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e4))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((e1) = (e3))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e4) (e4)) = (e0))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.19 do 0 intro. intros zenon_H220 zenon_H41 zenon_H161 zenon_H16d zenon_H50 zenon_H1fe zenon_H1e5 zenon_Hda zenon_Hcc zenon_Hb1 zenon_H99 zenon_Hc8 zenon_Haa zenon_H9b zenon_H15b zenon_H89 zenon_Hc2 zenon_Ha1 zenon_Hbb zenon_H1c8 zenon_H51 zenon_H116 zenon_He0 zenon_Hb zenon_H88 zenon_H7b zenon_H87 zenon_H77 zenon_H6e zenon_H57 zenon_Hed zenon_He6 zenon_He8 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H1c9 zenon_Hb9 zenon_H73 zenon_H9f zenon_H267 zenon_H21a zenon_H26e zenon_H279 zenon_H42 zenon_H217 zenon_H223 zenon_H14d zenon_H152 zenon_H157 zenon_H275 zenon_H26f zenon_H1ff zenon_H19a zenon_H17 zenon_H2d zenon_H18 zenon_H168 zenon_H18e zenon_H91 zenon_H81 zenon_H1fb zenon_H146 zenon_H1c4 zenon_H165 zenon_H1a9 zenon_H15f zenon_H13e zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.19 apply (zenon_L277_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.19 apply (zenon_L461_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.19 apply (zenon_L279_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.19 apply (zenon_L285_); trivial. % 40.94/41.19 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.19 (* end of lemma zenon_L462_ *) % 40.94/41.19 assert (zenon_L463_ : (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (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 (e1) (e4)) = (e3)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (op (e3) (e2)) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 40.94/41.19 do 0 intro. intros zenon_H1fe zenon_H1e5 zenon_Hda zenon_Hcc zenon_Hb1 zenon_H99 zenon_Hc8 zenon_Hab zenon_Haa zenon_H9b zenon_H32 zenon_H15b zenon_H89 zenon_Hc2 zenon_Ha1 zenon_Hb6 zenon_Hc3 zenon_Hbb zenon_H1ae zenon_H220 zenon_H161 zenon_H1c8 zenon_H146 zenon_H51 zenon_H18e zenon_H112 zenon_H115 zenon_H2c zenon_H116 zenon_He0 zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H57 zenon_H58 zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H168 zenon_H2d zenon_H17 zenon_H19a zenon_H1c9 zenon_Hb9 zenon_H73 zenon_H9f zenon_H60 zenon_H61 zenon_H8e zenon_H5f zenon_H267 zenon_H21a zenon_H26e zenon_H279 zenon_H42 zenon_H18 zenon_H217 zenon_H223 zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157 zenon_H275 zenon_H21c zenon_H26f zenon_H1ff zenon_H3b zenon_Hd3 zenon_H1fb zenon_H41 zenon_H16d zenon_H50 zenon_H22 zenon_H20 zenon_H1f zenon_H197 zenon_H16 zenon_H81 zenon_H91 zenon_Hc zenon_H92. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1df | zenon_intro zenon_H200 ]. % 40.94/41.19 apply (zenon_L312_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H201 ]. % 40.94/41.19 apply (zenon_L460_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H202 ]. % 40.94/41.19 apply (zenon_L455_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H203 | zenon_intro zenon_H1fc ]. % 40.94/41.19 exact (zenon_H1ff zenon_H203). % 40.94/41.19 apply (zenon_L354_); trivial. % 40.94/41.19 (* end of lemma zenon_L463_ *) % 40.94/41.19 assert (zenon_L464_ : (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e1)) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e4))) -> ((op (op (e3) (e2)) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e4) (e3)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.19 do 0 intro. intros zenon_H81 zenon_H197 zenon_H50 zenon_H16d zenon_H41 zenon_H1fb zenon_H1ff zenon_H26f zenon_H21c zenon_H275 zenon_H157 zenon_H152 zenon_H14d zenon_H223 zenon_H217 zenon_H279 zenon_H26e zenon_H21a zenon_H267 zenon_H9f zenon_H73 zenon_Hb9 zenon_H1c9 zenon_H19a zenon_H2d zenon_H168 zenon_He1 zenon_Hee zenon_Hba zenon_Hd4 zenon_He9 zenon_He6 zenon_Hed zenon_H57 zenon_H6e zenon_H77 zenon_H87 zenon_H88 zenon_H49 zenon_Hb zenon_He0 zenon_H116 zenon_H18e zenon_H51 zenon_H146 zenon_H1c8 zenon_H161 zenon_H220 zenon_Hbb zenon_Ha1 zenon_Hc2 zenon_H89 zenon_H15b zenon_Haa zenon_H1e5 zenon_H1fe zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H1c2 zenon_H42 zenon_H7b zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H92 zenon_Hd9 zenon_Hc3. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.19 apply (zenon_L53_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.19 apply (zenon_L463_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.19 apply (zenon_L279_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.19 apply (zenon_L294_); trivial. % 40.94/41.19 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.19 (* end of lemma zenon_L464_ *) % 40.94/41.19 assert (zenon_L465_ : (~((op (e4) (e4)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e4) (e3)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e3) (e4)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (op (e3) (e2)) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.19 do 0 intro. intros zenon_Hc3 zenon_Hd9 zenon_H92 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He8 zenon_Hd3 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H83 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H7b zenon_H42 zenon_H1c2 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H1fe zenon_H1e5 zenon_Haa zenon_H15b zenon_H89 zenon_Hc2 zenon_Ha1 zenon_Hbb zenon_H220 zenon_H161 zenon_H1c8 zenon_H51 zenon_H18e zenon_H116 zenon_He0 zenon_Hb zenon_H49 zenon_H88 zenon_H87 zenon_H77 zenon_H6e zenon_H57 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hee zenon_He1 zenon_H168 zenon_H2d zenon_H19a zenon_H1c9 zenon_Hb9 zenon_H73 zenon_H9f zenon_H267 zenon_H21a zenon_H26e zenon_H279 zenon_H217 zenon_H223 zenon_H14d zenon_H152 zenon_H157 zenon_H275 zenon_H21c zenon_H26f zenon_H1ff zenon_H1fb zenon_H41 zenon_H16d zenon_H50 zenon_H81 zenon_H146. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.19 apply (zenon_L263_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.19 apply (zenon_L300_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.19 apply (zenon_L266_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.19 apply (zenon_L464_); trivial. % 40.94/41.19 exact (zenon_H146 zenon_H144). % 40.94/41.19 (* end of lemma zenon_L465_ *) % 40.94/41.19 assert (zenon_L466_ : (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e4))) -> ((op (op (e3) (e2)) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e4) (e3)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e4) (e4)) = (e0))) -> False). % 40.94/41.19 do 0 intro. intros zenon_H1c4 zenon_H165 zenon_H1a9 zenon_H146 zenon_H81 zenon_H50 zenon_H16d zenon_H41 zenon_H1fb zenon_H1ff zenon_H26f zenon_H21c zenon_H275 zenon_H157 zenon_H152 zenon_H14d zenon_H223 zenon_H217 zenon_H279 zenon_H26e zenon_H21a zenon_H267 zenon_H9f zenon_H73 zenon_Hb9 zenon_H1c9 zenon_H19a zenon_H2d zenon_H168 zenon_He1 zenon_Hee zenon_Hba zenon_Hd4 zenon_He9 zenon_He6 zenon_Hed zenon_H57 zenon_H6e zenon_H77 zenon_H87 zenon_H88 zenon_H49 zenon_Hb zenon_He0 zenon_H116 zenon_H18e zenon_H51 zenon_H1c8 zenon_H161 zenon_H220 zenon_Hbb zenon_Ha1 zenon_Hc2 zenon_H89 zenon_H15b zenon_Haa zenon_H1e5 zenon_H1fe zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H42 zenon_H7b zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H92 zenon_Hd9 zenon_Hc3 zenon_H13e. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H166 | zenon_intro zenon_H1c5 ]. % 40.94/41.19 apply (zenon_L243_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1c6 ]. % 40.94/41.19 apply (zenon_L275_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1c7 ]. % 40.94/41.19 apply (zenon_L276_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H142 ]. % 40.94/41.19 apply (zenon_L465_); trivial. % 40.94/41.19 exact (zenon_H13e zenon_H142). % 40.94/41.19 (* end of lemma zenon_L466_ *) % 40.94/41.19 assert (zenon_L467_ : (~((op (e4) (e4)) = (e0))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e4)) = (e4))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> ((op (op (e3) (e2)) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> False). % 40.94/41.19 do 0 intro. intros zenon_H13e zenon_Hc3 zenon_Hd9 zenon_H15f zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1b3 zenon_He8 zenon_Hd3 zenon_H17 zenon_H18 zenon_H9b zenon_H83 zenon_Hc zenon_Hc8 zenon_Hb1 zenon_H7b zenon_H42 zenon_H91 zenon_H99 zenon_Hcc zenon_Hda zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H1fe zenon_H1e5 zenon_Haa zenon_H15b zenon_H89 zenon_Hc2 zenon_Ha1 zenon_Hbb zenon_H1c8 zenon_H51 zenon_H18e zenon_H116 zenon_He0 zenon_Hb zenon_H49 zenon_H88 zenon_H87 zenon_H77 zenon_H6e zenon_H57 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hee zenon_He1 zenon_H168 zenon_H2d zenon_H19a zenon_H1c9 zenon_Hb9 zenon_H73 zenon_H9f zenon_H267 zenon_H21a zenon_H26e zenon_H279 zenon_H217 zenon_H223 zenon_H14d zenon_H152 zenon_H157 zenon_H275 zenon_H26f zenon_H1ff zenon_H1fb zenon_H81 zenon_H146 zenon_H1a9 zenon_H165 zenon_H1c4 zenon_H34 zenon_H16 zenon_H32 zenon_H50 zenon_H16d zenon_H161 zenon_H1f zenon_H20 zenon_H41 zenon_H220 zenon_H3b zenon_H1ae zenon_H22. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H216 | zenon_intro zenon_H224 ]. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.19 apply (zenon_L12_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.19 apply (zenon_L462_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.19 apply (zenon_L41_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.19 exact (zenon_He1 zenon_He5). % 40.94/41.19 apply (zenon_L376_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1cc | zenon_intro zenon_H225 ]. % 40.94/41.19 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.19 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H21c | zenon_intro zenon_H226 ]. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.19 apply (zenon_L272_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.19 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.19 apply (zenon_L273_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.19 apply (zenon_L274_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.19 apply (zenon_L12_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.19 apply (zenon_L462_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.19 apply (zenon_L41_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.19 exact (zenon_He1 zenon_He5). % 40.94/41.19 apply (zenon_L466_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H221 | zenon_intro zenon_H1af ]. % 40.94/41.19 apply (zenon_L379_); trivial. % 40.94/41.19 apply (zenon_L281_); trivial. % 40.94/41.19 (* end of lemma zenon_L467_ *) % 40.94/41.19 assert (zenon_L468_ : ((~((op (e3) (e3)) = (op (e3) (e3))))/\(((op (op (e3) (e3)) (e3)) = (e3))/\(~((op (op (e3) (e3)) (e3)) = (e3))))) -> False). % 40.94/41.19 do 0 intro. intros zenon_H27d. % 40.94/41.19 apply (zenon_and_s _ _ zenon_H27d). zenon_intro zenon_H6a. zenon_intro zenon_H27e. % 40.94/41.19 apply zenon_H6a. apply refl_equal. % 40.94/41.19 (* end of lemma zenon_L468_ *) % 40.94/41.19 assert (zenon_L469_ : (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((op (op (e3) (e4)) (e4)) = (e3)) -> ((op (e3) (e4)) = (e1)) -> ((e3) = (op (e2) (e4))) -> False). % 40.94/41.19 do 0 intro. intros zenon_H1ae zenon_H27f zenon_H197 zenon_H22. % 40.94/41.19 cut (((op (op (e3) (e4)) (e4)) = (e3)) = ((op (e1) (e4)) = (op (e2) (e4)))). % 40.94/41.19 intro zenon_D_pnotp. % 40.94/41.19 apply zenon_H1ae. % 40.94/41.19 rewrite <- zenon_D_pnotp. % 40.94/41.19 exact zenon_H27f. % 40.94/41.19 cut (((e3) = (op (e2) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 40.94/41.19 cut (((op (op (e3) (e4)) (e4)) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H280]. % 40.94/41.19 congruence. % 40.94/41.19 elim (classic ((op (e1) (e4)) = (op (e1) (e4)))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a4 ]. % 40.94/41.19 cut (((op (e1) (e4)) = (op (e1) (e4))) = ((op (op (e3) (e4)) (e4)) = (op (e1) (e4)))). % 40.94/41.19 intro zenon_D_pnotp. % 40.94/41.19 apply zenon_H280. % 40.94/41.19 rewrite <- zenon_D_pnotp. % 40.94/41.19 exact zenon_H1a3. % 40.94/41.19 cut (((op (e1) (e4)) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1a4]. % 40.94/41.19 cut (((op (e1) (e4)) = (op (op (e3) (e4)) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H281]. % 40.94/41.19 congruence. % 40.94/41.19 cut (((e4) = (e4))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 40.94/41.19 cut (((e1) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 40.94/41.19 congruence. % 40.94/41.19 apply zenon_H198. apply sym_equal. exact zenon_H197. % 40.94/41.19 apply zenon_H97. apply refl_equal. % 40.94/41.19 apply zenon_H1a4. apply refl_equal. % 40.94/41.19 apply zenon_H1a4. apply refl_equal. % 40.94/41.19 exact (zenon_H23 zenon_H22). % 40.94/41.19 (* end of lemma zenon_L469_ *) % 40.94/41.19 assert (zenon_L470_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((e1) = (e3))) -> ((e3) = (op (e2) (e4))) -> ((op (op (e3) (e4)) (e4)) = (e3)) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.19 do 0 intro. intros zenon_H19a zenon_H17 zenon_H2d zenon_H49 zenon_Hc zenon_H4a zenon_H168 zenon_H34 zenon_H16 zenon_H32 zenon_H116 zenon_H2c zenon_H1f zenon_H20 zenon_H115 zenon_H112 zenon_H3b zenon_H18e zenon_H22 zenon_H27f zenon_H1ae zenon_H146. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.19 apply (zenon_L262_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.19 apply (zenon_L167_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.19 apply (zenon_L266_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.19 apply (zenon_L469_); trivial. % 40.94/41.19 exact (zenon_H146 zenon_H144). % 40.94/41.19 (* end of lemma zenon_L470_ *) % 40.94/41.19 assert (zenon_L471_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((e1) = (e3))) -> ((e3) = (op (e2) (e4))) -> ((op (op (e3) (e4)) (e4)) = (e3)) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.19 do 0 intro. intros zenon_H19a zenon_H17 zenon_H2d zenon_H1f zenon_H16 zenon_H18 zenon_H168 zenon_H92 zenon_Hc zenon_H91 zenon_H20 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H3b zenon_H18e zenon_H22 zenon_H27f zenon_H1ae zenon_H146. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.19 apply (zenon_L263_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.19 apply (zenon_L300_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.19 apply (zenon_L266_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.19 apply (zenon_L469_); trivial. % 40.94/41.19 exact (zenon_H146 zenon_H144). % 40.94/41.19 (* end of lemma zenon_L471_ *) % 40.94/41.19 assert (zenon_L472_ : (~((op (e0) (e4)) = (op (e4) (e0)))) -> ((op (unit) (e4)) = (e4)) -> ((unit) = (e0)) -> ((op (e4) (e0)) = (e4)) -> False). % 40.94/41.19 do 0 intro. intros zenon_H282 zenon_Hd3 zenon_H9 zenon_H9a. % 40.94/41.19 cut (((op (unit) (e4)) = (e4)) = ((op (e0) (e4)) = (op (e4) (e0)))). % 40.94/41.19 intro zenon_D_pnotp. % 40.94/41.19 apply zenon_H282. % 40.94/41.19 rewrite <- zenon_D_pnotp. % 40.94/41.19 exact zenon_Hd3. % 40.94/41.19 cut (((e4) = (op (e4) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 40.94/41.19 cut (((op (unit) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 40.94/41.19 congruence. % 40.94/41.19 elim (classic ((op (e0) (e4)) = (op (e0) (e4)))); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H1b8 ]. % 40.94/41.19 cut (((op (e0) (e4)) = (op (e0) (e4))) = ((op (unit) (e4)) = (op (e0) (e4)))). % 40.94/41.19 intro zenon_D_pnotp. % 40.94/41.19 apply zenon_H1b6. % 40.94/41.19 rewrite <- zenon_D_pnotp. % 40.94/41.19 exact zenon_H1b7. % 40.94/41.19 cut (((op (e0) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 40.94/41.19 cut (((op (e0) (e4)) = (op (unit) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 40.94/41.19 congruence. % 40.94/41.19 apply (zenon_L282_); trivial. % 40.94/41.19 apply zenon_H1b8. apply refl_equal. % 40.94/41.19 apply zenon_H1b8. apply refl_equal. % 40.94/41.19 apply zenon_H9d. apply sym_equal. exact zenon_H9a. % 40.94/41.19 (* end of lemma zenon_L472_ *) % 40.94/41.19 assert (zenon_L473_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e4) (e0)))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 40.94/41.19 do 0 intro. intros zenon_H3b zenon_Hd3 zenon_H282 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_H9a zenon_H99 zenon_H197 zenon_H16 zenon_H81 zenon_H20 zenon_H1bf zenon_Hb1. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 40.94/41.19 apply (zenon_L472_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 40.94/41.19 apply (zenon_L287_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 40.94/41.19 apply (zenon_L84_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 40.94/41.19 apply (zenon_L270_); trivial. % 40.94/41.19 apply (zenon_L290_); trivial. % 40.94/41.19 (* end of lemma zenon_L473_ *) % 40.94/41.19 assert (zenon_L474_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e4)) = (op (e4) (e0)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e3) (e4)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.19 do 0 intro. intros zenon_Hd9 zenon_H42 zenon_H15f zenon_H282 zenon_He8 zenon_Hd3 zenon_H17 zenon_H18 zenon_H9b zenon_H92 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H81 zenon_H16 zenon_H197 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 40.94/41.19 apply (zenon_L473_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 40.94/41.19 apply (zenon_L304_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 40.94/41.19 apply (zenon_L73_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 40.94/41.19 apply (zenon_L305_); trivial. % 40.94/41.19 exact (zenon_Hda zenon_Hde). % 40.94/41.19 (* end of lemma zenon_L474_ *) % 40.94/41.19 assert (zenon_L475_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e2)) -> ((e1) = (op (e4) (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e4)) = (op (e4) (e0)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e3) (e4)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 40.94/41.19 do 0 intro. intros zenon_He0 zenon_H2c zenon_H2d zenon_Hb zenon_H116 zenon_Hab zenon_H34 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_Hd9 zenon_H42 zenon_H15f zenon_H282 zenon_He8 zenon_Hd3 zenon_H17 zenon_H18 zenon_H9b zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H81 zenon_H16 zenon_H197 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.19 apply (zenon_L12_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.19 apply (zenon_L278_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.19 apply (zenon_L286_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.19 exact (zenon_He1 zenon_He5). % 40.94/41.19 apply (zenon_L474_); trivial. % 40.94/41.19 (* end of lemma zenon_L475_ *) % 40.94/41.19 assert (zenon_L476_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e4) (e0)))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 40.94/41.19 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_Hda zenon_Hcc zenon_H99 zenon_H91 zenon_H197 zenon_H81 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H9b zenon_H18 zenon_H17 zenon_He8 zenon_H282 zenon_H15f zenon_H42 zenon_Hd9 zenon_He1 zenon_H57 zenon_H6e zenon_H116 zenon_Hb zenon_H2d zenon_He0 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 40.94/41.19 apply (zenon_L277_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 40.94/41.19 apply (zenon_L475_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 40.94/41.19 apply (zenon_L279_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 40.94/41.19 apply (zenon_L285_); trivial. % 40.94/41.19 exact (zenon_Hc3 zenon_Hc7). % 40.94/41.19 (* end of lemma zenon_L476_ *) % 40.94/41.19 assert (zenon_L477_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e4)) = (op (e4) (e0)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.19 do 0 intro. intros zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H1c9 zenon_Hb9 zenon_H9f zenon_H19a zenon_H168 zenon_Hee zenon_Hd4 zenon_He9 zenon_He6 zenon_Hed zenon_H73 zenon_H77 zenon_H87 zenon_H7b zenon_H88 zenon_Hba zenon_Hbb zenon_H18e zenon_Hc3 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H4a zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_Hc zenon_H83 zenon_H32 zenon_H16 zenon_H34 zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_He0 zenon_H2d zenon_Hb zenon_H116 zenon_H6e zenon_H57 zenon_He1 zenon_Hd9 zenon_H42 zenon_H15f zenon_H282 zenon_He8 zenon_H17 zenon_H18 zenon_H9b zenon_Hc8 zenon_Hb1 zenon_H81 zenon_H91 zenon_H99 zenon_Hcc zenon_Hda zenon_Ha1 zenon_Hc2 zenon_H146. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.19 apply (zenon_L272_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.19 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.19 apply (zenon_L273_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.19 apply (zenon_L274_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.19 apply (zenon_L264_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.19 apply (zenon_L178_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.19 apply (zenon_L266_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.19 apply (zenon_L476_); trivial. % 40.94/41.19 exact (zenon_H146 zenon_H144). % 40.94/41.19 (* end of lemma zenon_L477_ *) % 40.94/41.19 assert (zenon_L478_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e4) (e0)))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.19 do 0 intro. intros zenon_H19a zenon_H2d zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H16 zenon_H81 zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H92 zenon_H9b zenon_H18 zenon_H17 zenon_Hd3 zenon_He8 zenon_H282 zenon_H15f zenon_H42 zenon_Hd9 zenon_H146. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 40.94/41.19 apply (zenon_L263_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 40.94/41.19 apply (zenon_L300_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 40.94/41.19 apply (zenon_L266_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 40.94/41.19 apply (zenon_L474_); trivial. % 40.94/41.19 exact (zenon_H146 zenon_H144). % 40.94/41.19 (* end of lemma zenon_L478_ *) % 40.94/41.19 assert (zenon_L479_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> ((e1) = (op (e4) (e2))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e4) (e0)))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 40.94/41.19 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_H116 zenon_Hb zenon_He0 zenon_Hb6 zenon_H49 zenon_H1b9 zenon_H115 zenon_H11f zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hc3 zenon_Hbb zenon_H9f zenon_Hb9 zenon_H1c9 zenon_H50 zenon_H16d zenon_H41 zenon_H51 zenon_H1c8 zenon_H88 zenon_H7b zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H34 zenon_Hed zenon_He6 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hee zenon_He1 zenon_H19a zenon_H2d zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H16 zenon_H81 zenon_H20 zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H9b zenon_H18 zenon_H17 zenon_Hd3 zenon_He8 zenon_H282 zenon_H15f zenon_H42 zenon_Hd9 zenon_H146. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 40.94/41.19 apply (zenon_L272_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 40.94/41.19 exact (zenon_H1c9 zenon_H1cc). % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 40.94/41.19 apply (zenon_L273_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 40.94/41.19 apply (zenon_L274_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 40.94/41.19 apply (zenon_L12_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 40.94/41.19 apply (zenon_L477_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 40.94/41.19 apply (zenon_L112_); trivial. % 40.94/41.19 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 40.94/41.19 exact (zenon_He1 zenon_He5). % 40.94/41.19 apply (zenon_L478_); trivial. % 40.94/41.19 (* end of lemma zenon_L479_ *) % 40.94/41.19 assert (zenon_L480_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e3) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 41.04/41.20 do 0 intro. intros zenon_He0 zenon_Hb zenon_H49 zenon_H34 zenon_H32 zenon_Hd3 zenon_H1e7 zenon_H81 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_H3b zenon_H166 zenon_H42 zenon_H165 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.20 apply (zenon_L12_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.20 apply (zenon_L242_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.20 apply (zenon_L314_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.20 exact (zenon_He1 zenon_He5). % 41.04/41.20 apply (zenon_L243_); trivial. % 41.04/41.20 (* end of lemma zenon_L480_ *) % 41.04/41.20 assert (zenon_L481_ : (~((op (e3) (e1)) = (op (op (e4) (e1)) (e1)))) -> ((op (e4) (e1)) = (e3)) -> False). % 41.04/41.20 do 0 intro. intros zenon_H283 zenon_H1bf. % 41.04/41.20 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 41.04/41.20 cut (((e3) = (op (e4) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 41.04/41.20 congruence. % 41.04/41.20 apply zenon_H1c0. apply sym_equal. exact zenon_H1bf. % 41.04/41.20 apply zenon_H12. apply refl_equal. % 41.04/41.20 (* end of lemma zenon_L481_ *) % 41.04/41.20 assert (zenon_L482_ : ((op (op (e4) (e1)) (e1)) = (e4)) -> ((op (e4) (e1)) = (e3)) -> ((op (e2) (e1)) = (e4)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H284 zenon_H1bf zenon_H249 zenon_H285. % 41.04/41.20 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 41.04/41.20 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e2) (e1)) = (op (e3) (e1)))). % 41.04/41.20 intro zenon_D_pnotp. % 41.04/41.20 apply zenon_H285. % 41.04/41.20 rewrite <- zenon_D_pnotp. % 41.04/41.20 exact zenon_H62. % 41.04/41.20 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 41.04/41.20 cut (((op (e3) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H286]. % 41.04/41.20 congruence. % 41.04/41.20 cut (((op (op (e4) (e1)) (e1)) = (e4)) = ((op (e3) (e1)) = (op (e2) (e1)))). % 41.04/41.20 intro zenon_D_pnotp. % 41.04/41.20 apply zenon_H286. % 41.04/41.20 rewrite <- zenon_D_pnotp. % 41.04/41.20 exact zenon_H284. % 41.04/41.20 cut (((e4) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H24d]. % 41.04/41.20 cut (((op (op (e4) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 41.04/41.20 congruence. % 41.04/41.20 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 41.04/41.20 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (op (e4) (e1)) (e1)) = (op (e3) (e1)))). % 41.04/41.20 intro zenon_D_pnotp. % 41.04/41.20 apply zenon_H287. % 41.04/41.20 rewrite <- zenon_D_pnotp. % 41.04/41.20 exact zenon_H62. % 41.04/41.20 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 41.04/41.20 cut (((op (e3) (e1)) = (op (op (e4) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H283]. % 41.04/41.20 congruence. % 41.04/41.20 apply (zenon_L481_); trivial. % 41.04/41.20 apply zenon_H63. apply refl_equal. % 41.04/41.20 apply zenon_H63. apply refl_equal. % 41.04/41.20 apply zenon_H24d. apply sym_equal. exact zenon_H249. % 41.04/41.20 apply zenon_H63. apply refl_equal. % 41.04/41.20 apply zenon_H63. apply refl_equal. % 41.04/41.20 (* end of lemma zenon_L482_ *) % 41.04/41.20 assert (zenon_L483_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((unit) = (e0)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H24e zenon_H14d zenon_H34 zenon_H11f zenon_H16 zenon_H246 zenon_H9 zenon_H58 zenon_Hbb zenon_H22 zenon_Hb9 zenon_H284 zenon_H1bf zenon_H285. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H14c | zenon_intro zenon_H24f ]. % 41.04/41.20 apply (zenon_L216_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H247 | zenon_intro zenon_H250 ]. % 41.04/41.20 apply (zenon_L407_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H251 ]. % 41.04/41.20 apply (zenon_L119_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H19e | zenon_intro zenon_H249 ]. % 41.04/41.20 apply (zenon_L273_); trivial. % 41.04/41.20 apply (zenon_L482_); trivial. % 41.04/41.20 (* end of lemma zenon_L483_ *) % 41.04/41.20 assert (zenon_L484_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> ((op (e1) (e4)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e1)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H3b zenon_H285 zenon_H284 zenon_Hb9 zenon_H22 zenon_Hbb zenon_H58 zenon_H246 zenon_H16 zenon_H11f zenon_H34 zenon_H14d zenon_H24e zenon_Hab zenon_Hc zenon_Haa zenon_Hc8 zenon_H9a zenon_H99 zenon_H81 zenon_H1e7 zenon_Hd3 zenon_H20 zenon_H1bf zenon_Hb1. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.20 apply (zenon_L483_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.20 apply (zenon_L56_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.20 apply (zenon_L84_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.20 apply (zenon_L313_); trivial. % 41.04/41.20 apply (zenon_L290_); trivial. % 41.04/41.20 (* end of lemma zenon_L484_ *) % 41.04/41.20 assert (zenon_L485_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e3) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.20 do 0 intro. intros zenon_Hc2 zenon_H2c zenon_H17 zenon_H2d zenon_Ha1 zenon_Hb1 zenon_Haa zenon_H32 zenon_Hd3 zenon_H1e7 zenon_H81 zenon_H1f zenon_H20 zenon_Hb6 zenon_H92 zenon_Hc zenon_H91 zenon_H83 zenon_H99 zenon_H9a zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H24e zenon_H14d zenon_H34 zenon_H11f zenon_H16 zenon_H246 zenon_H58 zenon_Hbb zenon_H22 zenon_Hb9 zenon_H284 zenon_H1bf zenon_H285 zenon_H3b zenon_Hc3. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.20 apply (zenon_L53_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.20 apply (zenon_L484_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.20 apply (zenon_L323_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.20 apply (zenon_L483_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.20 apply (zenon_L287_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.20 apply (zenon_L84_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.20 apply (zenon_L67_); trivial. % 41.04/41.20 apply (zenon_L44_); trivial. % 41.04/41.20 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.20 (* end of lemma zenon_L485_ *) % 41.04/41.20 assert (zenon_L486_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> ((op (e4) (e1)) = (e3)) -> ((op (e3) (e2)) = (e4)) -> False). % 41.04/41.20 do 0 intro. intros zenon_H9f zenon_H284 zenon_H1bf zenon_H1f8. % 41.04/41.20 cut (((op (op (e4) (e1)) (e1)) = (e4)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 41.04/41.20 intro zenon_D_pnotp. % 41.04/41.20 apply zenon_H9f. % 41.04/41.20 rewrite <- zenon_D_pnotp. % 41.04/41.20 exact zenon_H284. % 41.04/41.20 cut (((e4) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1fa]. % 41.04/41.20 cut (((op (op (e4) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 41.04/41.20 congruence. % 41.04/41.20 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 41.04/41.20 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (op (e4) (e1)) (e1)) = (op (e3) (e1)))). % 41.04/41.20 intro zenon_D_pnotp. % 41.04/41.20 apply zenon_H287. % 41.04/41.20 rewrite <- zenon_D_pnotp. % 41.04/41.20 exact zenon_H62. % 41.04/41.20 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 41.04/41.20 cut (((op (e3) (e1)) = (op (op (e4) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H283]. % 41.04/41.20 congruence. % 41.04/41.20 apply (zenon_L481_); trivial. % 41.04/41.20 apply zenon_H63. apply refl_equal. % 41.04/41.20 apply zenon_H63. apply refl_equal. % 41.04/41.20 apply zenon_H1fa. apply sym_equal. exact zenon_H1f8. % 41.04/41.20 (* end of lemma zenon_L486_ *) % 41.04/41.20 assert (zenon_L487_ : (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e4) (e1)) = (e3)) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e4))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H1fe zenon_H7b zenon_H1e5 zenon_Hc3 zenon_H285 zenon_Hb9 zenon_Hbb zenon_H58 zenon_H246 zenon_H11f zenon_H34 zenon_H14d zenon_H24e zenon_H15f zenon_H42 zenon_Hc8 zenon_H9a zenon_H99 zenon_H83 zenon_Hb6 zenon_H32 zenon_Haa zenon_Hb1 zenon_Ha1 zenon_Hc2 zenon_H1bf zenon_H284 zenon_H9f zenon_H1ff zenon_H19a zenon_H17 zenon_H2d zenon_H18 zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_H92 zenon_Hc zenon_H91 zenon_H81 zenon_H16 zenon_H1f zenon_H20 zenon_H22 zenon_H50 zenon_H16d zenon_H41 zenon_H1fb zenon_Hd3 zenon_H3b zenon_H146. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1df | zenon_intro zenon_H200 ]. % 41.04/41.20 apply (zenon_L312_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H201 ]. % 41.04/41.20 apply (zenon_L485_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H202 ]. % 41.04/41.20 apply (zenon_L486_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H203 | zenon_intro zenon_H1fc ]. % 41.04/41.20 exact (zenon_H1ff zenon_H203). % 41.04/41.20 apply (zenon_L355_); trivial. % 41.04/41.20 (* end of lemma zenon_L487_ *) % 41.04/41.20 assert (zenon_L488_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> ((op (e4) (e1)) = (e3)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (e3)) = (e2)) -> ((op (e3) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e3) (e4)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e1) (e4)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 41.04/41.20 do 0 intro. intros zenon_Hd9 zenon_H146 zenon_H1fb zenon_H41 zenon_H16d zenon_H50 zenon_H18e zenon_H2c zenon_H112 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H168 zenon_H2d zenon_H19a zenon_H1ff zenon_H9f zenon_H284 zenon_H1bf zenon_Hc2 zenon_Ha1 zenon_Hb1 zenon_Hb6 zenon_H83 zenon_H15f zenon_H24e zenon_H14d zenon_H34 zenon_H11f zenon_H246 zenon_H58 zenon_Hbb zenon_Hb9 zenon_H285 zenon_Hc3 zenon_H1e5 zenon_H1fe zenon_He8 zenon_H32 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H92 zenon_H1e7 zenon_H81 zenon_H1f zenon_H20 zenon_H22 zenon_Hc8 zenon_Hd4 zenon_Hd3 zenon_H7b zenon_H42 zenon_H1c2 zenon_H91 zenon_H99 zenon_Haa zenon_Hc zenon_Hab zenon_Hcc zenon_H3b zenon_Hda. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 41.04/41.20 apply (zenon_L487_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 41.04/41.20 apply (zenon_L365_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 41.04/41.20 apply (zenon_L458_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 41.04/41.20 apply (zenon_L366_); trivial. % 41.04/41.20 exact (zenon_Hda zenon_Hde). % 41.04/41.20 (* end of lemma zenon_L488_ *) % 41.04/41.20 assert (zenon_L489_ : (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e1) (e4)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e1)) = (e4)) -> ((op (e4) (e3)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e4) (e1)) = (e3)) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e4))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e0))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H1c4 zenon_H165 zenon_He1 zenon_H57 zenon_H6e zenon_H49 zenon_Hb zenon_He0 zenon_H115 zenon_H1a9 zenon_Hda zenon_H3b zenon_Hcc zenon_Hab zenon_Hc zenon_Haa zenon_H99 zenon_H91 zenon_H42 zenon_H7b zenon_Hd3 zenon_Hd4 zenon_Hc8 zenon_H22 zenon_H20 zenon_H1f zenon_H81 zenon_H1e7 zenon_H92 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_H32 zenon_He8 zenon_H1fe zenon_H1e5 zenon_Hc3 zenon_H285 zenon_Hb9 zenon_Hbb zenon_H58 zenon_H246 zenon_H11f zenon_H34 zenon_H14d zenon_H24e zenon_H15f zenon_H83 zenon_Hb6 zenon_Hb1 zenon_Ha1 zenon_Hc2 zenon_H1bf zenon_H284 zenon_H9f zenon_H1ff zenon_H19a zenon_H2d zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_H50 zenon_H16d zenon_H41 zenon_H1fb zenon_H146 zenon_Hd9 zenon_H13e. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H166 | zenon_intro zenon_H1c5 ]. % 41.04/41.20 apply (zenon_L480_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1c6 ]. % 41.04/41.20 apply (zenon_L275_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1c7 ]. % 41.04/41.20 apply (zenon_L276_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H142 ]. % 41.04/41.20 apply (zenon_L488_); trivial. % 41.04/41.20 exact (zenon_H13e zenon_H142). % 41.04/41.20 (* end of lemma zenon_L489_ *) % 41.04/41.20 assert (zenon_L490_ : (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e1) (e4)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e1)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e4) (e1)) = (e3)) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e4))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e0))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H116 zenon_H197 zenon_H1c4 zenon_H165 zenon_He1 zenon_H57 zenon_H6e zenon_H49 zenon_Hb zenon_He0 zenon_H115 zenon_H1a9 zenon_Hda zenon_H3b zenon_Hcc zenon_Hab zenon_Hc zenon_Haa zenon_H99 zenon_H91 zenon_H42 zenon_H7b zenon_Hd3 zenon_Hd4 zenon_Hc8 zenon_H22 zenon_H20 zenon_H1f zenon_H81 zenon_H1e7 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_H32 zenon_He8 zenon_H1fe zenon_H1e5 zenon_Hc3 zenon_H285 zenon_Hb9 zenon_Hbb zenon_H58 zenon_H246 zenon_H11f zenon_H34 zenon_H14d zenon_H24e zenon_H15f zenon_H83 zenon_Hb6 zenon_Hb1 zenon_Ha1 zenon_Hc2 zenon_H1bf zenon_H284 zenon_H9f zenon_H1ff zenon_H19a zenon_H2d zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_H50 zenon_H16d zenon_H41 zenon_H1fb zenon_H146 zenon_Hd9 zenon_H13e. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.20 apply (zenon_L12_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.20 apply (zenon_L278_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.20 apply (zenon_L286_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.20 exact (zenon_He1 zenon_He5). % 41.04/41.20 apply (zenon_L489_); trivial. % 41.04/41.20 (* end of lemma zenon_L490_ *) % 41.04/41.20 assert (zenon_L491_ : (~((op (e4) (e4)) = (e0))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> ((op (e4) (e1)) = (e3)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e4)) = (e4))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e3) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H13e zenon_Hd9 zenon_H146 zenon_H1fb zenon_H41 zenon_H16d zenon_H50 zenon_H18e zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H168 zenon_H2d zenon_H19a zenon_H1ff zenon_H9f zenon_H284 zenon_H1bf zenon_Hc2 zenon_Ha1 zenon_Hb1 zenon_H15f zenon_H24e zenon_H14d zenon_H246 zenon_Hbb zenon_H285 zenon_H1e5 zenon_H1fe zenon_He8 zenon_H17 zenon_H18 zenon_H9b zenon_Hc8 zenon_Hd4 zenon_H7b zenon_H42 zenon_H91 zenon_H99 zenon_Haa zenon_Hcc zenon_Hda zenon_H1a9 zenon_He0 zenon_Hb zenon_H6e zenon_H57 zenon_He1 zenon_H165 zenon_H1c4 zenon_H197 zenon_H116 zenon_H1e7 zenon_H81 zenon_Hb9 zenon_H58 zenon_Hb6 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.20 apply (zenon_L277_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.20 apply (zenon_L490_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.20 apply (zenon_L323_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.20 apply (zenon_L285_); trivial. % 41.04/41.20 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.20 (* end of lemma zenon_L491_ *) % 41.04/41.20 assert (zenon_L492_ : (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e1)) = (e4)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e4) (e1)) = (e3)) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e4))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e0))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.20 do 0 intro. intros zenon_Hc3 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H4a zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_Hc zenon_H83 zenon_H32 zenon_H16 zenon_H34 zenon_Hb6 zenon_H58 zenon_Hb9 zenon_H81 zenon_H1e7 zenon_H116 zenon_H1c4 zenon_H165 zenon_He1 zenon_H57 zenon_H6e zenon_Hb zenon_He0 zenon_H1a9 zenon_Hda zenon_Hcc zenon_Haa zenon_H99 zenon_H91 zenon_H42 zenon_H7b zenon_Hd4 zenon_Hc8 zenon_H9b zenon_H18 zenon_H17 zenon_He8 zenon_H1fe zenon_H1e5 zenon_H285 zenon_Hbb zenon_H246 zenon_H14d zenon_H24e zenon_H15f zenon_Hb1 zenon_Ha1 zenon_Hc2 zenon_H1bf zenon_H284 zenon_H9f zenon_H1ff zenon_H19a zenon_H2d zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H18e zenon_H50 zenon_H16d zenon_H41 zenon_H1fb zenon_Hd9 zenon_H13e zenon_H146. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.20 apply (zenon_L262_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.20 apply (zenon_L316_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.20 apply (zenon_L266_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.20 apply (zenon_L491_); trivial. % 41.04/41.20 exact (zenon_H146 zenon_H144). % 41.04/41.20 (* end of lemma zenon_L492_ *) % 41.04/41.20 assert (zenon_L493_ : (~((op (e4) (e4)) = (e0))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e4)) = (e4))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e4) (e1)) = (e3)) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 41.04/41.20 do 0 intro. intros zenon_H13e zenon_Hd9 zenon_H146 zenon_H18e zenon_H2c zenon_H112 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H168 zenon_H2d zenon_H19a zenon_Hc2 zenon_Ha1 zenon_Hb1 zenon_Hb6 zenon_H83 zenon_H15f zenon_H24e zenon_H14d zenon_H34 zenon_H11f zenon_H246 zenon_H58 zenon_Hbb zenon_Hb9 zenon_H285 zenon_Hc3 zenon_H1e5 zenon_H1fe zenon_He8 zenon_H32 zenon_H17 zenon_H18 zenon_H9b zenon_Hc8 zenon_Hd4 zenon_H7b zenon_H42 zenon_H99 zenon_Haa zenon_Hab zenon_Hcc zenon_Hda zenon_H1a9 zenon_H115 zenon_He0 zenon_Hb zenon_H49 zenon_H6e zenon_H57 zenon_He1 zenon_H165 zenon_H1c4 zenon_H116 zenon_H1bf zenon_H284 zenon_H9f zenon_H1ff zenon_H3b zenon_Hd3 zenon_H1fb zenon_H41 zenon_H16d zenon_H50 zenon_H22 zenon_H20 zenon_H1f zenon_H197 zenon_H16 zenon_H81 zenon_H91 zenon_Hc. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.20 apply (zenon_L12_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.20 apply (zenon_L278_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.20 apply (zenon_L286_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.20 exact (zenon_He1 zenon_He5). % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1df | zenon_intro zenon_H200 ]. % 41.04/41.20 apply (zenon_L312_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H201 ]. % 41.04/41.20 apply (zenon_L490_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H202 ]. % 41.04/41.20 apply (zenon_L486_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H203 | zenon_intro zenon_H1fc ]. % 41.04/41.20 exact (zenon_H1ff zenon_H203). % 41.04/41.20 apply (zenon_L354_); trivial. % 41.04/41.20 (* end of lemma zenon_L493_ *) % 41.04/41.20 assert (zenon_L494_ : (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e1)) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e0))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e3) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H91 zenon_H81 zenon_H197 zenon_H50 zenon_H16d zenon_H41 zenon_H1ff zenon_H9f zenon_H284 zenon_H1bf zenon_H116 zenon_H1c4 zenon_H165 zenon_He1 zenon_H57 zenon_H6e zenon_Hb zenon_He0 zenon_H115 zenon_H1a9 zenon_Hda zenon_Hcc zenon_Haa zenon_H99 zenon_H42 zenon_H7b zenon_Hd4 zenon_Hc8 zenon_H9b zenon_H18 zenon_H17 zenon_He8 zenon_H1fe zenon_H1e5 zenon_H285 zenon_Hb9 zenon_Hbb zenon_H246 zenon_H11f zenon_H14d zenon_H24e zenon_H15f zenon_Hb1 zenon_Ha1 zenon_Hc2 zenon_H19a zenon_H2d zenon_H168 zenon_H112 zenon_H2c zenon_H18e zenon_H146 zenon_Hd9 zenon_H13e zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1fb zenon_Hd3 zenon_H1fc zenon_H3b zenon_Hc3. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.20 apply (zenon_L277_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.20 apply (zenon_L493_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.20 apply (zenon_L279_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.20 apply (zenon_L334_); trivial. % 41.04/41.20 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.20 (* end of lemma zenon_L494_ *) % 41.04/41.20 assert (zenon_L495_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (e4)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e4) (e4)) = (e0))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e4)) = (e4))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e4) (e1)) = (e3)) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.20 do 0 intro. intros zenon_Hee zenon_Hba zenon_He9 zenon_He6 zenon_Hed zenon_H73 zenon_H77 zenon_H87 zenon_H88 zenon_Hc3 zenon_H3b zenon_H1fc zenon_Hd3 zenon_H1fb zenon_H4a zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_Hc zenon_H83 zenon_H32 zenon_H16 zenon_H34 zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H13e zenon_Hd9 zenon_H18e zenon_H2c zenon_H112 zenon_H168 zenon_H2d zenon_H19a zenon_Hc2 zenon_Ha1 zenon_Hb1 zenon_H15f zenon_H24e zenon_H14d zenon_H11f zenon_H246 zenon_Hbb zenon_Hb9 zenon_H285 zenon_H1e5 zenon_H1fe zenon_He8 zenon_H17 zenon_H18 zenon_H9b zenon_Hc8 zenon_Hd4 zenon_H7b zenon_H42 zenon_H99 zenon_Haa zenon_Hcc zenon_Hda zenon_H1a9 zenon_H115 zenon_He0 zenon_Hb zenon_H6e zenon_H57 zenon_He1 zenon_H165 zenon_H1c4 zenon_H116 zenon_H1bf zenon_H284 zenon_H9f zenon_H1ff zenon_H41 zenon_H16d zenon_H50 zenon_H81 zenon_H91 zenon_H146. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.20 apply (zenon_L264_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.20 apply (zenon_L167_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.20 apply (zenon_L266_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.20 apply (zenon_L494_); trivial. % 41.04/41.20 exact (zenon_H146 zenon_H144). % 41.04/41.20 (* end of lemma zenon_L495_ *) % 41.04/41.20 assert (zenon_L496_ : (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e4) (e4)) = (e0))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e4)) = (e4))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e4) (e1)) = (e3)) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H1b9 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hee zenon_Hba zenon_He9 zenon_He6 zenon_Hed zenon_H73 zenon_H77 zenon_H87 zenon_H88 zenon_Hc3 zenon_H3b zenon_Hd3 zenon_H1fb zenon_H4a zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_Hc zenon_H83 zenon_H32 zenon_H16 zenon_H34 zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H13e zenon_Hd9 zenon_H18e zenon_H2c zenon_H112 zenon_H168 zenon_H2d zenon_H19a zenon_Hc2 zenon_Ha1 zenon_Hb1 zenon_H15f zenon_H24e zenon_H14d zenon_H11f zenon_H246 zenon_Hbb zenon_Hb9 zenon_H285 zenon_H1e5 zenon_H1fe zenon_He8 zenon_H17 zenon_H18 zenon_H9b zenon_Hc8 zenon_Hd4 zenon_H7b zenon_H42 zenon_H99 zenon_Haa zenon_Hcc zenon_Hda zenon_H1a9 zenon_H115 zenon_He0 zenon_Hb zenon_H6e zenon_H57 zenon_He1 zenon_H165 zenon_H1c4 zenon_H116 zenon_H1bf zenon_H284 zenon_H9f zenon_H1ff zenon_H41 zenon_H16d zenon_H50 zenon_H81 zenon_H91 zenon_H146. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1df | zenon_intro zenon_H200 ]. % 41.04/41.20 apply (zenon_L312_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H201 ]. % 41.04/41.20 apply (zenon_L492_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H202 ]. % 41.04/41.20 apply (zenon_L486_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H203 | zenon_intro zenon_H1fc ]. % 41.04/41.20 exact (zenon_H1ff zenon_H203). % 41.04/41.20 apply (zenon_L495_); trivial. % 41.04/41.20 (* end of lemma zenon_L496_ *) % 41.04/41.20 assert (zenon_L497_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e4) (e4)) = (e0))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e4)) = (e4))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H1c8 zenon_H51 zenon_H1c9 zenon_H1b9 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hee zenon_Hba zenon_He9 zenon_He6 zenon_Hed zenon_H73 zenon_H77 zenon_H87 zenon_H88 zenon_Hc3 zenon_H3b zenon_Hd3 zenon_H1fb zenon_H4a zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_Hc zenon_H83 zenon_H32 zenon_H16 zenon_H34 zenon_H58 zenon_Hb6 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H13e zenon_Hd9 zenon_H18e zenon_H2c zenon_H112 zenon_H168 zenon_H2d zenon_H19a zenon_Hc2 zenon_Ha1 zenon_Hb1 zenon_H15f zenon_H24e zenon_H14d zenon_H11f zenon_H246 zenon_Hbb zenon_Hb9 zenon_H285 zenon_H1e5 zenon_H1fe zenon_He8 zenon_H17 zenon_H18 zenon_H9b zenon_Hc8 zenon_Hd4 zenon_H7b zenon_H42 zenon_H99 zenon_Haa zenon_Hcc zenon_Hda zenon_H1a9 zenon_H115 zenon_He0 zenon_Hb zenon_H6e zenon_H57 zenon_He1 zenon_H165 zenon_H1c4 zenon_H116 zenon_H284 zenon_H9f zenon_H1ff zenon_H41 zenon_H16d zenon_H50 zenon_H81 zenon_H91 zenon_H146. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 41.04/41.20 apply (zenon_L272_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 41.04/41.20 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 41.04/41.20 apply (zenon_L273_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 41.04/41.20 apply (zenon_L274_); trivial. % 41.04/41.20 apply (zenon_L496_); trivial. % 41.04/41.20 (* end of lemma zenon_L497_ *) % 41.04/41.20 assert (zenon_L498_ : (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e4))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> ((op (e3) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e4)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e4) (e3)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.20 do 0 intro. intros zenon_Haa zenon_Hd4 zenon_H1fe zenon_H1e5 zenon_H285 zenon_Hbb zenon_H246 zenon_H14d zenon_H24e zenon_Ha1 zenon_Hc2 zenon_H284 zenon_H9f zenon_H1ff zenon_H19a zenon_H2d zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H18e zenon_H50 zenon_H16d zenon_H41 zenon_H1fb zenon_H146 zenon_H1e7 zenon_H81 zenon_Hb9 zenon_H58 zenon_Hb6 zenon_Hda zenon_H3b zenon_Hcc zenon_H99 zenon_H91 zenon_H1c2 zenon_H42 zenon_H7b zenon_H20 zenon_H1bf zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H22 zenon_H1f zenon_Hc zenon_H83 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_Hd3 zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H92 zenon_Hd9 zenon_Hc3. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.20 apply (zenon_L53_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.20 apply (zenon_L488_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.20 apply (zenon_L323_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.20 apply (zenon_L294_); trivial. % 41.04/41.20 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.20 (* end of lemma zenon_L498_ *) % 41.04/41.20 assert (zenon_L499_ : (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e4) (e3)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e1)) = (e4)) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e4)) = (e0))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H1c4 zenon_H165 zenon_H1a9 zenon_Hc3 zenon_Hd9 zenon_H92 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_He8 zenon_Hd3 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H83 zenon_Hc zenon_H1f zenon_H22 zenon_H32 zenon_Hc8 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H7b zenon_H42 zenon_H91 zenon_H99 zenon_Hcc zenon_H3b zenon_Hda zenon_Hb6 zenon_H58 zenon_Hb9 zenon_H81 zenon_H1e7 zenon_H146 zenon_H1fb zenon_H41 zenon_H16d zenon_H50 zenon_H18e zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H168 zenon_H2d zenon_H19a zenon_H1ff zenon_H9f zenon_H284 zenon_Hc2 zenon_Ha1 zenon_H24e zenon_H14d zenon_H246 zenon_Hbb zenon_H285 zenon_H1e5 zenon_H1fe zenon_Hd4 zenon_Haa zenon_H13e. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H166 | zenon_intro zenon_H1c5 ]. % 41.04/41.20 apply (zenon_L243_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1c6 ]. % 41.04/41.20 apply (zenon_L275_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1c7 ]. % 41.04/41.20 apply (zenon_L276_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H142 ]. % 41.04/41.20 apply (zenon_L498_); trivial. % 41.04/41.20 exact (zenon_H13e zenon_H142). % 41.04/41.20 (* end of lemma zenon_L499_ *) % 41.04/41.20 assert (zenon_L500_ : (~((op (e4) (e4)) = (e0))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> ((op (e4) (e1)) = (e3)) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e4))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H13e zenon_Haa zenon_Hd4 zenon_H1fe zenon_H1e5 zenon_H285 zenon_Hbb zenon_H246 zenon_H14d zenon_H24e zenon_Ha1 zenon_Hc2 zenon_Hb9 zenon_H58 zenon_Hb6 zenon_Hda zenon_Hcc zenon_H99 zenon_H42 zenon_H7b zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H83 zenon_H9b zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_Hd9 zenon_Hc3 zenon_H1a9 zenon_H165 zenon_H1c4 zenon_H1bf zenon_H284 zenon_H9f zenon_H1ff zenon_H19a zenon_H17 zenon_H2d zenon_H18 zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_H92 zenon_Hc zenon_H91 zenon_H81 zenon_H16 zenon_H1f zenon_H20 zenon_H22 zenon_H50 zenon_H16d zenon_H41 zenon_H1fb zenon_Hd3 zenon_H3b zenon_H146. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1df | zenon_intro zenon_H200 ]. % 41.04/41.20 apply (zenon_L312_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H201 ]. % 41.04/41.20 apply (zenon_L499_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H202 ]. % 41.04/41.20 apply (zenon_L486_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H203 | zenon_intro zenon_H1fc ]. % 41.04/41.20 exact (zenon_H1ff zenon_H203). % 41.04/41.20 apply (zenon_L355_); trivial. % 41.04/41.20 (* end of lemma zenon_L500_ *) % 41.04/41.20 assert (zenon_L501_ : (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e4) (e4)) = (e0))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e4))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H116 zenon_Hb zenon_He0 zenon_H49 zenon_H1c9 zenon_H51 zenon_H1c8 zenon_H88 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_Hed zenon_He6 zenon_He9 zenon_Hba zenon_Hee zenon_He1 zenon_H13e zenon_Haa zenon_Hd4 zenon_H1fe zenon_H1e5 zenon_H285 zenon_Hbb zenon_H246 zenon_H14d zenon_H24e zenon_Ha1 zenon_Hc2 zenon_Hb9 zenon_H58 zenon_Hb6 zenon_Hda zenon_Hcc zenon_H99 zenon_H42 zenon_H7b zenon_Hb1 zenon_Hc8 zenon_H32 zenon_H83 zenon_H9b zenon_He8 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_Hd9 zenon_Hc3 zenon_H1a9 zenon_H165 zenon_H1c4 zenon_H284 zenon_H9f zenon_H1ff zenon_H19a zenon_H17 zenon_H2d zenon_H18 zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_Hc zenon_H91 zenon_H81 zenon_H16 zenon_H1f zenon_H20 zenon_H22 zenon_H50 zenon_H16d zenon_H41 zenon_H1fb zenon_Hd3 zenon_H3b zenon_H146. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 41.04/41.20 apply (zenon_L272_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 41.04/41.20 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 41.04/41.20 apply (zenon_L273_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 41.04/41.20 apply (zenon_L274_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.20 apply (zenon_L12_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.20 apply (zenon_L497_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.20 apply (zenon_L112_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.20 exact (zenon_He1 zenon_He5). % 41.04/41.20 apply (zenon_L500_); trivial. % 41.04/41.20 (* end of lemma zenon_L501_ *) % 41.04/41.20 assert (zenon_L502_ : (~((op (op (e4) (e2)) (e4)) = (e2))) -> ((op (e1) (e4)) = (e2)) -> ((e1) = (op (e4) (e2))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H288 zenon_Hab zenon_H34. % 41.04/41.20 cut (((op (e1) (e4)) = (e2)) = ((op (op (e4) (e2)) (e4)) = (e2))). % 41.04/41.20 intro zenon_D_pnotp. % 41.04/41.20 apply zenon_H288. % 41.04/41.20 rewrite <- zenon_D_pnotp. % 41.04/41.20 exact zenon_Hab. % 41.04/41.20 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.04/41.20 cut (((op (e1) (e4)) = (op (op (e4) (e2)) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H289]. % 41.04/41.20 congruence. % 41.04/41.20 elim (classic ((op (op (e4) (e2)) (e4)) = (op (op (e4) (e2)) (e4)))); [ zenon_intro zenon_H28a | zenon_intro zenon_H28b ]. % 41.04/41.20 cut (((op (op (e4) (e2)) (e4)) = (op (op (e4) (e2)) (e4))) = ((op (e1) (e4)) = (op (op (e4) (e2)) (e4)))). % 41.04/41.20 intro zenon_D_pnotp. % 41.04/41.20 apply zenon_H289. % 41.04/41.20 rewrite <- zenon_D_pnotp. % 41.04/41.20 exact zenon_H28a. % 41.04/41.20 cut (((op (op (e4) (e2)) (e4)) = (op (op (e4) (e2)) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H28b]. % 41.04/41.20 cut (((op (op (e4) (e2)) (e4)) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H28c]. % 41.04/41.20 congruence. % 41.04/41.20 cut (((e4) = (e4))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 41.04/41.20 cut (((op (e4) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 41.04/41.20 congruence. % 41.04/41.20 apply zenon_H11e. apply sym_equal. exact zenon_H34. % 41.04/41.20 apply zenon_H97. apply refl_equal. % 41.04/41.20 apply zenon_H28b. apply refl_equal. % 41.04/41.20 apply zenon_H28b. apply refl_equal. % 41.04/41.20 apply zenon_H7. apply refl_equal. % 41.04/41.20 (* end of lemma zenon_L502_ *) % 41.04/41.20 assert (zenon_L503_ : (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (op (e4) (e2)) (e4)) = (e2))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((unit) = (e0)) -> False). % 41.04/41.20 do 0 intro. intros zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H34 zenon_H288 zenon_H22 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H9. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1ba ]. % 41.04/41.20 apply (zenon_L275_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H113 | zenon_intro zenon_H1bb ]. % 41.04/41.20 apply (zenon_L164_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_Hab | zenon_intro zenon_H1bc ]. % 41.04/41.20 apply (zenon_L502_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H1af | zenon_intro zenon_H1b4 ]. % 41.04/41.20 apply (zenon_L281_); trivial. % 41.04/41.20 apply (zenon_L283_); trivial. % 41.04/41.20 (* end of lemma zenon_L503_ *) % 41.04/41.20 assert (zenon_L504_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (op (e4) (e2)) (e4)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H288 zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H4a zenon_Hc zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_H161 zenon_H16d zenon_H50 zenon_H32 zenon_H16 zenon_H34. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.20 apply (zenon_L503_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.20 apply (zenon_L17_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.20 apply (zenon_L8_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.20 apply (zenon_L350_); trivial. % 41.04/41.20 apply (zenon_L11_); trivial. % 41.04/41.20 (* end of lemma zenon_L504_ *) % 41.04/41.20 assert (zenon_L505_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (op (e4) (e2)) (e4)) = (e2))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 41.04/41.20 do 0 intro. intros zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H288 zenon_H34 zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H41 zenon_H16d zenon_H50 zenon_H22 zenon_H20 zenon_H1f zenon_Hbf zenon_H83 zenon_H91 zenon_Hc zenon_H92. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.20 apply (zenon_L503_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.20 apply (zenon_L249_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.20 apply (zenon_L8_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.20 apply (zenon_L67_); trivial. % 41.04/41.20 apply (zenon_L44_); trivial. % 41.04/41.20 (* end of lemma zenon_L505_ *) % 41.04/41.20 assert (zenon_L506_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (op (e4) (e2)) (e4)) = (e2))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.20 do 0 intro. intros zenon_Hc2 zenon_H17 zenon_H2d zenon_H18 zenon_Ha1 zenon_H16 zenon_H32 zenon_H58 zenon_Hb9 zenon_Hb6 zenon_H92 zenon_Hc zenon_H91 zenon_H83 zenon_H1f zenon_H20 zenon_H22 zenon_H50 zenon_H16d zenon_H41 zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H34 zenon_H288 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.20 apply (zenon_L53_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.20 apply (zenon_L502_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.20 apply (zenon_L123_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.20 apply (zenon_L505_); trivial. % 41.04/41.20 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.20 (* end of lemma zenon_L506_ *) % 41.04/41.20 assert (zenon_L507_ : ((~((op (e2) (e4)) = (op (e4) (e2))))/\(((op (op (e4) (e2)) (e2)) = (e4))/\(~((op (op (e4) (e2)) (e4)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H28d zenon_He0 zenon_Hb zenon_H161 zenon_H49 zenon_H88 zenon_H7b zenon_H81 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H61 zenon_H5f zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_Hc2 zenon_H17 zenon_H2d zenon_H18 zenon_Ha1 zenon_H16 zenon_H32 zenon_H58 zenon_Hb9 zenon_Hb6 zenon_Hc zenon_H91 zenon_H83 zenon_H1f zenon_H20 zenon_H22 zenon_H50 zenon_H16d zenon_H41 zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H34 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.20 apply (zenon_and_s _ _ zenon_H28d). zenon_intro zenon_H28f. zenon_intro zenon_H28e. % 41.04/41.20 apply (zenon_and_s _ _ zenon_H28e). zenon_intro zenon_H290. zenon_intro zenon_H288. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.20 apply (zenon_L12_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.20 apply (zenon_L504_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.20 apply (zenon_L112_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.20 exact (zenon_He1 zenon_He5). % 41.04/41.20 apply (zenon_L506_); trivial. % 41.04/41.20 (* end of lemma zenon_L507_ *) % 41.04/41.20 assert (zenon_L508_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> ((op (e0) (e3)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H3b zenon_H169 zenon_H1f1 zenon_Hd3 zenon_H41 zenon_H22 zenon_H20 zenon_H1f zenon_H161 zenon_H16d zenon_H50 zenon_H32 zenon_H16 zenon_H34. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.20 apply (zenon_L319_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.20 apply (zenon_L249_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.20 apply (zenon_L8_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.20 apply (zenon_L350_); trivial. % 41.04/41.20 apply (zenon_L11_); trivial. % 41.04/41.20 (* end of lemma zenon_L508_ *) % 41.04/41.20 assert (zenon_L509_ : (~((op (e0) (e3)) = (op (op (e4) (e3)) (e3)))) -> ((op (e4) (e3)) = (e0)) -> False). % 41.04/41.20 do 0 intro. intros zenon_H291 zenon_H292. % 41.04/41.20 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 41.04/41.20 cut (((e0) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H293]. % 41.04/41.20 congruence. % 41.04/41.20 apply zenon_H293. apply sym_equal. exact zenon_H292. % 41.04/41.20 apply zenon_H1e. apply refl_equal. % 41.04/41.20 (* end of lemma zenon_L509_ *) % 41.04/41.20 assert (zenon_L510_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (op (e4) (e3)) (e3)) = (e4)) -> ((op (e4) (e3)) = (e0)) -> ((op (e1) (e3)) = (e4)) -> False). % 41.04/41.20 do 0 intro. intros zenon_H220 zenon_H294 zenon_H292 zenon_H22b. % 41.04/41.20 cut (((op (op (e4) (e3)) (e3)) = (e4)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 41.04/41.20 intro zenon_D_pnotp. % 41.04/41.20 apply zenon_H220. % 41.04/41.20 rewrite <- zenon_D_pnotp. % 41.04/41.20 exact zenon_H294. % 41.04/41.20 cut (((e4) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H232]. % 41.04/41.20 cut (((op (op (e4) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H295]. % 41.04/41.20 congruence. % 41.04/41.20 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 41.04/41.20 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (op (e4) (e3)) (e3)) = (op (e0) (e3)))). % 41.04/41.20 intro zenon_D_pnotp. % 41.04/41.20 apply zenon_H295. % 41.04/41.20 rewrite <- zenon_D_pnotp. % 41.04/41.20 exact zenon_H52. % 41.04/41.20 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 41.04/41.20 cut (((op (e0) (e3)) = (op (op (e4) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H291]. % 41.04/41.20 congruence. % 41.04/41.20 apply (zenon_L509_); trivial. % 41.04/41.20 apply zenon_H53. apply refl_equal. % 41.04/41.20 apply zenon_H53. apply refl_equal. % 41.04/41.20 apply zenon_H232. apply sym_equal. exact zenon_H22b. % 41.04/41.20 (* end of lemma zenon_L510_ *) % 41.04/41.20 assert (zenon_L511_ : ((e3) = (op (e2) (e4))) -> ((op (e4) (e3)) = (e2)) -> (~((op (op (e4) (e3)) (e4)) = (e3))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H22 zenon_H92 zenon_H296. % 41.04/41.20 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H18f | zenon_intro zenon_H1e ]. % 41.04/41.20 cut (((e3) = (e3)) = ((op (op (e4) (e3)) (e4)) = (e3))). % 41.04/41.20 intro zenon_D_pnotp. % 41.04/41.20 apply zenon_H296. % 41.04/41.20 rewrite <- zenon_D_pnotp. % 41.04/41.20 exact zenon_H18f. % 41.04/41.20 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 41.04/41.20 cut (((e3) = (op (op (e4) (e3)) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H297]. % 41.04/41.20 congruence. % 41.04/41.20 cut (((e3) = (op (e2) (e4))) = ((e3) = (op (op (e4) (e3)) (e4)))). % 41.04/41.20 intro zenon_D_pnotp. % 41.04/41.20 apply zenon_H297. % 41.04/41.20 rewrite <- zenon_D_pnotp. % 41.04/41.20 exact zenon_H22. % 41.04/41.20 cut (((op (e2) (e4)) = (op (op (e4) (e3)) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H298]. % 41.04/41.20 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 41.04/41.20 congruence. % 41.04/41.20 apply zenon_H1e. apply refl_equal. % 41.04/41.20 cut (((e4) = (e4))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 41.04/41.20 cut (((e2) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H93]. % 41.04/41.20 congruence. % 41.04/41.20 apply zenon_H93. apply sym_equal. exact zenon_H92. % 41.04/41.20 apply zenon_H97. apply refl_equal. % 41.04/41.20 apply zenon_H1e. apply refl_equal. % 41.04/41.20 apply zenon_H1e. apply refl_equal. % 41.04/41.20 (* end of lemma zenon_L511_ *) % 41.04/41.20 assert (zenon_L512_ : (~((op (e0) (e3)) = (op (e4) (e3)))) -> ((op (unit) (e3)) = (e3)) -> ((unit) = (e0)) -> ((op (e4) (e3)) = (e3)) -> False). % 41.04/41.20 do 0 intro. intros zenon_H299 zenon_H20 zenon_H9 zenon_H29a. % 41.04/41.20 cut (((op (unit) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e4) (e3)))). % 41.04/41.20 intro zenon_D_pnotp. % 41.04/41.20 apply zenon_H299. % 41.04/41.20 rewrite <- zenon_D_pnotp. % 41.04/41.20 exact zenon_H20. % 41.04/41.20 cut (((e3) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H29b]. % 41.04/41.20 cut (((op (unit) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 41.04/41.20 congruence. % 41.04/41.20 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 41.04/41.20 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (unit) (e3)) = (op (e0) (e3)))). % 41.04/41.20 intro zenon_D_pnotp. % 41.04/41.20 apply zenon_H195. % 41.04/41.20 rewrite <- zenon_D_pnotp. % 41.04/41.20 exact zenon_H52. % 41.04/41.20 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 41.04/41.20 cut (((op (e0) (e3)) = (op (unit) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 41.04/41.20 congruence. % 41.04/41.20 apply (zenon_L267_); trivial. % 41.04/41.20 apply zenon_H53. apply refl_equal. % 41.04/41.20 apply zenon_H53. apply refl_equal. % 41.04/41.20 apply zenon_H29b. apply sym_equal. exact zenon_H29a. % 41.04/41.20 (* end of lemma zenon_L512_ *) % 41.04/41.20 assert (zenon_L513_ : (((op (e4) (e3)) = (e0))\/(((op (e4) (e3)) = (e1))\/(((op (e4) (e3)) = (e2))\/(((op (e4) (e3)) = (e3))\/((op (e4) (e3)) = (e4)))))) -> ((op (e1) (e3)) = (e4)) -> ((op (op (e4) (e3)) (e3)) = (e4)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((e1) = (op (e4) (e2))) -> (~((op (op (e4) (e3)) (e4)) = (e3))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((unit) = (e0)) -> False). % 41.04/41.20 do 0 intro. intros zenon_H29c zenon_H22b zenon_H294 zenon_H220 zenon_H91 zenon_H34 zenon_H296 zenon_H22 zenon_H20 zenon_H299 zenon_Hcc zenon_H99 zenon_H9. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H29c); [ zenon_intro zenon_H292 | zenon_intro zenon_H29d ]. % 41.04/41.20 apply (zenon_L510_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H29d); [ zenon_intro zenon_H233 | zenon_intro zenon_H29e ]. % 41.04/41.20 apply (zenon_L385_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H29e); [ zenon_intro zenon_H92 | zenon_intro zenon_H29f ]. % 41.04/41.20 apply (zenon_L511_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H29f); [ zenon_intro zenon_H29a | zenon_intro zenon_Hcd ]. % 41.04/41.20 apply (zenon_L512_); trivial. % 41.04/41.20 apply (zenon_L74_); trivial. % 41.04/41.20 (* end of lemma zenon_L513_ *) % 41.04/41.20 assert (zenon_L514_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e0) (e3)) = (op (e4) (e3)))) -> (~((op (op (e4) (e3)) (e4)) = (e3))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (op (e4) (e3)) (e3)) = (e4)) -> ((op (e1) (e3)) = (e4)) -> (((op (e4) (e3)) = (e0))\/(((op (e4) (e3)) = (e1))\/(((op (e4) (e3)) = (e2))\/(((op (e4) (e3)) = (e3))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H3b zenon_H99 zenon_Hcc zenon_H299 zenon_H296 zenon_H91 zenon_H220 zenon_H294 zenon_H22b zenon_H29c zenon_H41 zenon_H22 zenon_H20 zenon_H1f zenon_H161 zenon_H16d zenon_H50 zenon_H32 zenon_H16 zenon_H34. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.20 apply (zenon_L513_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.20 apply (zenon_L249_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.20 apply (zenon_L8_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.20 apply (zenon_L350_); trivial. % 41.04/41.20 apply (zenon_L11_); trivial. % 41.04/41.20 (* end of lemma zenon_L514_ *) % 41.04/41.20 assert (zenon_L515_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (op (e4) (e3)) (e3)) = (e4)) -> ((op (e4) (e3)) = (e0)) -> ((op (e2) (e3)) = (e4)) -> False). % 41.04/41.20 do 0 intro. intros zenon_H2a0 zenon_H294 zenon_H292 zenon_H2a1. % 41.04/41.20 cut (((op (op (e4) (e3)) (e3)) = (e4)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 41.04/41.20 intro zenon_D_pnotp. % 41.04/41.20 apply zenon_H2a0. % 41.04/41.20 rewrite <- zenon_D_pnotp. % 41.04/41.20 exact zenon_H294. % 41.04/41.20 cut (((e4) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2a2]. % 41.04/41.20 cut (((op (op (e4) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H295]. % 41.04/41.20 congruence. % 41.04/41.20 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 41.04/41.20 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (op (e4) (e3)) (e3)) = (op (e0) (e3)))). % 41.04/41.20 intro zenon_D_pnotp. % 41.04/41.20 apply zenon_H295. % 41.04/41.20 rewrite <- zenon_D_pnotp. % 41.04/41.20 exact zenon_H52. % 41.04/41.20 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 41.04/41.20 cut (((op (e0) (e3)) = (op (op (e4) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H291]. % 41.04/41.20 congruence. % 41.04/41.20 apply (zenon_L509_); trivial. % 41.04/41.20 apply zenon_H53. apply refl_equal. % 41.04/41.20 apply zenon_H53. apply refl_equal. % 41.04/41.20 apply zenon_H2a2. apply sym_equal. exact zenon_H2a1. % 41.04/41.20 (* end of lemma zenon_L515_ *) % 41.04/41.20 assert (zenon_L516_ : (((op (e4) (e3)) = (e0))\/(((op (e4) (e3)) = (e1))\/(((op (e4) (e3)) = (e2))\/(((op (e4) (e3)) = (e3))\/((op (e4) (e3)) = (e4)))))) -> ((op (e2) (e3)) = (e4)) -> ((op (op (e4) (e3)) (e3)) = (e4)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((e1) = (op (e4) (e2))) -> (~((op (op (e4) (e3)) (e4)) = (e3))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((unit) = (e0)) -> False). % 41.04/41.20 do 0 intro. intros zenon_H29c zenon_H2a1 zenon_H294 zenon_H2a0 zenon_H91 zenon_H34 zenon_H296 zenon_H22 zenon_H20 zenon_H299 zenon_Hcc zenon_H99 zenon_H9. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H29c); [ zenon_intro zenon_H292 | zenon_intro zenon_H29d ]. % 41.04/41.20 apply (zenon_L515_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H29d); [ zenon_intro zenon_H233 | zenon_intro zenon_H29e ]. % 41.04/41.20 apply (zenon_L385_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H29e); [ zenon_intro zenon_H92 | zenon_intro zenon_H29f ]. % 41.04/41.20 apply (zenon_L511_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H29f); [ zenon_intro zenon_H29a | zenon_intro zenon_Hcd ]. % 41.04/41.20 apply (zenon_L512_); trivial. % 41.04/41.20 apply (zenon_L74_); trivial. % 41.04/41.20 (* end of lemma zenon_L516_ *) % 41.04/41.20 assert (zenon_L517_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e0) (e3)) = (op (e4) (e3)))) -> (~((op (op (e4) (e3)) (e4)) = (e3))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (op (e4) (e3)) (e3)) = (e4)) -> ((op (e2) (e3)) = (e4)) -> (((op (e4) (e3)) = (e0))\/(((op (e4) (e3)) = (e1))\/(((op (e4) (e3)) = (e2))\/(((op (e4) (e3)) = (e3))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H3b zenon_H99 zenon_Hcc zenon_H299 zenon_H296 zenon_H91 zenon_H2a0 zenon_H294 zenon_H2a1 zenon_H29c zenon_H41 zenon_H22 zenon_H20 zenon_H1f zenon_H161 zenon_H16d zenon_H50 zenon_H32 zenon_H16 zenon_H34. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.20 apply (zenon_L516_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.20 apply (zenon_L249_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.20 apply (zenon_L8_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.20 apply (zenon_L350_); trivial. % 41.04/41.20 apply (zenon_L11_); trivial. % 41.04/41.20 (* end of lemma zenon_L517_ *) % 41.04/41.20 assert (zenon_L518_ : ((~((op (e3) (e4)) = (op (e4) (e3))))/\(((op (op (e4) (e3)) (e3)) = (e4))/\(~((op (op (e4) (e3)) (e4)) = (e3))))) -> (((op (e0) (e3)) = (e4))\/(((op (e1) (e3)) = (e4))\/(((op (e2) (e3)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e4) (e3)) = (e0))\/(((op (e4) (e3)) = (e1))\/(((op (e4) (e3)) = (e2))\/(((op (e4) (e3)) = (e3))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e4) (e3)))) -> (~((op (e3) (e3)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H2a3 zenon_H2a4 zenon_H169 zenon_H220 zenon_H34 zenon_H16 zenon_H32 zenon_H50 zenon_H16d zenon_H161 zenon_H1f zenon_H20 zenon_H22 zenon_H41 zenon_H29c zenon_H2a0 zenon_H299 zenon_H1ff zenon_H3b zenon_Hcc zenon_Hb1 zenon_H99 zenon_H91 zenon_H57 zenon_Hba zenon_H58 zenon_Hd3 zenon_Hd4. % 41.04/41.20 apply (zenon_and_s _ _ zenon_H2a3). zenon_intro zenon_H2a6. zenon_intro zenon_H2a5. % 41.04/41.20 apply (zenon_and_s _ _ zenon_H2a5). zenon_intro zenon_H294. zenon_intro zenon_H296. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H1f1 | zenon_intro zenon_H2a7 ]. % 41.04/41.20 apply (zenon_L508_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H22b | zenon_intro zenon_H2a8 ]. % 41.04/41.20 apply (zenon_L514_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H2a1 | zenon_intro zenon_H2a9 ]. % 41.04/41.20 apply (zenon_L517_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H203 | zenon_intro zenon_Hcd ]. % 41.04/41.20 exact (zenon_H1ff zenon_H203). % 41.04/41.20 apply (zenon_L81_); trivial. % 41.04/41.20 (* end of lemma zenon_L518_ *) % 41.04/41.20 assert (zenon_L519_ : ((~((op (e4) (e4)) = (op (e4) (e4))))/\(((op (op (e4) (e4)) (e4)) = (e4))/\(~((op (op (e4) (e4)) (e4)) = (e4))))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H2aa. % 41.04/41.20 apply (zenon_and_s _ _ zenon_H2aa). zenon_intro zenon_Hd6. zenon_intro zenon_H2ab. % 41.04/41.20 apply zenon_Hd6. apply refl_equal. % 41.04/41.20 (* end of lemma zenon_L519_ *) % 41.04/41.20 assert (zenon_L520_ : (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((e0) = (e3))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (e4) (e1)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e0))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H1c4 zenon_H2c zenon_H2d zenon_H1f zenon_H20 zenon_H49 zenon_Hc zenon_H4a zenon_H165 zenon_H115 zenon_H34 zenon_H11f zenon_H1a9 zenon_H22 zenon_He8 zenon_Ha5 zenon_Hd3 zenon_H7b zenon_H42 zenon_H99 zenon_H32 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H3b zenon_H13e. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H166 | zenon_intro zenon_H1c5 ]. % 41.04/41.20 apply (zenon_L242_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1c6 ]. % 41.04/41.20 apply (zenon_L275_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1c7 ]. % 41.04/41.20 apply (zenon_L276_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H142 ]. % 41.04/41.20 apply (zenon_L365_); trivial. % 41.04/41.20 exact (zenon_H13e zenon_H142). % 41.04/41.20 (* end of lemma zenon_L520_ *) % 41.04/41.20 assert (zenon_L521_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H3b zenon_H7b zenon_H7c zenon_H5f zenon_H81 zenon_Hb1 zenon_Ha5 zenon_H99 zenon_H32 zenon_H16 zenon_H34. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.20 apply (zenon_L35_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.20 apply (zenon_L36_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.20 apply (zenon_L58_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.20 apply (zenon_L60_); trivial. % 41.04/41.20 apply (zenon_L11_); trivial. % 41.04/41.20 (* end of lemma zenon_L521_ *) % 41.04/41.20 assert (zenon_L522_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H88 zenon_H68 zenon_H61 zenon_H73 zenon_H1f zenon_H22 zenon_H6e zenon_H58 zenon_H59 zenon_H57 zenon_H20 zenon_H77 zenon_H9f zenon_H8e zenon_H89 zenon_H3b zenon_H7b zenon_H5f zenon_H81 zenon_Hb1 zenon_Ha5 zenon_H99 zenon_H32 zenon_H16 zenon_H34. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H60 | zenon_intro zenon_H8a ]. % 41.04/41.20 apply (zenon_L27_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H72 | zenon_intro zenon_H8b ]. % 41.04/41.20 apply (zenon_L31_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H8b); [ zenon_intro zenon_H76 | zenon_intro zenon_H8c ]. % 41.04/41.20 apply (zenon_L113_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H8d | zenon_intro zenon_H7c ]. % 41.04/41.20 exact (zenon_H89 zenon_H8d). % 41.04/41.20 apply (zenon_L521_); trivial. % 41.04/41.20 (* end of lemma zenon_L522_ *) % 41.04/41.20 assert (zenon_L523_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e4) (e4)) = (e0))) -> ((op (unit) (e0)) = (e0)) -> (~((e0) = (e3))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (e4) (e1)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.20 do 0 intro. intros zenon_He0 zenon_Hb zenon_H13e zenon_H42 zenon_H1a9 zenon_H11f zenon_H115 zenon_H165 zenon_H49 zenon_H1c4 zenon_H81 zenon_H5f zenon_H7b zenon_H89 zenon_H8e zenon_H9f zenon_H77 zenon_H57 zenon_H6e zenon_H73 zenon_H61 zenon_H68 zenon_H88 zenon_He1 zenon_Hc2 zenon_H2c zenon_H2d zenon_Ha1 zenon_H91 zenon_Hb1 zenon_Haa zenon_H34 zenon_H1f zenon_H58 zenon_H20 zenon_H22 zenon_Hb9 zenon_Hb6 zenon_He8 zenon_Ha5 zenon_Hd3 zenon_H83 zenon_Hc zenon_H99 zenon_H32 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H3b zenon_Hc3. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.20 apply (zenon_L12_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.20 apply (zenon_L520_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.20 apply (zenon_L522_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.20 exact (zenon_He1 zenon_He5). % 41.04/41.20 apply (zenon_L126_); trivial. % 41.04/41.20 (* end of lemma zenon_L523_ *) % 41.04/41.20 assert (zenon_L524_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e4) (e1)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e2)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> False). % 41.04/41.20 do 0 intro. intros zenon_H3b zenon_Hc8 zenon_H32 zenon_Ha5 zenon_H91 zenon_H99 zenon_Hd3 zenon_Hc9 zenon_He9. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.20 apply (zenon_L70_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.20 apply (zenon_L71_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.20 apply (zenon_L58_); trivial. % 41.04/41.20 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.20 apply (zenon_L72_); trivial. % 41.04/41.20 apply (zenon_L107_); trivial. % 41.04/41.20 (* end of lemma zenon_L524_ *) % 41.04/41.20 assert (zenon_L525_ : ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e4) (e4)) = (e0))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e1)) = (e4)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((e0) = (e3))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> False). % 41.04/41.20 do 0 intro. intros zenon_Hf1 zenon_Hc8 zenon_He9 zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H17 zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H1c4 zenon_H13e zenon_H9b zenon_H99 zenon_Ha5 zenon_H7b zenon_He8 zenon_Hd3 zenon_H1a9 zenon_H11f zenon_H115 zenon_H165 zenon_H42 zenon_H49 zenon_H88 zenon_H81 zenon_Hb1 zenon_H89 zenon_H8e zenon_H9f zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_He1 zenon_Hc2 zenon_H83 zenon_Hb6 zenon_Hb9 zenon_Haa zenon_Ha1 zenon_H91 zenon_He0. % 41.04/41.20 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 41.04/41.20 apply (zenon_L523_); trivial. % 41.04/41.20 apply (zenon_L524_); trivial. % 41.04/41.20 (* end of lemma zenon_L525_ *) % 41.04/41.20 assert (zenon_L526_ : ((~((op (e4) (e4)) = (e1)))\/((op (e4) (e1)) = (e4))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e3)) = (e1))\/((op (e0) (e4)) = (e1)))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e4) (e4)) = (e0))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e3)) = (op (e4) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e4) (e3)))) -> (((op (e4) (e3)) = (e0))\/(((op (e4) (e3)) = (e1))\/(((op (e4) (e3)) = (e2))\/(((op (e4) (e3)) = (e3))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e4))\/(((op (e1) (e3)) = (e4))\/(((op (e2) (e3)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e4) (e3)) = (e4)))))) -> (((~((op (e0) (e0)) = (op (e0) (e0))))/\(((op (op (e0) (e0)) (e0)) = (e0))/\(~((op (op (e0) (e0)) (e0)) = (e0)))))\/(((~((op (e1) (e0)) = (op (e0) (e1))))/\(((op (op (e0) (e1)) (e1)) = (e0))/\(~((op (op (e0) (e1)) (e0)) = (e1)))))\/(((~((op (e2) (e0)) = (op (e0) (e2))))/\(((op (op (e0) (e2)) (e2)) = (e0))/\(~((op (op (e0) (e2)) (e0)) = (e2)))))\/(((~((op (e3) (e0)) = (op (e0) (e3))))/\(((op (op (e0) (e3)) (e3)) = (e0))/\(~((op (op (e0) (e3)) (e0)) = (e3)))))\/(((~((op (e4) (e0)) = (op (e0) (e4))))/\(((op (op (e0) (e4)) (e4)) = (e0))/\(~((op (op (e0) (e4)) (e0)) = (e4)))))\/(((~((op (e0) (e1)) = (op (e1) (e0))))/\(((op (op (e1) (e0)) (e0)) = (e1))/\(~((op (op (e1) (e0)) (e1)) = (e0)))))\/(((~((op (e1) (e1)) = (op (e1) (e1))))/\(((op (op (e1) (e1)) (e1)) = (e1))/\(~((op (op (e1) (e1)) (e1)) = (e1)))))\/(((~((op (e2) (e1)) = (op (e1) (e2))))/\(((op (op (e1) (e2)) (e2)) = (e1))/\(~((op (op (e1) (e2)) (e1)) = (e2)))))\/(((~((op (e3) (e1)) = (op (e1) (e3))))/\(((op (op (e1) (e3)) (e3)) = (e1))/\(~((op (op (e1) (e3)) (e1)) = (e3)))))\/(((~((op (e4) (e1)) = (op (e1) (e4))))/\(((op (op (e1) (e4)) (e4)) = (e1))/\(~((op (op (e1) (e4)) (e1)) = (e4)))))\/(((~((op (e0) (e2)) = (op (e2) (e0))))/\(((op (op (e2) (e0)) (e0)) = (e2))/\(~((op (op (e2) (e0)) (e2)) = (e0)))))\/(((~((op (e1) (e2)) = (op (e2) (e1))))/\(((op (op (e2) (e1)) (e1)) = (e2))/\(~((op (op (e2) (e1)) (e2)) = (e1)))))\/(((~((op (e2) (e2)) = (op (e2) (e2))))/\(((op (op (e2) (e2)) (e2)) = (e2))/\(~((op (op (e2) (e2)) (e2)) = (e2)))))\/(((~((op (e3) (e2)) = (op (e2) (e3))))/\(((op (op (e2) (e3)) (e3)) = (e2))/\(~((op (op (e2) (e3)) (e2)) = (e3)))))\/(((~((op (e4) (e2)) = (op (e2) (e4))))/\(((op (op (e2) (e4)) (e4)) = (e2))/\(~((op (op (e2) (e4)) (e2)) = (e4)))))\/(((~((op (e0) (e3)) = (op (e3) (e0))))/\(((op (op (e3) (e0)) (e0)) = (e3))/\(~((op (op (e3) (e0)) (e3)) = (e0)))))\/(((~((op (e1) (e3)) = (op (e3) (e1))))/\(((op (op (e3) (e1)) (e1)) = (e3))/\(~((op (op (e3) (e1)) (e3)) = (e1)))))\/(((~((op (e2) (e3)) = (op (e3) (e2))))/\(((op (op (e3) (e2)) (e2)) = (e3))/\(~((op (op (e3) (e2)) (e3)) = (e2)))))\/(((~((op (e3) (e3)) = (op (e3) (e3))))/\(((op (op (e3) (e3)) (e3)) = (e3))/\(~((op (op (e3) (e3)) (e3)) = (e3)))))\/(((~((op (e4) (e3)) = (op (e3) (e4))))/\(((op (op (e3) (e4)) (e4)) = (e3))/\(~((op (op (e3) (e4)) (e3)) = (e4)))))\/(((~((op (e0) (e4)) = (op (e4) (e0))))/\(((op (op (e4) (e0)) (e0)) = (e4))/\(~((op (op (e4) (e0)) (e4)) = (e0)))))\/(((~((op (e1) (e4)) = (op (e4) (e1))))/\(((op (op (e4) (e1)) (e1)) = (e4))/\(~((op (op (e4) (e1)) (e4)) = (e1)))))\/(((~((op (e2) (e4)) = (op (e4) (e2))))/\(((op (op (e4) (e2)) (e2)) = (e4))/\(~((op (op (e4) (e2)) (e4)) = (e2)))))\/(((~((op (e3) (e4)) = (op (e4) (e3))))/\(((op (op (e4) (e3)) (e3)) = (e4))/\(~((op (op (e4) (e3)) (e4)) = (e3)))))\/((~((op (e4) (e4)) = (op (e4) (e4))))/\(((op (op (e4) (e4)) (e4)) = (e4))/\(~((op (op (e4) (e4)) (e4)) = (e4))))))))))))))))))))))))))))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> False). % 41.04/41.21 do 0 intro. intros zenon_H2ac zenon_H17e zenon_H17 zenon_He0 zenon_He1 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_H91 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_H136 zenon_H49 zenon_Hb zenon_Hc zenon_H18 zenon_H16 zenon_H1f zenon_H20 zenon_H22 zenon_H2d zenon_H2c zenon_H32 zenon_H34 zenon_H3b zenon_H51 zenon_H168 zenon_H17d zenon_H16d zenon_H50 zenon_H42 zenon_H41 zenon_H1c8 zenon_H165 zenon_H11f zenon_H1a9 zenon_Ha1 zenon_H8e zenon_Hb6 zenon_H1b9 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_Hc2 zenon_Hbb zenon_H13e zenon_H1c4 zenon_H1d5 zenon_H10b zenon_H60 zenon_H9f zenon_Hb9 zenon_H1c9 zenon_H116 zenon_H115 zenon_H112 zenon_H18e zenon_H19a zenon_H14d zenon_H152 zenon_H157 zenon_H15b zenon_Haa zenon_H89 zenon_H169 zenon_H1e5 zenon_H1f4 zenon_H161 zenon_H1ff zenon_H1fb zenon_H1fe zenon_H20c zenon_H20f zenon_H223 zenon_H220 zenon_H21a zenon_H217 zenon_H23c zenon_Hf6 zenon_Hf7 zenon_H22d zenon_H237 zenon_H236 zenon_H111 zenon_H240 zenon_H246 zenon_H24e zenon_H256 zenon_H26a zenon_H267 zenon_H261 zenon_H260 zenon_H26e zenon_H275 zenon_H279 zenon_H285 zenon_H299 zenon_H29c zenon_H2a0 zenon_H2a4 zenon_H2ad zenon_Hf1. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H146 | zenon_intro zenon_Ha5 ]. % 41.04/41.21 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 41.04/41.21 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H172 | zenon_intro zenon_H2ae ]. % 41.04/41.21 apply (zenon_L251_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H17c | zenon_intro zenon_H2af ]. % 41.04/41.21 apply (zenon_L265_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H2b1 | zenon_intro zenon_H2b0 ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2b1). zenon_intro zenon_H2b3. zenon_intro zenon_H2b2. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2b2). zenon_intro zenon_H2b4. zenon_intro zenon_H1ce. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L250_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L309_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H2b6 | zenon_intro zenon_H2b5 ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2b6). zenon_intro zenon_H2b8. zenon_intro zenon_H2b7. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2b7). zenon_intro zenon_H2b9. zenon_intro zenon_H1ea. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L94_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L348_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2ba ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2bb). zenon_intro zenon_H2bd. zenon_intro zenon_H2bc. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2bc). zenon_intro zenon_H2be. zenon_intro zenon_H204. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L250_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L361_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H2c0 | zenon_intro zenon_H2bf ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2c0). zenon_intro zenon_H213. zenon_intro zenon_H2c1. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L94_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L369_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H214 | zenon_intro zenon_H2c2 ]. % 41.04/41.21 apply (zenon_L370_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H2c4 | zenon_intro zenon_H2c3 ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2c4). zenon_intro zenon_H2c6. zenon_intro zenon_H2c5. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2c5). zenon_intro zenon_H21b. zenon_intro zenon_H2c7. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L250_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L380_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2c3); [ zenon_intro zenon_H2c9 | zenon_intro zenon_H2c8 ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2c9). zenon_intro zenon_H2cb. zenon_intro zenon_H2ca. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2ca). zenon_intro zenon_H22a. zenon_intro zenon_H2cc. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L94_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L393_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2c8); [ zenon_intro zenon_H2ce | zenon_intro zenon_H2cd ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2ce). zenon_intro zenon_H2d0. zenon_intro zenon_H2cf. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2cf). zenon_intro zenon_H241. zenon_intro zenon_H2d1. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L250_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L399_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2cd); [ zenon_intro zenon_H2d3 | zenon_intro zenon_H2d2 ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2d3). zenon_intro zenon_H245. zenon_intro zenon_H2d4. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L94_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L406_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H2d6 | zenon_intro zenon_H2d5 ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2d6). zenon_intro zenon_H2d8. zenon_intro zenon_H2d7. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2d7). zenon_intro zenon_H2d9. zenon_intro zenon_H24a. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L250_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L416_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_H252 | zenon_intro zenon_H2da ]. % 41.04/41.21 apply (zenon_L417_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H2dc | zenon_intro zenon_H2db ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2de. zenon_intro zenon_H2dd. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2dd). zenon_intro zenon_H257. zenon_intro zenon_H2df. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L94_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L422_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H2e1 | zenon_intro zenon_H2e0 ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2e1). zenon_intro zenon_H2e3. zenon_intro zenon_H2e2. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2e2). zenon_intro zenon_H259. zenon_intro zenon_H2e4. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L250_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L426_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H2e6 | zenon_intro zenon_H2e5 ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2e6). zenon_intro zenon_H25d. zenon_intro zenon_H2e7. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L94_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L435_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2e9 | zenon_intro zenon_H2e8 ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2e9). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2ea). zenon_intro zenon_H262. zenon_intro zenon_H2ec. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L250_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L449_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2e8); [ zenon_intro zenon_H2ee | zenon_intro zenon_H2ed ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H2f0. zenon_intro zenon_H2ef. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H26f. zenon_intro zenon_H2f1. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L94_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L467_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2ed); [ zenon_intro zenon_H27d | zenon_intro zenon_H2f2 ]. % 41.04/41.21 apply (zenon_L468_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2f2); [ zenon_intro zenon_H2f4 | zenon_intro zenon_H2f3 ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H2f6. zenon_intro zenon_H2f5. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2f5). zenon_intro zenon_H27f. zenon_intro zenon_H2f7. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.21 apply (zenon_L12_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.21 apply (zenon_L470_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.21 apply (zenon_L41_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.21 exact (zenon_He1 zenon_He5). % 41.04/41.21 apply (zenon_L471_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H2f9 | zenon_intro zenon_H2f8 ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2f9). zenon_intro zenon_H282. zenon_intro zenon_H2fa. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L250_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L479_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H2fc | zenon_intro zenon_H2fb ]. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2fc). zenon_intro zenon_H2fe. zenon_intro zenon_H2fd. % 41.04/41.21 apply (zenon_and_s _ _ zenon_H2fd). zenon_intro zenon_H284. zenon_intro zenon_H2ff. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L94_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L501_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H28d | zenon_intro zenon_H300 ]. % 41.04/41.21 apply (zenon_L507_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2a3 | zenon_intro zenon_H2aa ]. % 41.04/41.21 apply (zenon_L518_); trivial. % 41.04/41.21 apply (zenon_L519_); trivial. % 41.04/41.21 apply (zenon_L99_); trivial. % 41.04/41.21 apply (zenon_L345_); trivial. % 41.04/41.21 apply (zenon_L525_); trivial. % 41.04/41.21 (* end of lemma zenon_L526_ *) % 41.04/41.21 assert (zenon_L527_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e0) (e4)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 41.04/41.21 do 0 intro. intros zenon_He0 zenon_Hb zenon_H49 zenon_H34 zenon_H32 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H9b zenon_H7b zenon_H5f zenon_H89 zenon_H8e zenon_H77 zenon_H61 zenon_H9f zenon_H73 zenon_H58 zenon_H57 zenon_H68 zenon_H88 zenon_He1 zenon_H3b zenon_H17a zenon_H168 zenon_H18 zenon_H16 zenon_H22 zenon_H20 zenon_H1f zenon_H2d zenon_H17 zenon_H2c zenon_H91 zenon_Hc. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.21 apply (zenon_L12_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.21 apply (zenon_L262_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.21 apply (zenon_L238_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.21 exact (zenon_He1 zenon_He5). % 41.04/41.21 apply (zenon_L263_); trivial. % 41.04/41.21 (* end of lemma zenon_L527_ *) % 41.04/41.21 assert (zenon_L528_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (op (e0) (e2)) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.21 do 0 intro. intros zenon_Hc2 zenon_Hb1 zenon_H1bf zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H1d5 zenon_H91 zenon_H50 zenon_H17 zenon_H10b zenon_H136 zenon_Hba zenon_H1ce zenon_Hb zenon_Ha1 zenon_He1 zenon_H57 zenon_H6e zenon_H197 zenon_H81 zenon_H116 zenon_H2d zenon_He0 zenon_H58 zenon_Hb9 zenon_Hb6 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.21 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.21 apply (zenon_L277_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.21 apply (zenon_L303_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.21 apply (zenon_L123_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.21 apply (zenon_L285_); trivial. % 41.04/41.21 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.21 (* end of lemma zenon_L528_ *) % 41.04/41.21 assert (zenon_L529_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (op (e0) (e2)) (e0)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.21 do 0 intro. intros zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H87 zenon_Hed zenon_He6 zenon_He8 zenon_He9 zenon_Hd4 zenon_Hd9 zenon_Hee zenon_H1c9 zenon_H60 zenon_H19a zenon_H168 zenon_H88 zenon_H68 zenon_H73 zenon_H9f zenon_H61 zenon_H77 zenon_H8e zenon_H89 zenon_H5f zenon_H7b zenon_H9b zenon_H18e zenon_Hc3 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H4a zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_Hc zenon_H83 zenon_H32 zenon_H16 zenon_H34 zenon_Hb6 zenon_Hb9 zenon_H58 zenon_He0 zenon_H2d zenon_H116 zenon_H81 zenon_H6e zenon_H57 zenon_He1 zenon_Ha1 zenon_Hb zenon_H1ce zenon_Hba zenon_H136 zenon_H10b zenon_H17 zenon_H50 zenon_H91 zenon_H1d5 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_Hb1 zenon_Hc2 zenon_H146. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 41.04/41.21 apply (zenon_L272_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 41.04/41.21 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.21 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 41.04/41.21 apply (zenon_L273_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 41.04/41.21 apply (zenon_L274_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.21 apply (zenon_L527_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.21 apply (zenon_L316_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.21 apply (zenon_L266_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.21 apply (zenon_L528_); trivial. % 41.04/41.21 exact (zenon_H146 zenon_H144). % 41.04/41.21 (* end of lemma zenon_L529_ *) % 41.04/41.21 assert (zenon_L530_ : (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e4) (e4)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (op (e0) (e2)) (e0)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (unit) (e1)) = (e1)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 41.04/41.21 do 0 intro. intros zenon_H146 zenon_Hc2 zenon_H6e zenon_H81 zenon_H116 zenon_H2d zenon_He0 zenon_Hb9 zenon_Hb6 zenon_H83 zenon_H49 zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hc3 zenon_H18e zenon_H168 zenon_H19a zenon_H60 zenon_H1c9 zenon_Hee zenon_Hd9 zenon_Hd4 zenon_He9 zenon_He8 zenon_He6 zenon_Hed zenon_H87 zenon_H16d zenon_H41 zenon_H51 zenon_H1c8 zenon_H34 zenon_H32 zenon_H9b zenon_H7b zenon_H5f zenon_H89 zenon_H8e zenon_H77 zenon_H61 zenon_H9f zenon_H73 zenon_H58 zenon_H57 zenon_H68 zenon_H88 zenon_He1 zenon_Ha1 zenon_Hd3 zenon_Hb zenon_H1ce zenon_Hba zenon_H136 zenon_H16 zenon_H3b zenon_H10b zenon_H17 zenon_H22 zenon_H1f zenon_H50 zenon_H91 zenon_Hc zenon_H1d5 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H20 zenon_Hb1. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 41.04/41.21 apply (zenon_L272_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 41.04/41.21 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.21 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 41.04/41.21 apply (zenon_L273_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 41.04/41.21 apply (zenon_L51_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.21 apply (zenon_L12_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.21 apply (zenon_L529_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.21 apply (zenon_L238_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.21 exact (zenon_He1 zenon_He5). % 41.04/41.21 apply (zenon_L302_); trivial. % 41.04/41.21 (* end of lemma zenon_L530_ *) % 41.04/41.21 assert (zenon_L531_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (op (e0) (e2)) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 41.04/41.21 do 0 intro. intros zenon_H15b zenon_Hb1 zenon_H20 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H1d5 zenon_Hc zenon_H91 zenon_H50 zenon_H1f zenon_H22 zenon_H17 zenon_H10b zenon_H3b zenon_H16 zenon_H136 zenon_Hba zenon_H1ce zenon_Hb zenon_Hd3 zenon_Ha1 zenon_He1 zenon_H88 zenon_H68 zenon_H57 zenon_H58 zenon_H73 zenon_H9f zenon_H61 zenon_H77 zenon_H8e zenon_H89 zenon_H5f zenon_H7b zenon_H9b zenon_H32 zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H87 zenon_Hed zenon_He6 zenon_He8 zenon_He9 zenon_Hd4 zenon_Hd9 zenon_Hee zenon_H1c9 zenon_H60 zenon_H19a zenon_H168 zenon_H18e zenon_Hc3 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H115 zenon_H1b9 zenon_H49 zenon_H83 zenon_Hb6 zenon_Hb9 zenon_He0 zenon_H2d zenon_H116 zenon_H81 zenon_H6e zenon_Hc2 zenon_H146 zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L250_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L530_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 (* end of lemma zenon_L531_ *) % 41.04/41.21 assert (zenon_L532_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (op (e0) (e4)) (e0)) = (e4))) -> ((op (e4) (e0)) = (e4)) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.21 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_Hda zenon_H19a zenon_H17 zenon_H2d zenon_H18 zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H18e zenon_H91 zenon_H81 zenon_H50 zenon_H16d zenon_H41 zenon_H1fb zenon_H146 zenon_H20c zenon_H161 zenon_H204 zenon_H9a zenon_H20f zenon_He1 zenon_H57 zenon_H6e zenon_H197 zenon_H116 zenon_Hb zenon_He0 zenon_H58 zenon_Hb9 zenon_Hb6 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.21 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.21 apply (zenon_L277_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.21 apply (zenon_L357_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.21 apply (zenon_L123_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.21 apply (zenon_L285_); trivial. % 41.04/41.21 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.21 (* end of lemma zenon_L532_ *) % 41.04/41.21 assert (zenon_L533_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e4) (e0)) = (e4)) -> (~((op (op (e0) (e4)) (e0)) = (e4))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.21 do 0 intro. intros zenon_H88 zenon_H73 zenon_H9f zenon_H77 zenon_H89 zenon_H7b zenon_H9b zenon_Hc8 zenon_Hcc zenon_H99 zenon_Hc3 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H4a zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_Hc zenon_H83 zenon_H32 zenon_H16 zenon_H34 zenon_Hb6 zenon_Hb9 zenon_H58 zenon_He0 zenon_Hb zenon_H116 zenon_H6e zenon_H57 zenon_He1 zenon_H20f zenon_H9a zenon_H204 zenon_H161 zenon_H20c zenon_H1fb zenon_H41 zenon_H16d zenon_H50 zenon_H81 zenon_H91 zenon_H18e zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H168 zenon_H18 zenon_H2d zenon_H17 zenon_H19a zenon_Hda zenon_Ha1 zenon_Hc2 zenon_H146. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.21 apply (zenon_L527_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.21 apply (zenon_L167_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.21 apply (zenon_L266_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.21 apply (zenon_L532_); trivial. % 41.04/41.21 exact (zenon_H146 zenon_H144). % 41.04/41.21 (* end of lemma zenon_L533_ *) % 41.04/41.21 assert (zenon_L534_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e2))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e4) (e0)) = (e4)) -> (~((op (op (e0) (e4)) (e0)) = (e4))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 41.04/41.21 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_H6e zenon_H116 zenon_Hb zenon_He0 zenon_Hb9 zenon_Hb6 zenon_H83 zenon_H49 zenon_H1b9 zenon_H115 zenon_H11f zenon_H1ad zenon_H1ae zenon_Hc3 zenon_H34 zenon_H32 zenon_H99 zenon_Hcc zenon_Hc8 zenon_H9b zenon_H7b zenon_H89 zenon_H77 zenon_H9f zenon_H73 zenon_H58 zenon_H57 zenon_H88 zenon_He1 zenon_H20f zenon_H9a zenon_H204 zenon_H1b3 zenon_H161 zenon_H20c zenon_H146 zenon_H3b zenon_Hd3 zenon_H1fb zenon_H41 zenon_H16d zenon_H50 zenon_H22 zenon_H20 zenon_H1f zenon_H16 zenon_H81 zenon_H91 zenon_Hc zenon_H18e zenon_H2c zenon_H112 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H168 zenon_H18 zenon_H2d zenon_H17 zenon_H19a zenon_Hda. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.21 apply (zenon_L12_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.21 apply (zenon_L533_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.21 apply (zenon_L238_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.21 exact (zenon_He1 zenon_He5). % 41.04/41.21 apply (zenon_L356_); trivial. % 41.04/41.21 (* end of lemma zenon_L534_ *) % 41.04/41.21 assert (zenon_L535_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (op (e1) (e2)) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> False). % 41.04/41.21 do 0 intro. intros zenon_H223 zenon_Hc zenon_H91 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H5f zenon_H217 zenon_He1 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_H49 zenon_Hb zenon_H2d zenon_H17 zenon_H2c zenon_He0 zenon_H9f zenon_Hb9 zenon_H19a zenon_H168 zenon_H116 zenon_H115 zenon_H112 zenon_H18e zenon_H51 zenon_H146 zenon_H1c8 zenon_H1c9 zenon_H21b zenon_H21a zenon_H34 zenon_H16 zenon_H32 zenon_H50 zenon_H16d zenon_H161 zenon_H1f zenon_H20 zenon_H41 zenon_H220 zenon_H3b zenon_H1ae zenon_H22. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H216 | zenon_intro zenon_H224 ]. % 41.04/41.21 apply (zenon_L452_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1cc | zenon_intro zenon_H225 ]. % 41.04/41.21 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.21 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H21c | zenon_intro zenon_H226 ]. % 41.04/41.21 apply (zenon_L377_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H221 | zenon_intro zenon_H1af ]. % 41.04/41.21 apply (zenon_L379_); trivial. % 41.04/41.21 apply (zenon_L281_); trivial. % 41.04/41.21 (* end of lemma zenon_L535_ *) % 41.04/41.21 assert (zenon_L536_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> ((op (op (e1) (e2)) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (unit)) = (e3)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 41.04/41.21 do 0 intro. intros zenon_H15b zenon_H89 zenon_Hc2 zenon_Ha1 zenon_Haa zenon_Hb6 zenon_Hda zenon_H8e zenon_Hc3 zenon_Hbb zenon_H22 zenon_H1ae zenon_H3b zenon_H220 zenon_H41 zenon_H20 zenon_H1f zenon_H161 zenon_H16d zenon_H50 zenon_H32 zenon_H16 zenon_H21a zenon_H21b zenon_H1c9 zenon_H1c8 zenon_H146 zenon_H51 zenon_H18e zenon_H112 zenon_H115 zenon_H116 zenon_H168 zenon_H19a zenon_Hb9 zenon_H9f zenon_He0 zenon_H2c zenon_H17 zenon_H2d zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H217 zenon_H5f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc zenon_H223 zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.21 apply (zenon_L240_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.21 apply (zenon_L535_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.21 apply (zenon_L216_); trivial. % 41.04/41.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.21 apply (zenon_L217_); trivial. % 41.04/41.21 apply (zenon_L218_); trivial. % 41.04/41.21 (* end of lemma zenon_L536_ *) % 41.04/41.21 assert (zenon_L537_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (op (e1) (e3)) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H19a zenon_H168 zenon_H18e zenon_Hc3 zenon_He0 zenon_H17 zenon_H2d zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H1f zenon_H20 zenon_H68 zenon_H32 zenon_H16 zenon_Hed zenon_He6 zenon_He8 zenon_H9b zenon_Hb1 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H22 zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc zenon_Hb6 zenon_Hb9 zenon_H237 zenon_H22a zenon_H22d zenon_Hf6 zenon_H51 zenon_Hbb zenon_Hf7 zenon_H89 zenon_H9f zenon_H8e zenon_H60 zenon_H236 zenon_H220 zenon_H41 zenon_H161 zenon_H16d zenon_H50 zenon_H116 zenon_H111 zenon_H23c zenon_Ha1 zenon_Hc2 zenon_H146. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.22 apply (zenon_L264_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.22 apply (zenon_L167_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.22 apply (zenon_L266_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.22 apply (zenon_L390_); trivial. % 41.04/41.22 exact (zenon_H146 zenon_H144). % 41.04/41.22 (* end of lemma zenon_L537_ *) % 41.04/41.22 assert (zenon_L538_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> ((op (op (e1) (e3)) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H15b zenon_H146 zenon_Hc2 zenon_Ha1 zenon_H23c zenon_H111 zenon_H116 zenon_H50 zenon_H16d zenon_H161 zenon_H41 zenon_H220 zenon_H236 zenon_H60 zenon_H8e zenon_H9f zenon_H89 zenon_Hf7 zenon_Hbb zenon_H51 zenon_Hf6 zenon_H22d zenon_H22a zenon_H237 zenon_Hb9 zenon_Hb6 zenon_Hc zenon_H91 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H1b9 zenon_H115 zenon_H2c zenon_H112 zenon_H1ad zenon_H22 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_He1 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_Hb1 zenon_H9b zenon_He8 zenon_He6 zenon_Hed zenon_H16 zenon_H32 zenon_H68 zenon_H20 zenon_H1f zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_H49 zenon_Hb zenon_H2d zenon_H17 zenon_He0 zenon_Hc3 zenon_H18e zenon_H168 zenon_H19a zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.22 apply (zenon_L250_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.22 apply (zenon_L537_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.22 apply (zenon_L216_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.22 apply (zenon_L217_); trivial. % 41.04/41.22 apply (zenon_L218_); trivial. % 41.04/41.22 (* end of lemma zenon_L538_ *) % 41.04/41.22 assert (zenon_L539_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (e3) (e4)) = (e1)) -> ((op (op (e1) (e4)) (e4)) = (e1)) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.22 do 0 intro. intros zenon_Hc2 zenon_H17 zenon_H2d zenon_Ha1 zenon_H197 zenon_H241 zenon_H240 zenon_H16 zenon_H32 zenon_H1f zenon_H58 zenon_H20 zenon_Hb9 zenon_Hb6 zenon_H92 zenon_Hc zenon_H91 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H22 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.22 apply (zenon_L53_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.22 apply (zenon_L394_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.22 apply (zenon_L123_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.22 apply (zenon_L288_); trivial. % 41.04/41.22 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.22 (* end of lemma zenon_L539_ *) % 41.04/41.22 assert (zenon_L540_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> ((op (op (e1) (e4)) (e4)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H19a zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H18e zenon_Hc3 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H22 zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc zenon_H92 zenon_Hb6 zenon_Hb9 zenon_H20 zenon_H58 zenon_H1f zenon_H32 zenon_H16 zenon_H240 zenon_H241 zenon_Ha1 zenon_H2d zenon_H17 zenon_Hc2 zenon_H146. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.22 apply (zenon_L263_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.22 apply (zenon_L300_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.22 apply (zenon_L266_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.22 apply (zenon_L539_); trivial. % 41.04/41.22 exact (zenon_H146 zenon_H144). % 41.04/41.22 (* end of lemma zenon_L540_ *) % 41.04/41.22 assert (zenon_L541_ : (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> ((op (op (e1) (e4)) (e4)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H49 zenon_Hbb zenon_He0 zenon_Hb zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_Hed zenon_He6 zenon_He8 zenon_H9b zenon_Hb1 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H19a zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H18e zenon_Hc3 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H22 zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc zenon_Hb6 zenon_Hb9 zenon_H20 zenon_H58 zenon_H1f zenon_H32 zenon_H16 zenon_H240 zenon_H241 zenon_Ha1 zenon_H2d zenon_H17 zenon_Hc2 zenon_H146. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.22 apply (zenon_L12_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.22 apply (zenon_L396_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.22 apply (zenon_L112_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.22 exact (zenon_He1 zenon_He5). % 41.04/41.22 apply (zenon_L540_); trivial. % 41.04/41.22 (* end of lemma zenon_L541_ *) % 41.04/41.22 assert (zenon_L542_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (op (e1) (e4)) (e4)) = (e1)) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H15b zenon_H89 zenon_Haa zenon_Hda zenon_H9f zenon_H41 zenon_H51 zenon_H50 zenon_H146 zenon_Hc2 zenon_H17 zenon_H2d zenon_Ha1 zenon_H241 zenon_H240 zenon_H16 zenon_H32 zenon_H1f zenon_H58 zenon_H20 zenon_Hb9 zenon_Hb6 zenon_Hc zenon_H91 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H1b9 zenon_H115 zenon_H2c zenon_H112 zenon_H1ad zenon_H22 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3 zenon_H18e zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H168 zenon_H19a zenon_He1 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_Hb1 zenon_H9b zenon_He8 zenon_He6 zenon_Hed zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_Hb zenon_He0 zenon_Hbb zenon_H49 zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.22 apply (zenon_L240_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.22 apply (zenon_L541_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.22 apply (zenon_L216_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.22 apply (zenon_L217_); trivial. % 41.04/41.22 apply (zenon_L218_); trivial. % 41.04/41.22 (* end of lemma zenon_L542_ *) % 41.04/41.22 assert (zenon_L543_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H115 zenon_H116 zenon_H83 zenon_H87 zenon_H6e zenon_Hed zenon_He6 zenon_He8 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hd9 zenon_Hee zenon_H1c9 zenon_Hb9 zenon_H49 zenon_Hb1 zenon_Hbb zenon_He0 zenon_Hb zenon_H34 zenon_H32 zenon_Hcc zenon_H9b zenon_H7b zenon_H89 zenon_H77 zenon_H9f zenon_H73 zenon_H58 zenon_H57 zenon_H88 zenon_He1 zenon_H19a zenon_H17 zenon_H2d zenon_H1f zenon_H168 zenon_H20 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_H22 zenon_Hc zenon_H91 zenon_H81 zenon_H16 zenon_H99 zenon_H9a zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H245 zenon_Hba zenon_H3b zenon_H146. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 41.04/41.22 apply (zenon_L272_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 41.04/41.22 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 41.04/41.22 apply (zenon_L273_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 41.04/41.22 apply (zenon_L274_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.22 apply (zenon_L12_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.22 apply (zenon_L527_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.22 apply (zenon_L178_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.22 apply (zenon_L266_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.22 apply (zenon_L401_); trivial. % 41.04/41.22 exact (zenon_H146 zenon_H144). % 41.04/41.22 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.22 apply (zenon_L238_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.22 exact (zenon_He1 zenon_He5). % 41.04/41.22 apply (zenon_L403_); trivial. % 41.04/41.22 (* end of lemma zenon_L543_ *) % 41.04/41.22 assert (zenon_L544_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e4) (e4)) = (e1))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e0)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((e3) = (op (e2) (e4))) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H15b zenon_H146 zenon_H3b zenon_Hba zenon_H245 zenon_H42 zenon_H18 zenon_Hc8 zenon_H9a zenon_H99 zenon_H16 zenon_H81 zenon_H91 zenon_Hc zenon_H22 zenon_H18e zenon_H2c zenon_H112 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H20 zenon_H168 zenon_H1f zenon_H2d zenon_H17 zenon_H19a zenon_He1 zenon_H88 zenon_H57 zenon_H58 zenon_H73 zenon_H9f zenon_H77 zenon_H89 zenon_H7b zenon_H9b zenon_Hcc zenon_H32 zenon_Hb zenon_He0 zenon_Hbb zenon_Hb1 zenon_H49 zenon_Hb9 zenon_H1c9 zenon_Hee zenon_Hd9 zenon_Hd4 zenon_He9 zenon_Hd3 zenon_He8 zenon_He6 zenon_Hed zenon_H6e zenon_H87 zenon_H83 zenon_H116 zenon_H115 zenon_H50 zenon_H16d zenon_H41 zenon_H51 zenon_H1c8 zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.22 apply (zenon_L250_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.22 apply (zenon_L543_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.22 apply (zenon_L216_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.22 apply (zenon_L217_); trivial. % 41.04/41.22 apply (zenon_L218_); trivial. % 41.04/41.22 (* end of lemma zenon_L544_ *) % 41.04/41.22 assert (zenon_L545_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (op (e2) (e1)) (e2)) = (e1))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H19a zenon_H17 zenon_H2d zenon_H168 zenon_Hb1 zenon_H1bf zenon_H116 zenon_H2c zenon_H115 zenon_H112 zenon_H18e zenon_H34 zenon_H16 zenon_H32 zenon_H81 zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_Hc zenon_H4a zenon_H24e zenon_H14d zenon_H11f zenon_H246 zenon_H58 zenon_H6e zenon_Hba zenon_Hbb zenon_H3b zenon_Hb9 zenon_H24a zenon_H146. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.22 apply (zenon_L262_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.22 apply (zenon_L316_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.22 apply (zenon_L266_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.22 apply (zenon_L411_); trivial. % 41.04/41.22 exact (zenon_H146 zenon_H144). % 41.04/41.22 (* end of lemma zenon_L545_ *) % 41.04/41.22 assert (zenon_L546_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (op (e2) (e1)) (e2)) = (e1))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_He0 zenon_Hb zenon_H88 zenon_H7b zenon_H83 zenon_H87 zenon_H77 zenon_H57 zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hd9 zenon_Hee zenon_He1 zenon_H18 zenon_H91 zenon_H1c9 zenon_H73 zenon_H5f zenon_H9f zenon_H99 zenon_H9a zenon_H9b zenon_H61 zenon_H19a zenon_H17 zenon_H2d zenon_H168 zenon_Hb1 zenon_H116 zenon_H2c zenon_H115 zenon_H112 zenon_H18e zenon_H34 zenon_H16 zenon_H32 zenon_H81 zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_Hc zenon_H4a zenon_H24e zenon_H14d zenon_H11f zenon_H246 zenon_H58 zenon_H6e zenon_Hba zenon_Hbb zenon_H3b zenon_Hb9 zenon_H24a zenon_H146. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 41.04/41.22 apply (zenon_L272_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 41.04/41.22 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 41.04/41.22 apply (zenon_L273_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 41.04/41.22 apply (zenon_L51_); trivial. % 41.04/41.22 apply (zenon_L545_); trivial. % 41.04/41.22 (* end of lemma zenon_L546_ *) % 41.04/41.22 assert (zenon_L547_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (op (e2) (e1)) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.22 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_H81 zenon_H197 zenon_Haa zenon_H24e zenon_H14d zenon_H246 zenon_H6e zenon_Hba zenon_Hbb zenon_H24a zenon_He1 zenon_H57 zenon_H49 zenon_Hb zenon_H2d zenon_H17 zenon_He0 zenon_H16 zenon_H32 zenon_H1f zenon_H58 zenon_H20 zenon_Hb9 zenon_Hb6 zenon_H92 zenon_Hc zenon_H91 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H22 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.22 apply (zenon_L53_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.22 apply (zenon_L413_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.22 apply (zenon_L123_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.22 apply (zenon_L288_); trivial. % 41.04/41.22 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.22 (* end of lemma zenon_L547_ *) % 41.04/41.22 assert (zenon_L548_ : (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (op (e2) (e1)) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H116 zenon_Hb1 zenon_H1c9 zenon_Hee zenon_Hd9 zenon_Hd4 zenon_He9 zenon_He8 zenon_He6 zenon_Hed zenon_H87 zenon_H83 zenon_H50 zenon_H16d zenon_H41 zenon_H51 zenon_H1c8 zenon_H9b zenon_H7b zenon_H89 zenon_H77 zenon_H9f zenon_H73 zenon_H88 zenon_H19a zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H18e zenon_Hc3 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H22 zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc zenon_Hb6 zenon_Hb9 zenon_H20 zenon_H58 zenon_H1f zenon_H32 zenon_H16 zenon_He0 zenon_H17 zenon_H2d zenon_Hb zenon_H49 zenon_H57 zenon_He1 zenon_H24a zenon_Hbb zenon_Hba zenon_H6e zenon_H246 zenon_H14d zenon_H24e zenon_Haa zenon_H81 zenon_Ha1 zenon_Hc2 zenon_H146. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.22 apply (zenon_L12_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.22 apply (zenon_L546_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.22 apply (zenon_L238_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.22 exact (zenon_He1 zenon_He5). % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.22 apply (zenon_L263_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.22 apply (zenon_L300_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.22 apply (zenon_L266_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.22 apply (zenon_L547_); trivial. % 41.04/41.22 exact (zenon_H146 zenon_H144). % 41.04/41.22 (* end of lemma zenon_L548_ *) % 41.04/41.22 assert (zenon_L549_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (op (e2) (e1)) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H15b zenon_Hda zenon_H146 zenon_Hc2 zenon_Ha1 zenon_H81 zenon_Haa zenon_H24e zenon_H246 zenon_H6e zenon_Hba zenon_Hbb zenon_H24a zenon_He1 zenon_H57 zenon_H49 zenon_Hb zenon_H2d zenon_H17 zenon_He0 zenon_H16 zenon_H32 zenon_H1f zenon_H58 zenon_H20 zenon_Hb9 zenon_Hb6 zenon_Hc zenon_H91 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H1b9 zenon_H115 zenon_H2c zenon_H112 zenon_H1ad zenon_H22 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3 zenon_H18e zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H168 zenon_H19a zenon_H88 zenon_H73 zenon_H9f zenon_H77 zenon_H89 zenon_H7b zenon_H9b zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H83 zenon_H87 zenon_Hed zenon_He6 zenon_He8 zenon_He9 zenon_Hd4 zenon_Hd9 zenon_Hee zenon_H1c9 zenon_Hb1 zenon_H116 zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.22 apply (zenon_L240_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.22 apply (zenon_L548_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.22 apply (zenon_L216_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.22 apply (zenon_L217_); trivial. % 41.04/41.22 apply (zenon_L218_); trivial. % 41.04/41.22 (* end of lemma zenon_L549_ *) % 41.04/41.22 assert (zenon_L550_ : (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (op (e2) (e3)) (e3)) = (e2)) -> ((op (e2) (e3)) = (e1)) -> ((op (e1) (e4)) = (e2)) -> False). % 41.04/41.22 do 0 intro. intros zenon_H116 zenon_H257 zenon_H22c zenon_Hab. % 41.04/41.22 cut (((op (op (e2) (e3)) (e3)) = (e2)) = ((op (e1) (e3)) = (op (e1) (e4)))). % 41.04/41.22 intro zenon_D_pnotp. % 41.04/41.22 apply zenon_H116. % 41.04/41.22 rewrite <- zenon_D_pnotp. % 41.04/41.22 exact zenon_H257. % 41.04/41.22 cut (((e2) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 41.04/41.22 cut (((op (op (e2) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H258]. % 41.04/41.22 congruence. % 41.04/41.22 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 41.04/41.22 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (op (e2) (e3)) (e3)) = (op (e1) (e3)))). % 41.04/41.22 intro zenon_D_pnotp. % 41.04/41.22 apply zenon_H258. % 41.04/41.22 rewrite <- zenon_D_pnotp. % 41.04/41.22 exact zenon_H2e. % 41.04/41.22 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.04/41.22 cut (((op (e1) (e3)) = (op (op (e2) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H255]. % 41.04/41.22 congruence. % 41.04/41.22 apply (zenon_L419_); trivial. % 41.04/41.22 apply zenon_H2f. apply refl_equal. % 41.04/41.22 apply zenon_H2f. apply refl_equal. % 41.04/41.22 apply zenon_Hac. apply sym_equal. exact zenon_Hab. % 41.04/41.22 (* end of lemma zenon_L550_ *) % 41.04/41.22 assert (zenon_L551_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e1) (e4)) = (e2)) -> ((op (op (e2) (e3)) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e3) (e3)) = (e1))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H236 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_H88 zenon_H57 zenon_H73 zenon_H9f zenon_H77 zenon_H89 zenon_H7b zenon_H9b zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_Hf7 zenon_Hbb zenon_H6e zenon_He0 zenon_Hb zenon_H49 zenon_H81 zenon_H83 zenon_H87 zenon_Hed zenon_He6 zenon_He8 zenon_Hb1 zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hd9 zenon_Hee zenon_He1 zenon_H51 zenon_Hc zenon_Hf6 zenon_H16 zenon_H32 zenon_H2c zenon_H17 zenon_H2d zenon_H1f zenon_H20 zenon_H22 zenon_H18 zenon_H3b zenon_Hab zenon_H257 zenon_H116 zenon_H237 zenon_H34 zenon_H91. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H178 | zenon_intro zenon_H238 ]. % 41.04/41.22 apply (zenon_L382_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H10f | zenon_intro zenon_H239 ]. % 41.04/41.22 apply (zenon_L383_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H22c | zenon_intro zenon_H23a ]. % 41.04/41.22 apply (zenon_L550_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H23b | zenon_intro zenon_H233 ]. % 41.04/41.22 exact (zenon_H237 zenon_H23b). % 41.04/41.22 apply (zenon_L385_); trivial. % 41.04/41.22 (* end of lemma zenon_L551_ *) % 41.04/41.22 assert (zenon_L552_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (op (e2) (e3)) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.22 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_H91 zenon_H237 zenon_H116 zenon_H257 zenon_H18 zenon_H2d zenon_H17 zenon_Hf6 zenon_H51 zenon_He1 zenon_Hee zenon_Hd9 zenon_Hd4 zenon_He9 zenon_Hb1 zenon_He8 zenon_He6 zenon_Hed zenon_H87 zenon_H81 zenon_Hb zenon_He0 zenon_H6e zenon_Hbb zenon_Hf7 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H9b zenon_H7b zenon_H89 zenon_H77 zenon_H9f zenon_H73 zenon_H57 zenon_H88 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H236 zenon_H58 zenon_Hb9 zenon_Hb6 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.22 apply (zenon_L277_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.22 apply (zenon_L551_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.22 apply (zenon_L123_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.22 apply (zenon_L285_); trivial. % 41.04/41.22 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.22 (* end of lemma zenon_L552_ *) % 41.04/41.22 assert (zenon_L553_ : (~((op (e4) (e4)) = (e2))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e4) (e3)))) -> ((op (op (e2) (e3)) (e3)) = (e2)) -> ((op (e2) (e3)) = (e1)) -> False). % 41.04/41.22 do 0 intro. intros zenon_Hc3 zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H49 zenon_Hc zenon_H83 zenon_Hb6 zenon_Hb9 zenon_H236 zenon_H60 zenon_Hf7 zenon_Hbb zenon_H6e zenon_He0 zenon_Hb zenon_H81 zenon_H87 zenon_Hed zenon_He6 zenon_He8 zenon_Hb1 zenon_He9 zenon_Hd4 zenon_Hd9 zenon_Hee zenon_H51 zenon_Hf6 zenon_H17 zenon_H2d zenon_H18 zenon_H116 zenon_H237 zenon_H91 zenon_Ha1 zenon_Hc2 zenon_H34 zenon_H16 zenon_H32 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H9b zenon_H7b zenon_H5f zenon_H3b zenon_H89 zenon_H8e zenon_H77 zenon_H20 zenon_H61 zenon_H9f zenon_H73 zenon_H58 zenon_H57 zenon_H22 zenon_H1f zenon_H68 zenon_H88 zenon_He1 zenon_H256 zenon_H257 zenon_H22c. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.22 apply (zenon_L12_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.22 apply (zenon_L552_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.22 apply (zenon_L238_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.22 exact (zenon_He1 zenon_He5). % 41.04/41.22 apply (zenon_L420_); trivial. % 41.04/41.22 (* end of lemma zenon_L553_ *) % 41.04/41.22 assert (zenon_L554_ : ((op (op (e2) (e3)) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e4) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H257 zenon_H256 zenon_He1 zenon_H88 zenon_H68 zenon_H1f zenon_H22 zenon_H57 zenon_H58 zenon_H73 zenon_H9f zenon_H61 zenon_H20 zenon_H77 zenon_H8e zenon_H89 zenon_H3b zenon_H5f zenon_H7b zenon_H9b zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H32 zenon_H16 zenon_Hc2 zenon_Ha1 zenon_H116 zenon_H18 zenon_H2d zenon_H17 zenon_Hf6 zenon_H51 zenon_Hee zenon_Hd9 zenon_Hd4 zenon_He9 zenon_Hb1 zenon_He8 zenon_He6 zenon_Hed zenon_H87 zenon_H81 zenon_Hb zenon_He0 zenon_H6e zenon_Hbb zenon_Hf7 zenon_H60 zenon_H236 zenon_Hb9 zenon_Hb6 zenon_H83 zenon_Hc zenon_H49 zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_Hc3 zenon_H237 zenon_H34 zenon_H91. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H178 | zenon_intro zenon_H238 ]. % 41.04/41.22 apply (zenon_L382_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H10f | zenon_intro zenon_H239 ]. % 41.04/41.22 apply (zenon_L383_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H22c | zenon_intro zenon_H23a ]. % 41.04/41.22 apply (zenon_L553_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H23b | zenon_intro zenon_H233 ]. % 41.04/41.22 exact (zenon_H237 zenon_H23b). % 41.04/41.22 apply (zenon_L385_); trivial. % 41.04/41.22 (* end of lemma zenon_L554_ *) % 41.04/41.22 assert (zenon_L555_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (op (e2) (e4)) (e4)) = (e2)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.22 do 0 intro. intros zenon_Hc2 zenon_H17 zenon_H2d zenon_Ha1 zenon_H259 zenon_H16 zenon_H32 zenon_H1f zenon_H58 zenon_H20 zenon_Hb9 zenon_Hb6 zenon_H92 zenon_Hc zenon_H91 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H22 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.22 apply (zenon_L53_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.22 apply (zenon_L423_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.22 apply (zenon_L123_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.22 apply (zenon_L288_); trivial. % 41.04/41.22 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.22 (* end of lemma zenon_L555_ *) % 41.04/41.22 assert (zenon_L556_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (op (e2) (e4)) (e4)) = (e2)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.22 do 0 intro. intros zenon_He0 zenon_Hb zenon_H49 zenon_H83 zenon_H9b zenon_H7b zenon_H5f zenon_H89 zenon_H8e zenon_H77 zenon_H61 zenon_H9f zenon_H73 zenon_H57 zenon_H68 zenon_H88 zenon_He1 zenon_Hc2 zenon_H17 zenon_H2d zenon_Ha1 zenon_H259 zenon_H16 zenon_H32 zenon_H1f zenon_H58 zenon_H20 zenon_Hb9 zenon_Hb6 zenon_Hc zenon_H91 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H22 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.22 apply (zenon_L12_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.22 apply (zenon_L424_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.22 apply (zenon_L238_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.22 exact (zenon_He1 zenon_He5). % 41.04/41.22 apply (zenon_L555_); trivial. % 41.04/41.22 (* end of lemma zenon_L556_ *) % 41.04/41.22 assert (zenon_L557_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((op (op (e2) (e4)) (e4)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H15b zenon_H50 zenon_H51 zenon_H16d zenon_H41 zenon_Hc3 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H22 zenon_H1ad zenon_H112 zenon_H2c zenon_H115 zenon_H1b9 zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc zenon_Hb6 zenon_Hb9 zenon_H20 zenon_H58 zenon_H1f zenon_H32 zenon_H16 zenon_H259 zenon_Ha1 zenon_H2d zenon_H17 zenon_Hc2 zenon_He1 zenon_H88 zenon_H68 zenon_H57 zenon_H73 zenon_H9f zenon_H61 zenon_H77 zenon_H8e zenon_H89 zenon_H5f zenon_H7b zenon_H9b zenon_H83 zenon_H49 zenon_Hb zenon_He0 zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.22 apply (zenon_L250_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.22 apply (zenon_L556_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.22 apply (zenon_L216_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.22 apply (zenon_L217_); trivial. % 41.04/41.22 apply (zenon_L218_); trivial. % 41.04/41.22 (* end of lemma zenon_L557_ *) % 41.04/41.22 assert (zenon_L558_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e0)))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H3b zenon_H60 zenon_H25d zenon_H4a zenon_Hc zenon_H49 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H20 zenon_H1bf zenon_Hb1. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.22 apply (zenon_L427_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.22 apply (zenon_L17_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.22 apply (zenon_L84_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.22 apply (zenon_L102_); trivial. % 41.04/41.22 apply (zenon_L290_); trivial. % 41.04/41.22 (* end of lemma zenon_L558_ *) % 41.04/41.22 assert (zenon_L559_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (e3))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e0)))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H1c8 zenon_H146 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H1f zenon_H81 zenon_H18e zenon_H112 zenon_H115 zenon_H2c zenon_H116 zenon_He0 zenon_Hb zenon_H88 zenon_H7b zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H57 zenon_H58 zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_H9b zenon_Hd3 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H168 zenon_H18 zenon_H2d zenon_H17 zenon_H91 zenon_H19a zenon_H1c9 zenon_H22 zenon_Hb9 zenon_H34 zenon_H16 zenon_H32 zenon_H73 zenon_H5f zenon_H9f zenon_H61 zenon_H3b zenon_H60 zenon_H25d zenon_H4a zenon_Hc zenon_H49 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H20 zenon_Hb1. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 41.04/41.22 apply (zenon_L272_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 41.04/41.22 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 41.04/41.22 apply (zenon_L273_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 41.04/41.22 apply (zenon_L274_); trivial. % 41.04/41.22 apply (zenon_L558_); trivial. % 41.04/41.22 (* end of lemma zenon_L559_ *) % 41.04/41.22 assert (zenon_L560_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e0)))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 41.04/41.22 do 0 intro. intros zenon_He0 zenon_H2c zenon_H17 zenon_H2d zenon_H18 zenon_Hb zenon_Hb1 zenon_H1bf zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H49 zenon_H34 zenon_H32 zenon_H6e zenon_H58 zenon_H57 zenon_He1 zenon_H3b zenon_H60 zenon_H25d zenon_Hab zenon_Haa zenon_H22 zenon_H20 zenon_H1f zenon_H197 zenon_H16 zenon_H81 zenon_H91 zenon_Hc. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.22 apply (zenon_L12_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.22 apply (zenon_L558_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.22 apply (zenon_L286_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.22 exact (zenon_He1 zenon_He5). % 41.04/41.22 apply (zenon_L428_); trivial. % 41.04/41.22 (* end of lemma zenon_L560_ *) % 41.04/41.22 assert (zenon_L561_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e3)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.22 do 0 intro. intros zenon_Hc2 zenon_Ha1 zenon_H81 zenon_H197 zenon_Haa zenon_H25d zenon_H60 zenon_He1 zenon_H57 zenon_H6e zenon_H49 zenon_H1bf zenon_Hb1 zenon_Hb zenon_H2d zenon_H17 zenon_He0 zenon_H16 zenon_H32 zenon_H1f zenon_H58 zenon_H20 zenon_Hb9 zenon_Hb6 zenon_H92 zenon_Hc zenon_H91 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H1b9 zenon_H115 zenon_H34 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H22 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.22 apply (zenon_L53_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.22 apply (zenon_L560_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.22 apply (zenon_L123_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.22 apply (zenon_L288_); trivial. % 41.04/41.22 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.22 (* end of lemma zenon_L561_ *) % 41.04/41.22 assert (zenon_L562_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H9f zenon_H1c9 zenon_H116 zenon_H50 zenon_H16d zenon_H41 zenon_H51 zenon_H1c8 zenon_H88 zenon_H7b zenon_H83 zenon_H87 zenon_H77 zenon_H73 zenon_Hed zenon_He6 zenon_He8 zenon_H9b zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_H19a zenon_H168 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H18e zenon_Hc3 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H22 zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc zenon_Hb6 zenon_Hb9 zenon_H20 zenon_H58 zenon_H1f zenon_H32 zenon_H16 zenon_He0 zenon_H17 zenon_H2d zenon_Hb zenon_Hb1 zenon_H49 zenon_H6e zenon_H57 zenon_He1 zenon_H60 zenon_H25d zenon_Haa zenon_H81 zenon_Ha1 zenon_Hc2 zenon_H146. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 41.04/41.22 apply (zenon_L272_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 41.04/41.22 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 41.04/41.22 apply (zenon_L273_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 41.04/41.22 apply (zenon_L51_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.22 apply (zenon_L12_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.22 apply (zenon_L559_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.22 apply (zenon_L112_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.22 exact (zenon_He1 zenon_He5). % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.22 apply (zenon_L263_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.22 apply (zenon_L300_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.22 apply (zenon_L266_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.22 apply (zenon_L561_); trivial. % 41.04/41.22 exact (zenon_H146 zenon_H144). % 41.04/41.22 (* end of lemma zenon_L562_ *) % 41.04/41.22 assert (zenon_L563_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e3)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H15b zenon_H89 zenon_Hda zenon_Hbb zenon_H146 zenon_Hc2 zenon_Ha1 zenon_H81 zenon_Haa zenon_H25d zenon_H60 zenon_He1 zenon_H57 zenon_H6e zenon_H49 zenon_Hb1 zenon_Hb zenon_H2d zenon_H17 zenon_He0 zenon_H16 zenon_H32 zenon_H1f zenon_H58 zenon_H20 zenon_Hb9 zenon_Hb6 zenon_Hc zenon_H91 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H1b9 zenon_H115 zenon_H2c zenon_H112 zenon_H1ad zenon_H22 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3 zenon_H18e zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H168 zenon_H19a zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_H9b zenon_He8 zenon_He6 zenon_Hed zenon_H73 zenon_H77 zenon_H87 zenon_H83 zenon_H7b zenon_H88 zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H116 zenon_H1c9 zenon_H9f zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.22 apply (zenon_L240_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.22 apply (zenon_L562_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.22 apply (zenon_L216_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.22 apply (zenon_L217_); trivial. % 41.04/41.22 apply (zenon_L218_); trivial. % 41.04/41.22 (* end of lemma zenon_L563_ *) % 41.04/41.22 assert (zenon_L564_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (op (e3) (e1)) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 41.04/41.22 do 0 intro. intros zenon_H1c8 zenon_H146 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H18e zenon_H116 zenon_H168 zenon_H19a zenon_H1c9 zenon_Hb9 zenon_H9f zenon_H60 zenon_H26a zenon_H8e zenon_H260 zenon_H262 zenon_H261 zenon_H267 zenon_He0 zenon_H17 zenon_H2d zenon_Hb zenon_H49 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H1f zenon_H20 zenon_H68 zenon_H32 zenon_H16 zenon_Hed zenon_He6 zenon_He8 zenon_H9b zenon_Hb1 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H22 zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H34 zenon_H115 zenon_H1b9 zenon_H15f zenon_H42 zenon_H18 zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H91 zenon_Hc. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 41.04/41.22 apply (zenon_L272_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 41.04/41.22 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 41.04/41.22 apply (zenon_L273_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 41.04/41.22 apply (zenon_L274_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H25e | zenon_intro zenon_H26b ]. % 41.04/41.22 apply (zenon_L437_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H263 | zenon_intro zenon_H26c ]. % 41.04/41.22 apply (zenon_L438_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H268 | zenon_intro zenon_H26d ]. % 41.04/41.22 apply (zenon_L440_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_He5 | zenon_intro zenon_Hbf ]. % 41.04/41.22 exact (zenon_He1 zenon_He5). % 41.04/41.22 apply (zenon_L324_); trivial. % 41.04/41.22 (* end of lemma zenon_L564_ *) % 41.04/41.22 assert (zenon_L565_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> ((op (op (e3) (e1)) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 41.04/41.22 do 0 intro. intros zenon_H15b zenon_Hc zenon_H91 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H18 zenon_H42 zenon_H1b9 zenon_H115 zenon_H2c zenon_H112 zenon_H1ad zenon_H22 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_He1 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_Hb1 zenon_H9b zenon_He8 zenon_He6 zenon_Hed zenon_H16 zenon_H32 zenon_H68 zenon_H20 zenon_H1f zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_H49 zenon_Hb zenon_H2d zenon_H17 zenon_He0 zenon_H267 zenon_H261 zenon_H262 zenon_H260 zenon_H8e zenon_H26a zenon_H60 zenon_H9f zenon_Hb9 zenon_H1c9 zenon_H19a zenon_H168 zenon_H116 zenon_H18e zenon_H50 zenon_H16d zenon_H41 zenon_H51 zenon_H146 zenon_H1c8 zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.22 apply (zenon_L250_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.22 apply (zenon_L564_); trivial. % 41.04/41.22 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.22 apply (zenon_L216_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.23 apply (zenon_L217_); trivial. % 41.04/41.23 apply (zenon_L218_); trivial. % 41.04/41.23 (* end of lemma zenon_L565_ *) % 41.04/41.23 assert (zenon_L566_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((e1) = (e3))) -> ((e3) = (op (e2) (e4))) -> ((op (op (e3) (e4)) (e4)) = (e3)) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.23 do 0 intro. intros zenon_He0 zenon_Hb zenon_H115 zenon_H116 zenon_H49 zenon_H34 zenon_H32 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H9b zenon_H7b zenon_H89 zenon_H77 zenon_H9f zenon_H73 zenon_H58 zenon_H57 zenon_H88 zenon_He1 zenon_H19a zenon_H17 zenon_H2d zenon_H1f zenon_H16 zenon_H18 zenon_H168 zenon_Hc zenon_H91 zenon_H20 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H3b zenon_H18e zenon_H22 zenon_H27f zenon_H1ae zenon_H146. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.23 apply (zenon_L12_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.23 apply (zenon_L470_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.23 apply (zenon_L238_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.23 exact (zenon_He1 zenon_He5). % 41.04/41.23 apply (zenon_L471_); trivial. % 41.04/41.23 (* end of lemma zenon_L566_ *) % 41.04/41.23 assert (zenon_L567_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e4)) = (op (e4) (e0)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.23 do 0 intro. intros zenon_H19a zenon_H17 zenon_H2d zenon_H49 zenon_Hc zenon_H4a zenon_H168 zenon_H34 zenon_H32 zenon_H116 zenon_H2c zenon_H1f zenon_H115 zenon_H112 zenon_H18e zenon_H22 zenon_Hb1 zenon_H1bf zenon_H20 zenon_H81 zenon_H16 zenon_H99 zenon_H9a zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H282 zenon_Hd3 zenon_H3b zenon_H146. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.23 apply (zenon_L262_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.23 apply (zenon_L167_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.23 apply (zenon_L266_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.23 apply (zenon_L473_); trivial. % 41.04/41.23 exact (zenon_H146 zenon_H144). % 41.04/41.23 (* end of lemma zenon_L567_ *) % 41.04/41.23 assert (zenon_L568_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e4)) = (op (e4) (e0)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.23 do 0 intro. intros zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_He0 zenon_Hb zenon_H88 zenon_H7b zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H57 zenon_H58 zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_H9b zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H91 zenon_H1c9 zenon_Hb9 zenon_H73 zenon_H5f zenon_H9f zenon_H60 zenon_H61 zenon_H19a zenon_H17 zenon_H2d zenon_H49 zenon_Hc zenon_H4a zenon_H168 zenon_H34 zenon_H32 zenon_H116 zenon_H2c zenon_H1f zenon_H115 zenon_H112 zenon_H18e zenon_H22 zenon_Hb1 zenon_H20 zenon_H81 zenon_H16 zenon_H99 zenon_H9a zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H282 zenon_Hd3 zenon_H3b zenon_H146. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 41.04/41.23 apply (zenon_L272_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 41.04/41.23 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 41.04/41.23 apply (zenon_L273_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 41.04/41.23 apply (zenon_L274_); trivial. % 41.04/41.23 apply (zenon_L567_); trivial. % 41.04/41.23 (* end of lemma zenon_L568_ *) % 41.04/41.23 assert (zenon_L569_ : (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e4)) = (op (e4) (e0)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.23 do 0 intro. intros zenon_H115 zenon_H116 zenon_H49 zenon_Hb9 zenon_H1c9 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_He8 zenon_He6 zenon_Hed zenon_H6e zenon_H87 zenon_H83 zenon_Hb zenon_He0 zenon_H50 zenon_H16d zenon_H41 zenon_H51 zenon_H1c8 zenon_H34 zenon_H32 zenon_Hcc zenon_H9b zenon_H7b zenon_H89 zenon_H77 zenon_H9f zenon_H73 zenon_H58 zenon_H57 zenon_H88 zenon_He1 zenon_H19a zenon_H17 zenon_H2d zenon_H1f zenon_H168 zenon_Hc zenon_H91 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_H22 zenon_Hb1 zenon_H20 zenon_H81 zenon_H16 zenon_H99 zenon_H9a zenon_Hc8 zenon_H18 zenon_H42 zenon_H15f zenon_H282 zenon_Hd3 zenon_H3b zenon_H146. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 41.04/41.23 apply (zenon_L272_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 41.04/41.23 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 41.04/41.23 apply (zenon_L273_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 41.04/41.23 apply (zenon_L51_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.23 apply (zenon_L12_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.23 apply (zenon_L568_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.23 apply (zenon_L238_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.23 exact (zenon_He1 zenon_He5). % 41.04/41.23 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.23 apply (zenon_L263_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.23 apply (zenon_L300_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.23 apply (zenon_L266_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.23 apply (zenon_L473_); trivial. % 41.04/41.23 exact (zenon_H146 zenon_H144). % 41.04/41.23 (* end of lemma zenon_L569_ *) % 41.04/41.23 assert (zenon_L570_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e4) (e4)) = (e1))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e4) (e0)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((e3) = (op (e2) (e4))) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 41.04/41.23 do 0 intro. intros zenon_H15b zenon_H146 zenon_H3b zenon_Hd3 zenon_H282 zenon_H42 zenon_H18 zenon_Hc8 zenon_H9a zenon_H99 zenon_H16 zenon_H81 zenon_H20 zenon_Hb1 zenon_H22 zenon_H18e zenon_H2c zenon_H112 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H91 zenon_Hc zenon_H168 zenon_H1f zenon_H2d zenon_H17 zenon_H19a zenon_He1 zenon_H88 zenon_H57 zenon_H58 zenon_H73 zenon_H9f zenon_H77 zenon_H89 zenon_H7b zenon_H9b zenon_Hcc zenon_H32 zenon_H1c8 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_He0 zenon_Hb zenon_H83 zenon_H87 zenon_H6e zenon_Hed zenon_He6 zenon_He8 zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_H1c9 zenon_Hb9 zenon_H49 zenon_H116 zenon_H115 zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.23 apply (zenon_L250_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.23 apply (zenon_L569_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.23 apply (zenon_L216_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.23 apply (zenon_L217_); trivial. % 41.04/41.23 apply (zenon_L218_); trivial. % 41.04/41.23 (* end of lemma zenon_L570_ *) % 41.04/41.23 assert (zenon_L571_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e4) (e1)) = (e3)) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e4)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 41.04/41.23 do 0 intro. intros zenon_H3b zenon_H285 zenon_H1bf zenon_H284 zenon_Hb9 zenon_Hbb zenon_H58 zenon_H246 zenon_H11f zenon_H14d zenon_H24e zenon_H4a zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_Hbf zenon_Hc zenon_H83 zenon_H32 zenon_H16 zenon_H34. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.23 apply (zenon_L483_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.23 apply (zenon_L17_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.23 apply (zenon_L8_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.23 apply (zenon_L67_); trivial. % 41.04/41.23 apply (zenon_L11_); trivial. % 41.04/41.23 (* end of lemma zenon_L571_ *) % 41.04/41.23 assert (zenon_L572_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e3) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.23 do 0 intro. intros zenon_Hc2 zenon_H2c zenon_H17 zenon_H2d zenon_H18 zenon_Ha1 zenon_Hb1 zenon_Hd3 zenon_H1e7 zenon_H81 zenon_H99 zenon_H9a zenon_Hc8 zenon_Haa zenon_Hb6 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H24e zenon_H14d zenon_H11f zenon_H246 zenon_H58 zenon_Hbb zenon_Hb9 zenon_H284 zenon_H1bf zenon_H285 zenon_H3b zenon_Hc3. % 41.04/41.23 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.23 apply (zenon_L277_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.23 apply (zenon_L484_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.23 apply (zenon_L123_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.23 apply (zenon_L571_); trivial. % 41.04/41.23 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.23 (* end of lemma zenon_L572_ *) % 41.04/41.23 assert (zenon_L573_ : (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((e1) = (op (e4) (e2))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (e1) (e4)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 41.04/41.23 do 0 intro. intros zenon_H1fe zenon_H32 zenon_H7b zenon_H1f zenon_H50 zenon_H16d zenon_H41 zenon_H1e5 zenon_H81 zenon_H24e zenon_H14d zenon_H34 zenon_H11f zenon_H16 zenon_H246 zenon_H58 zenon_Hbb zenon_H22 zenon_Hb9 zenon_H285 zenon_H284 zenon_H9f zenon_H1ff zenon_H3b zenon_Hd3 zenon_H1fb zenon_Hab zenon_Hc zenon_Haa zenon_Hc8 zenon_Hcc zenon_H9a zenon_H99 zenon_H20 zenon_H1bf zenon_Hb1. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1df | zenon_intro zenon_H200 ]. % 41.04/41.23 apply (zenon_L312_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H201 ]. % 41.04/41.23 apply (zenon_L484_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H202 ]. % 41.04/41.23 apply (zenon_L486_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H203 | zenon_intro zenon_H1fc ]. % 41.04/41.23 exact (zenon_H1ff zenon_H203). % 41.04/41.23 apply (zenon_L333_); trivial. % 41.04/41.23 (* end of lemma zenon_L573_ *) % 41.04/41.23 assert (zenon_L574_ : (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e3) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.23 do 0 intro. intros zenon_Hc2 zenon_H2c zenon_H17 zenon_H2d zenon_Ha1 zenon_Hb1 zenon_H1bf zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_Haa zenon_H1ff zenon_H9f zenon_H284 zenon_H285 zenon_Hb9 zenon_Hbb zenon_H246 zenon_H11f zenon_H14d zenon_H24e zenon_H81 zenon_H1e5 zenon_H41 zenon_H16d zenon_H50 zenon_H7b zenon_H1fe zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1fb zenon_Hd3 zenon_H1fc zenon_H3b zenon_Hc3. % 41.04/41.23 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.23 apply (zenon_L317_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.23 apply (zenon_L573_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.23 apply (zenon_L279_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.23 apply (zenon_L334_); trivial. % 41.04/41.23 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.23 (* end of lemma zenon_L574_ *) % 41.04/41.23 assert (zenon_L575_ : (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (e1)) = (e3)) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.23 do 0 intro. intros zenon_H18 zenon_Hc2 zenon_H2c zenon_H17 zenon_H2d zenon_Ha1 zenon_Hb1 zenon_H1bf zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_Haa zenon_H1ff zenon_H9f zenon_H284 zenon_H285 zenon_Hb9 zenon_Hbb zenon_H246 zenon_H11f zenon_H14d zenon_H24e zenon_H81 zenon_H1e5 zenon_H41 zenon_H16d zenon_H50 zenon_H7b zenon_H1fe zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1fb zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1df | zenon_intro zenon_H200 ]. % 41.04/41.23 apply (zenon_L312_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H201 ]. % 41.04/41.23 apply (zenon_L572_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H202 ]. % 41.04/41.23 apply (zenon_L486_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H203 | zenon_intro zenon_H1fc ]. % 41.04/41.23 exact (zenon_H1ff zenon_H203). % 41.04/41.23 apply (zenon_L574_); trivial. % 41.04/41.23 (* end of lemma zenon_L575_ *) % 41.04/41.23 assert (zenon_L576_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.23 do 0 intro. intros zenon_H1c8 zenon_H146 zenon_H51 zenon_H18e zenon_H112 zenon_H115 zenon_H116 zenon_He0 zenon_Hb zenon_H88 zenon_H87 zenon_H77 zenon_H6e zenon_H57 zenon_Hed zenon_He6 zenon_He8 zenon_H9b zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H168 zenon_H91 zenon_H19a zenon_H1c9 zenon_H73 zenon_H18 zenon_Hc2 zenon_H2c zenon_H17 zenon_H2d zenon_Ha1 zenon_Hb1 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_Haa zenon_H1ff zenon_H9f zenon_H284 zenon_H285 zenon_Hb9 zenon_Hbb zenon_H246 zenon_H11f zenon_H14d zenon_H24e zenon_H81 zenon_H1e5 zenon_H41 zenon_H16d zenon_H50 zenon_H7b zenon_H1fe zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_Hb6 zenon_H58 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1fb zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 41.04/41.23 apply (zenon_L272_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 41.04/41.23 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 41.04/41.23 apply (zenon_L273_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 41.04/41.23 apply (zenon_L274_); trivial. % 41.04/41.23 apply (zenon_L575_); trivial. % 41.04/41.23 (* end of lemma zenon_L576_ *) % 41.04/41.23 assert (zenon_L577_ : (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> ((op (e1) (e1)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e4))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.23 do 0 intro. intros zenon_H49 zenon_H1c9 zenon_Hb zenon_He0 zenon_H116 zenon_H115 zenon_H51 zenon_H1c8 zenon_H88 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_H9b zenon_He9 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_He1 zenon_H1fe zenon_H7b zenon_H1e5 zenon_Hc3 zenon_H285 zenon_Hb9 zenon_Hbb zenon_H58 zenon_H246 zenon_H11f zenon_H34 zenon_H14d zenon_H24e zenon_H15f zenon_H42 zenon_Hc8 zenon_H9a zenon_H99 zenon_H83 zenon_Hb6 zenon_H32 zenon_Haa zenon_Hb1 zenon_Ha1 zenon_Hc2 zenon_H284 zenon_H9f zenon_H1ff zenon_H19a zenon_H17 zenon_H2d zenon_H18 zenon_H168 zenon_H60 zenon_H68 zenon_H5f zenon_H8e zenon_H61 zenon_H112 zenon_H2c zenon_H18e zenon_Hc zenon_H91 zenon_H81 zenon_H16 zenon_H1f zenon_H20 zenon_H22 zenon_H50 zenon_H16d zenon_H41 zenon_H1fb zenon_Hd3 zenon_H3b zenon_H146. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 41.04/41.23 apply (zenon_L272_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 41.04/41.23 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 41.04/41.23 apply (zenon_L273_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 41.04/41.23 apply (zenon_L274_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.23 apply (zenon_L12_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.23 apply (zenon_L576_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.23 apply (zenon_L112_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.23 exact (zenon_He1 zenon_He5). % 41.04/41.23 apply (zenon_L487_); trivial. % 41.04/41.23 (* end of lemma zenon_L577_ *) % 41.04/41.23 assert (zenon_L578_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e4) (e4)) = (e1))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (op (e4) (e1)) (e1)) = (e4)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (unit) (e0)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> False). % 41.04/41.23 do 0 intro. intros zenon_H15b zenon_H89 zenon_Hda zenon_H146 zenon_H3b zenon_Hd3 zenon_H1fb zenon_H41 zenon_H16d zenon_H50 zenon_H22 zenon_H20 zenon_H1f zenon_H16 zenon_H81 zenon_H91 zenon_Hc zenon_H18e zenon_H2c zenon_H112 zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H168 zenon_H18 zenon_H2d zenon_H17 zenon_H19a zenon_H1ff zenon_H9f zenon_H284 zenon_Hc2 zenon_Ha1 zenon_Hb1 zenon_Haa zenon_H32 zenon_Hb6 zenon_H83 zenon_H99 zenon_H9a zenon_Hc8 zenon_H42 zenon_H24e zenon_H246 zenon_H58 zenon_Hbb zenon_Hb9 zenon_H285 zenon_Hc3 zenon_H1e5 zenon_H7b zenon_H1fe zenon_He1 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_He9 zenon_H9b zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H88 zenon_H1c8 zenon_H51 zenon_H115 zenon_H116 zenon_He0 zenon_Hb zenon_H1c9 zenon_H49 zenon_H14d zenon_H152 zenon_H11f zenon_H34 zenon_H157. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.23 apply (zenon_L240_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.23 apply (zenon_L577_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.23 apply (zenon_L216_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.23 apply (zenon_L217_); trivial. % 41.04/41.23 apply (zenon_L218_); trivial. % 41.04/41.23 (* end of lemma zenon_L578_ *) % 41.04/41.23 assert (zenon_L579_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (op (e4) (e2)) (e4)) = (e2))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.23 do 0 intro. intros zenon_He0 zenon_Hb zenon_H161 zenon_H49 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H9b zenon_H7b zenon_H5f zenon_H89 zenon_H8e zenon_H77 zenon_H61 zenon_H9f zenon_H73 zenon_H57 zenon_H68 zenon_H88 zenon_He1 zenon_Hc2 zenon_H17 zenon_H2d zenon_H18 zenon_Ha1 zenon_H16 zenon_H32 zenon_H58 zenon_Hb9 zenon_Hb6 zenon_Hc zenon_H91 zenon_H83 zenon_H1f zenon_H20 zenon_H22 zenon_H50 zenon_H16d zenon_H41 zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H34 zenon_H288 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.23 apply (zenon_L12_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.23 apply (zenon_L504_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.23 apply (zenon_L238_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.23 exact (zenon_He1 zenon_He5). % 41.04/41.23 apply (zenon_L506_); trivial. % 41.04/41.23 (* end of lemma zenon_L579_ *) % 41.04/41.23 assert (zenon_L580_ : ((~((op (e2) (e4)) = (op (e4) (e2))))/\(((op (op (e4) (e2)) (e2)) = (e4))/\(~((op (op (e4) (e2)) (e4)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.23 do 0 intro. intros zenon_H28d zenon_He0 zenon_Hb zenon_H161 zenon_H49 zenon_H99 zenon_H9a zenon_Hcc zenon_Hc8 zenon_H9b zenon_H7b zenon_H5f zenon_H89 zenon_H8e zenon_H77 zenon_H61 zenon_H9f zenon_H73 zenon_H57 zenon_H68 zenon_H88 zenon_He1 zenon_Hc2 zenon_H17 zenon_H2d zenon_H18 zenon_Ha1 zenon_H16 zenon_H32 zenon_H58 zenon_Hb9 zenon_Hb6 zenon_Hc zenon_H91 zenon_H83 zenon_H1f zenon_H20 zenon_H22 zenon_H50 zenon_H16d zenon_H41 zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H34 zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H28d). zenon_intro zenon_H28f. zenon_intro zenon_H28e. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H28e). zenon_intro zenon_H290. zenon_intro zenon_H288. % 41.04/41.23 apply (zenon_L579_); trivial. % 41.04/41.23 (* end of lemma zenon_L580_ *) % 41.04/41.23 assert (zenon_L581_ : (((~((op (e0) (e0)) = (op (e0) (e0))))/\(((op (op (e0) (e0)) (e0)) = (e0))/\(~((op (op (e0) (e0)) (e0)) = (e0)))))\/(((~((op (e1) (e0)) = (op (e0) (e1))))/\(((op (op (e0) (e1)) (e1)) = (e0))/\(~((op (op (e0) (e1)) (e0)) = (e1)))))\/(((~((op (e2) (e0)) = (op (e0) (e2))))/\(((op (op (e0) (e2)) (e2)) = (e0))/\(~((op (op (e0) (e2)) (e0)) = (e2)))))\/(((~((op (e3) (e0)) = (op (e0) (e3))))/\(((op (op (e0) (e3)) (e3)) = (e0))/\(~((op (op (e0) (e3)) (e0)) = (e3)))))\/(((~((op (e4) (e0)) = (op (e0) (e4))))/\(((op (op (e0) (e4)) (e4)) = (e0))/\(~((op (op (e0) (e4)) (e0)) = (e4)))))\/(((~((op (e0) (e1)) = (op (e1) (e0))))/\(((op (op (e1) (e0)) (e0)) = (e1))/\(~((op (op (e1) (e0)) (e1)) = (e0)))))\/(((~((op (e1) (e1)) = (op (e1) (e1))))/\(((op (op (e1) (e1)) (e1)) = (e1))/\(~((op (op (e1) (e1)) (e1)) = (e1)))))\/(((~((op (e2) (e1)) = (op (e1) (e2))))/\(((op (op (e1) (e2)) (e2)) = (e1))/\(~((op (op (e1) (e2)) (e1)) = (e2)))))\/(((~((op (e3) (e1)) = (op (e1) (e3))))/\(((op (op (e1) (e3)) (e3)) = (e1))/\(~((op (op (e1) (e3)) (e1)) = (e3)))))\/(((~((op (e4) (e1)) = (op (e1) (e4))))/\(((op (op (e1) (e4)) (e4)) = (e1))/\(~((op (op (e1) (e4)) (e1)) = (e4)))))\/(((~((op (e0) (e2)) = (op (e2) (e0))))/\(((op (op (e2) (e0)) (e0)) = (e2))/\(~((op (op (e2) (e0)) (e2)) = (e0)))))\/(((~((op (e1) (e2)) = (op (e2) (e1))))/\(((op (op (e2) (e1)) (e1)) = (e2))/\(~((op (op (e2) (e1)) (e2)) = (e1)))))\/(((~((op (e2) (e2)) = (op (e2) (e2))))/\(((op (op (e2) (e2)) (e2)) = (e2))/\(~((op (op (e2) (e2)) (e2)) = (e2)))))\/(((~((op (e3) (e2)) = (op (e2) (e3))))/\(((op (op (e2) (e3)) (e3)) = (e2))/\(~((op (op (e2) (e3)) (e2)) = (e3)))))\/(((~((op (e4) (e2)) = (op (e2) (e4))))/\(((op (op (e2) (e4)) (e4)) = (e2))/\(~((op (op (e2) (e4)) (e2)) = (e4)))))\/(((~((op (e0) (e3)) = (op (e3) (e0))))/\(((op (op (e3) (e0)) (e0)) = (e3))/\(~((op (op (e3) (e0)) (e3)) = (e0)))))\/(((~((op (e1) (e3)) = (op (e3) (e1))))/\(((op (op (e3) (e1)) (e1)) = (e3))/\(~((op (op (e3) (e1)) (e3)) = (e1)))))\/(((~((op (e2) (e3)) = (op (e3) (e2))))/\(((op (op (e3) (e2)) (e2)) = (e3))/\(~((op (op (e3) (e2)) (e3)) = (e2)))))\/(((~((op (e3) (e3)) = (op (e3) (e3))))/\(((op (op (e3) (e3)) (e3)) = (e3))/\(~((op (op (e3) (e3)) (e3)) = (e3)))))\/(((~((op (e4) (e3)) = (op (e3) (e4))))/\(((op (op (e3) (e4)) (e4)) = (e3))/\(~((op (op (e3) (e4)) (e3)) = (e4)))))\/(((~((op (e0) (e4)) = (op (e4) (e0))))/\(((op (op (e4) (e0)) (e0)) = (e4))/\(~((op (op (e4) (e0)) (e4)) = (e0)))))\/(((~((op (e1) (e4)) = (op (e4) (e1))))/\(((op (op (e4) (e1)) (e1)) = (e4))/\(~((op (op (e4) (e1)) (e4)) = (e1)))))\/(((~((op (e2) (e4)) = (op (e4) (e2))))/\(((op (op (e4) (e2)) (e2)) = (e4))/\(~((op (op (e4) (e2)) (e4)) = (e2)))))\/(((~((op (e3) (e4)) = (op (e4) (e3))))/\(((op (op (e4) (e3)) (e3)) = (e4))/\(~((op (op (e4) (e3)) (e4)) = (e3)))))\/((~((op (e4) (e4)) = (op (e4) (e4))))/\(((op (op (e4) (e4)) (e4)) = (e4))/\(~((op (op (e4) (e4)) (e4)) = (e4))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e3)) = (e1))\/((op (e0) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e4) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e4) (e4)) = (e4))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e0) (e3)) = (op (e4) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e4) (e3)) = (e0))\/(((op (e4) (e3)) = (e1))\/(((op (e4) (e3)) = (e2))\/(((op (e4) (e3)) = (e3))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (((op (e0) (e3)) = (e4))\/(((op (e1) (e3)) = (e4))\/(((op (e2) (e3)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e4) (e3)) = (e4)))))) -> False). % 41.04/41.23 do 0 intro. intros zenon_H2ad zenon_H17e zenon_H17d zenon_H136 zenon_H10b zenon_H1d5 zenon_H1f4 zenon_H20c zenon_H20f zenon_H22d zenon_H111 zenon_H23c zenon_H240 zenon_H237 zenon_H236 zenon_Hf7 zenon_Hf6 zenon_H256 zenon_H26a zenon_H260 zenon_H261 zenon_H1ad zenon_H223 zenon_H217 zenon_H279 zenon_H26e zenon_H21a zenon_H267 zenon_H275 zenon_H157 zenon_H152 zenon_H14d zenon_H1c9 zenon_H116 zenon_H51 zenon_H1c8 zenon_H87 zenon_H6e zenon_Hed zenon_He6 zenon_He8 zenon_He9 zenon_Hd9 zenon_Hee zenon_H1fe zenon_H1e5 zenon_H285 zenon_Hbb zenon_H246 zenon_H24e zenon_H42 zenon_Haa zenon_H19a zenon_H168 zenon_H60 zenon_H18e zenon_H81 zenon_H1fb zenon_H146 zenon_Hda zenon_H15b zenon_Hc3 zenon_H1b3 zenon_H1ae zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H83 zenon_Hc zenon_Hb6 zenon_Hb9 zenon_Ha1 zenon_H18 zenon_H2d zenon_H17 zenon_Hc2 zenon_He1 zenon_H88 zenon_H68 zenon_H73 zenon_H9f zenon_H61 zenon_H77 zenon_H8e zenon_H89 zenon_H5f zenon_H7b zenon_H9b zenon_Hc8 zenon_H9a zenon_H49 zenon_Hb zenon_He0 zenon_Hd4 zenon_Hd3 zenon_H58 zenon_Hba zenon_H57 zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_H1ff zenon_H299 zenon_H2a0 zenon_H29c zenon_H41 zenon_H22 zenon_H20 zenon_H1f zenon_H161 zenon_H16d zenon_H50 zenon_H32 zenon_H16 zenon_H34 zenon_H220 zenon_H169 zenon_H2a4. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H172 | zenon_intro zenon_H2ae ]. % 41.04/41.23 apply (zenon_L251_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H17c | zenon_intro zenon_H2af ]. % 41.04/41.23 apply (zenon_L265_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H2b1 | zenon_intro zenon_H2b0 ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2b1). zenon_intro zenon_H2b3. zenon_intro zenon_H2b2. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2b2). zenon_intro zenon_H2b4. zenon_intro zenon_H1ce. % 41.04/41.23 apply (zenon_L531_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H2b6 | zenon_intro zenon_H2b5 ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2b6). zenon_intro zenon_H2b8. zenon_intro zenon_H2b7. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2b7). zenon_intro zenon_H2b9. zenon_intro zenon_H1ea. % 41.04/41.23 apply (zenon_L339_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2ba ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2bb). zenon_intro zenon_H2bd. zenon_intro zenon_H2bc. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2bc). zenon_intro zenon_H2be. zenon_intro zenon_H204. % 41.04/41.23 apply (zenon_L534_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H2c0 | zenon_intro zenon_H2bf ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2c0). zenon_intro zenon_H213. zenon_intro zenon_H2c1. % 41.04/41.23 apply (zenon_L364_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H214 | zenon_intro zenon_H2c2 ]. % 41.04/41.23 apply (zenon_L370_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H2c4 | zenon_intro zenon_H2c3 ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2c4). zenon_intro zenon_H2c6. zenon_intro zenon_H2c5. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2c5). zenon_intro zenon_H21b. zenon_intro zenon_H2c7. % 41.04/41.23 apply (zenon_L536_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2c3); [ zenon_intro zenon_H2c9 | zenon_intro zenon_H2c8 ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2c9). zenon_intro zenon_H2cb. zenon_intro zenon_H2ca. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2ca). zenon_intro zenon_H22a. zenon_intro zenon_H2cc. % 41.04/41.23 apply (zenon_L538_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2c8); [ zenon_intro zenon_H2ce | zenon_intro zenon_H2cd ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2ce). zenon_intro zenon_H2d0. zenon_intro zenon_H2cf. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2cf). zenon_intro zenon_H241. zenon_intro zenon_H2d1. % 41.04/41.23 apply (zenon_L542_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2cd); [ zenon_intro zenon_H2d3 | zenon_intro zenon_H2d2 ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2d3). zenon_intro zenon_H245. zenon_intro zenon_H2d4. % 41.04/41.23 apply (zenon_L544_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H2d6 | zenon_intro zenon_H2d5 ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2d6). zenon_intro zenon_H2d8. zenon_intro zenon_H2d7. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2d7). zenon_intro zenon_H2d9. zenon_intro zenon_H24a. % 41.04/41.23 apply (zenon_L549_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_H252 | zenon_intro zenon_H2da ]. % 41.04/41.23 apply (zenon_L417_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H2dc | zenon_intro zenon_H2db ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2de. zenon_intro zenon_H2dd. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2dd). zenon_intro zenon_H257. zenon_intro zenon_H2df. % 41.04/41.23 apply (zenon_L554_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H2e1 | zenon_intro zenon_H2e0 ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2e1). zenon_intro zenon_H2e3. zenon_intro zenon_H2e2. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2e2). zenon_intro zenon_H259. zenon_intro zenon_H2e4. % 41.04/41.23 apply (zenon_L557_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H2e6 | zenon_intro zenon_H2e5 ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2e6). zenon_intro zenon_H25d. zenon_intro zenon_H2e7. % 41.04/41.23 apply (zenon_L563_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2e9 | zenon_intro zenon_H2e8 ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2e9). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2ea). zenon_intro zenon_H262. zenon_intro zenon_H2ec. % 41.04/41.23 apply (zenon_L565_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2e8); [ zenon_intro zenon_H2ee | zenon_intro zenon_H2ed ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H2f0. zenon_intro zenon_H2ef. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H26f. zenon_intro zenon_H2f1. % 41.04/41.23 apply (zenon_L457_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2ed); [ zenon_intro zenon_H27d | zenon_intro zenon_H2f2 ]. % 41.04/41.23 apply (zenon_L468_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2f2); [ zenon_intro zenon_H2f4 | zenon_intro zenon_H2f3 ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H2f6. zenon_intro zenon_H2f5. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2f5). zenon_intro zenon_H27f. zenon_intro zenon_H2f7. % 41.04/41.23 apply (zenon_L566_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H2f9 | zenon_intro zenon_H2f8 ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2f9). zenon_intro zenon_H282. zenon_intro zenon_H2fa. % 41.04/41.23 apply (zenon_L570_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H2fc | zenon_intro zenon_H2fb ]. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2fc). zenon_intro zenon_H2fe. zenon_intro zenon_H2fd. % 41.04/41.23 apply (zenon_and_s _ _ zenon_H2fd). zenon_intro zenon_H284. zenon_intro zenon_H2ff. % 41.04/41.23 apply (zenon_L578_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H28d | zenon_intro zenon_H300 ]. % 41.04/41.23 apply (zenon_L580_); trivial. % 41.04/41.23 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H2a3 | zenon_intro zenon_H2aa ]. % 41.04/41.23 apply (zenon_L518_); trivial. % 41.04/41.23 apply (zenon_L519_); trivial. % 41.04/41.23 (* end of lemma zenon_L581_ *) % 41.04/41.23 assert (zenon_L582_ : (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e3)) = (e1))\/((op (e0) (e4)) = (e1)))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e1))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e4) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e4) (e3)))) -> (((op (e4) (e3)) = (e0))\/(((op (e4) (e3)) = (e1))\/(((op (e4) (e3)) = (e2))\/(((op (e4) (e3)) = (e3))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e4))\/(((op (e1) (e3)) = (e4))\/(((op (e2) (e3)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e4) (e3)) = (e4)))))) -> (((~((op (e0) (e0)) = (op (e0) (e0))))/\(((op (op (e0) (e0)) (e0)) = (e0))/\(~((op (op (e0) (e0)) (e0)) = (e0)))))\/(((~((op (e1) (e0)) = (op (e0) (e1))))/\(((op (op (e0) (e1)) (e1)) = (e0))/\(~((op (op (e0) (e1)) (e0)) = (e1)))))\/(((~((op (e2) (e0)) = (op (e0) (e2))))/\(((op (op (e0) (e2)) (e2)) = (e0))/\(~((op (op (e0) (e2)) (e0)) = (e2)))))\/(((~((op (e3) (e0)) = (op (e0) (e3))))/\(((op (op (e0) (e3)) (e3)) = (e0))/\(~((op (op (e0) (e3)) (e0)) = (e3)))))\/(((~((op (e4) (e0)) = (op (e0) (e4))))/\(((op (op (e0) (e4)) (e4)) = (e0))/\(~((op (op (e0) (e4)) (e0)) = (e4)))))\/(((~((op (e0) (e1)) = (op (e1) (e0))))/\(((op (op (e1) (e0)) (e0)) = (e1))/\(~((op (op (e1) (e0)) (e1)) = (e0)))))\/(((~((op (e1) (e1)) = (op (e1) (e1))))/\(((op (op (e1) (e1)) (e1)) = (e1))/\(~((op (op (e1) (e1)) (e1)) = (e1)))))\/(((~((op (e2) (e1)) = (op (e1) (e2))))/\(((op (op (e1) (e2)) (e2)) = (e1))/\(~((op (op (e1) (e2)) (e1)) = (e2)))))\/(((~((op (e3) (e1)) = (op (e1) (e3))))/\(((op (op (e1) (e3)) (e3)) = (e1))/\(~((op (op (e1) (e3)) (e1)) = (e3)))))\/(((~((op (e4) (e1)) = (op (e1) (e4))))/\(((op (op (e1) (e4)) (e4)) = (e1))/\(~((op (op (e1) (e4)) (e1)) = (e4)))))\/(((~((op (e0) (e2)) = (op (e2) (e0))))/\(((op (op (e2) (e0)) (e0)) = (e2))/\(~((op (op (e2) (e0)) (e2)) = (e0)))))\/(((~((op (e1) (e2)) = (op (e2) (e1))))/\(((op (op (e2) (e1)) (e1)) = (e2))/\(~((op (op (e2) (e1)) (e2)) = (e1)))))\/(((~((op (e2) (e2)) = (op (e2) (e2))))/\(((op (op (e2) (e2)) (e2)) = (e2))/\(~((op (op (e2) (e2)) (e2)) = (e2)))))\/(((~((op (e3) (e2)) = (op (e2) (e3))))/\(((op (op (e2) (e3)) (e3)) = (e2))/\(~((op (op (e2) (e3)) (e2)) = (e3)))))\/(((~((op (e4) (e2)) = (op (e2) (e4))))/\(((op (op (e2) (e4)) (e4)) = (e2))/\(~((op (op (e2) (e4)) (e2)) = (e4)))))\/(((~((op (e0) (e3)) = (op (e3) (e0))))/\(((op (op (e3) (e0)) (e0)) = (e3))/\(~((op (op (e3) (e0)) (e3)) = (e0)))))\/(((~((op (e1) (e3)) = (op (e3) (e1))))/\(((op (op (e3) (e1)) (e1)) = (e3))/\(~((op (op (e3) (e1)) (e3)) = (e1)))))\/(((~((op (e2) (e3)) = (op (e3) (e2))))/\(((op (op (e3) (e2)) (e2)) = (e3))/\(~((op (op (e3) (e2)) (e3)) = (e2)))))\/(((~((op (e3) (e3)) = (op (e3) (e3))))/\(((op (op (e3) (e3)) (e3)) = (e3))/\(~((op (op (e3) (e3)) (e3)) = (e3)))))\/(((~((op (e4) (e3)) = (op (e3) (e4))))/\(((op (op (e3) (e4)) (e4)) = (e3))/\(~((op (op (e3) (e4)) (e3)) = (e4)))))\/(((~((op (e0) (e4)) = (op (e4) (e0))))/\(((op (op (e4) (e0)) (e0)) = (e4))/\(~((op (op (e4) (e0)) (e4)) = (e0)))))\/(((~((op (e1) (e4)) = (op (e4) (e1))))/\(((op (op (e4) (e1)) (e1)) = (e4))/\(~((op (op (e4) (e1)) (e4)) = (e1)))))\/(((~((op (e2) (e4)) = (op (e4) (e2))))/\(((op (op (e4) (e2)) (e2)) = (e4))/\(~((op (op (e4) (e2)) (e4)) = (e2)))))\/(((~((op (e3) (e4)) = (op (e4) (e3))))/\(((op (op (e4) (e3)) (e3)) = (e4))/\(~((op (op (e4) (e3)) (e4)) = (e3)))))\/((~((op (e4) (e4)) = (op (e4) (e4))))/\(((op (op (e4) (e4)) (e4)) = (e4))/\(~((op (op (e4) (e4)) (e4)) = (e4))))))))))))))))))))))))))))) -> False). % 41.04/41.24 do 0 intro. intros zenon_H17e zenon_H17 zenon_He0 zenon_He1 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_H91 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_H136 zenon_H49 zenon_Hb zenon_Hc zenon_H18 zenon_H16 zenon_H1f zenon_H20 zenon_H22 zenon_H2d zenon_H2c zenon_H32 zenon_H34 zenon_H3b zenon_H51 zenon_H168 zenon_H17d zenon_H16d zenon_H50 zenon_H42 zenon_H41 zenon_H1c8 zenon_H8e zenon_H89 zenon_Hc2 zenon_Hc3 zenon_H1b9 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H11f zenon_Hb6 zenon_H10b zenon_H1d5 zenon_Ha1 zenon_H60 zenon_H9a zenon_H9f zenon_Hb9 zenon_H1c9 zenon_H116 zenon_H115 zenon_H112 zenon_H18e zenon_H146 zenon_H19a zenon_H14d zenon_H152 zenon_H157 zenon_H15b zenon_Haa zenon_Hbb zenon_H1fe zenon_H1fb zenon_H1ff zenon_H161 zenon_H169 zenon_H1f4 zenon_H1e5 zenon_H20c zenon_H20f zenon_H223 zenon_H220 zenon_H21a zenon_H217 zenon_H23c zenon_Hf6 zenon_Hf7 zenon_H22d zenon_H237 zenon_H236 zenon_H111 zenon_H240 zenon_H24e zenon_H246 zenon_H256 zenon_H260 zenon_H261 zenon_H267 zenon_H26a zenon_H26e zenon_H275 zenon_H279 zenon_H285 zenon_H299 zenon_H29c zenon_H2a0 zenon_H2a4 zenon_H2ad. % 41.04/41.24 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 41.04/41.24 apply (zenon_L581_); trivial. % 41.04/41.24 apply (zenon_L99_); trivial. % 41.04/41.24 (* end of lemma zenon_L582_ *) % 41.04/41.24 assert (zenon_L583_ : ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (((~((op (e0) (e0)) = (op (e0) (e0))))/\(((op (op (e0) (e0)) (e0)) = (e0))/\(~((op (op (e0) (e0)) (e0)) = (e0)))))\/(((~((op (e1) (e0)) = (op (e0) (e1))))/\(((op (op (e0) (e1)) (e1)) = (e0))/\(~((op (op (e0) (e1)) (e0)) = (e1)))))\/(((~((op (e2) (e0)) = (op (e0) (e2))))/\(((op (op (e0) (e2)) (e2)) = (e0))/\(~((op (op (e0) (e2)) (e0)) = (e2)))))\/(((~((op (e3) (e0)) = (op (e0) (e3))))/\(((op (op (e0) (e3)) (e3)) = (e0))/\(~((op (op (e0) (e3)) (e0)) = (e3)))))\/(((~((op (e4) (e0)) = (op (e0) (e4))))/\(((op (op (e0) (e4)) (e4)) = (e0))/\(~((op (op (e0) (e4)) (e0)) = (e4)))))\/(((~((op (e0) (e1)) = (op (e1) (e0))))/\(((op (op (e1) (e0)) (e0)) = (e1))/\(~((op (op (e1) (e0)) (e1)) = (e0)))))\/(((~((op (e1) (e1)) = (op (e1) (e1))))/\(((op (op (e1) (e1)) (e1)) = (e1))/\(~((op (op (e1) (e1)) (e1)) = (e1)))))\/(((~((op (e2) (e1)) = (op (e1) (e2))))/\(((op (op (e1) (e2)) (e2)) = (e1))/\(~((op (op (e1) (e2)) (e1)) = (e2)))))\/(((~((op (e3) (e1)) = (op (e1) (e3))))/\(((op (op (e1) (e3)) (e3)) = (e1))/\(~((op (op (e1) (e3)) (e1)) = (e3)))))\/(((~((op (e4) (e1)) = (op (e1) (e4))))/\(((op (op (e1) (e4)) (e4)) = (e1))/\(~((op (op (e1) (e4)) (e1)) = (e4)))))\/(((~((op (e0) (e2)) = (op (e2) (e0))))/\(((op (op (e2) (e0)) (e0)) = (e2))/\(~((op (op (e2) (e0)) (e2)) = (e0)))))\/(((~((op (e1) (e2)) = (op (e2) (e1))))/\(((op (op (e2) (e1)) (e1)) = (e2))/\(~((op (op (e2) (e1)) (e2)) = (e1)))))\/(((~((op (e2) (e2)) = (op (e2) (e2))))/\(((op (op (e2) (e2)) (e2)) = (e2))/\(~((op (op (e2) (e2)) (e2)) = (e2)))))\/(((~((op (e3) (e2)) = (op (e2) (e3))))/\(((op (op (e2) (e3)) (e3)) = (e2))/\(~((op (op (e2) (e3)) (e2)) = (e3)))))\/(((~((op (e4) (e2)) = (op (e2) (e4))))/\(((op (op (e2) (e4)) (e4)) = (e2))/\(~((op (op (e2) (e4)) (e2)) = (e4)))))\/(((~((op (e0) (e3)) = (op (e3) (e0))))/\(((op (op (e3) (e0)) (e0)) = (e3))/\(~((op (op (e3) (e0)) (e3)) = (e0)))))\/(((~((op (e1) (e3)) = (op (e3) (e1))))/\(((op (op (e3) (e1)) (e1)) = (e3))/\(~((op (op (e3) (e1)) (e3)) = (e1)))))\/(((~((op (e2) (e3)) = (op (e3) (e2))))/\(((op (op (e3) (e2)) (e2)) = (e3))/\(~((op (op (e3) (e2)) (e3)) = (e2)))))\/(((~((op (e3) (e3)) = (op (e3) (e3))))/\(((op (op (e3) (e3)) (e3)) = (e3))/\(~((op (op (e3) (e3)) (e3)) = (e3)))))\/(((~((op (e4) (e3)) = (op (e3) (e4))))/\(((op (op (e3) (e4)) (e4)) = (e3))/\(~((op (op (e3) (e4)) (e3)) = (e4)))))\/(((~((op (e0) (e4)) = (op (e4) (e0))))/\(((op (op (e4) (e0)) (e0)) = (e4))/\(~((op (op (e4) (e0)) (e4)) = (e0)))))\/(((~((op (e1) (e4)) = (op (e4) (e1))))/\(((op (op (e4) (e1)) (e1)) = (e4))/\(~((op (op (e4) (e1)) (e4)) = (e1)))))\/(((~((op (e2) (e4)) = (op (e4) (e2))))/\(((op (op (e4) (e2)) (e2)) = (e4))/\(~((op (op (e4) (e2)) (e4)) = (e2)))))\/(((~((op (e3) (e4)) = (op (e4) (e3))))/\(((op (op (e4) (e3)) (e3)) = (e4))/\(~((op (op (e4) (e3)) (e4)) = (e3)))))\/((~((op (e4) (e4)) = (op (e4) (e4))))/\(((op (op (e4) (e4)) (e4)) = (e4))/\(~((op (op (e4) (e4)) (e4)) = (e4))))))))))))))))))))))))))))) -> (((op (e0) (e3)) = (e4))\/(((op (e1) (e3)) = (e4))\/(((op (e2) (e3)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e4) (e3)) = (e0))\/(((op (e4) (e3)) = (e1))\/(((op (e4) (e3)) = (e2))\/(((op (e4) (e3)) = (e3))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e3)) = (op (e4) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e4) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e3)) = (e1))\/((op (e0) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> False). % 41.04/41.24 do 0 intro. intros zenon_Hf1 zenon_H2ad zenon_H2a4 zenon_H2a0 zenon_H29c zenon_H299 zenon_H285 zenon_H279 zenon_H275 zenon_H26e zenon_H26a zenon_H267 zenon_H261 zenon_H260 zenon_H256 zenon_H246 zenon_H24e zenon_H240 zenon_H111 zenon_H236 zenon_H237 zenon_H22d zenon_Hf7 zenon_Hf6 zenon_H23c zenon_H217 zenon_H21a zenon_H220 zenon_H223 zenon_H20f zenon_H20c zenon_H1e5 zenon_H1f4 zenon_H169 zenon_H161 zenon_H1ff zenon_H1fb zenon_H1fe zenon_Hbb zenon_Haa zenon_H15b zenon_H157 zenon_H152 zenon_H14d zenon_H19a zenon_H146 zenon_H18e zenon_H112 zenon_H115 zenon_H116 zenon_H1c9 zenon_Hb9 zenon_H9f zenon_H9a zenon_H60 zenon_Ha1 zenon_H1d5 zenon_H10b zenon_Hb6 zenon_H11f zenon_H1ad zenon_H1ae zenon_H1b3 zenon_H1b9 zenon_Hc2 zenon_H89 zenon_H8e zenon_H1c8 zenon_H41 zenon_H42 zenon_H50 zenon_H16d zenon_H17d zenon_H168 zenon_H51 zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H49 zenon_H136 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_He1 zenon_He0 zenon_H17 zenon_H17e. % 41.04/41.24 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 41.04/41.24 apply (zenon_L582_); trivial. % 41.04/41.24 apply (zenon_L246_); trivial. % 41.04/41.24 (* end of lemma zenon_L583_ *) % 41.04/41.24 assert (zenon_L584_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (e0)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e1)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> False). % 41.04/41.24 do 0 intro. intros zenon_H3b zenon_H9b zenon_H9a zenon_H32 zenon_Hb1 zenon_H99 zenon_Hd3 zenon_Ha5 zenon_He8. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.24 apply (zenon_L55_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.24 apply (zenon_L49_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.24 apply (zenon_L58_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.24 apply (zenon_L60_); trivial. % 41.04/41.24 apply (zenon_L124_); trivial. % 41.04/41.24 (* end of lemma zenon_L584_ *) % 41.04/41.24 assert (zenon_L585_ : ((~((op (e4) (e4)) = (e1)))\/((op (e4) (e1)) = (e4))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e3)) = (e1))\/((op (e0) (e4)) = (e1)))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e4) (e0)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e4))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e4) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e4) (e3)))) -> (((op (e4) (e3)) = (e0))\/(((op (e4) (e3)) = (e1))\/(((op (e4) (e3)) = (e2))\/(((op (e4) (e3)) = (e3))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e4))\/(((op (e1) (e3)) = (e4))\/(((op (e2) (e3)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e4) (e3)) = (e4)))))) -> (((~((op (e0) (e0)) = (op (e0) (e0))))/\(((op (op (e0) (e0)) (e0)) = (e0))/\(~((op (op (e0) (e0)) (e0)) = (e0)))))\/(((~((op (e1) (e0)) = (op (e0) (e1))))/\(((op (op (e0) (e1)) (e1)) = (e0))/\(~((op (op (e0) (e1)) (e0)) = (e1)))))\/(((~((op (e2) (e0)) = (op (e0) (e2))))/\(((op (op (e0) (e2)) (e2)) = (e0))/\(~((op (op (e0) (e2)) (e0)) = (e2)))))\/(((~((op (e3) (e0)) = (op (e0) (e3))))/\(((op (op (e0) (e3)) (e3)) = (e0))/\(~((op (op (e0) (e3)) (e0)) = (e3)))))\/(((~((op (e4) (e0)) = (op (e0) (e4))))/\(((op (op (e0) (e4)) (e4)) = (e0))/\(~((op (op (e0) (e4)) (e0)) = (e4)))))\/(((~((op (e0) (e1)) = (op (e1) (e0))))/\(((op (op (e1) (e0)) (e0)) = (e1))/\(~((op (op (e1) (e0)) (e1)) = (e0)))))\/(((~((op (e1) (e1)) = (op (e1) (e1))))/\(((op (op (e1) (e1)) (e1)) = (e1))/\(~((op (op (e1) (e1)) (e1)) = (e1)))))\/(((~((op (e2) (e1)) = (op (e1) (e2))))/\(((op (op (e1) (e2)) (e2)) = (e1))/\(~((op (op (e1) (e2)) (e1)) = (e2)))))\/(((~((op (e3) (e1)) = (op (e1) (e3))))/\(((op (op (e1) (e3)) (e3)) = (e1))/\(~((op (op (e1) (e3)) (e1)) = (e3)))))\/(((~((op (e4) (e1)) = (op (e1) (e4))))/\(((op (op (e1) (e4)) (e4)) = (e1))/\(~((op (op (e1) (e4)) (e1)) = (e4)))))\/(((~((op (e0) (e2)) = (op (e2) (e0))))/\(((op (op (e2) (e0)) (e0)) = (e2))/\(~((op (op (e2) (e0)) (e2)) = (e0)))))\/(((~((op (e1) (e2)) = (op (e2) (e1))))/\(((op (op (e2) (e1)) (e1)) = (e2))/\(~((op (op (e2) (e1)) (e2)) = (e1)))))\/(((~((op (e2) (e2)) = (op (e2) (e2))))/\(((op (op (e2) (e2)) (e2)) = (e2))/\(~((op (op (e2) (e2)) (e2)) = (e2)))))\/(((~((op (e3) (e2)) = (op (e2) (e3))))/\(((op (op (e2) (e3)) (e3)) = (e2))/\(~((op (op (e2) (e3)) (e2)) = (e3)))))\/(((~((op (e4) (e2)) = (op (e2) (e4))))/\(((op (op (e2) (e4)) (e4)) = (e2))/\(~((op (op (e2) (e4)) (e2)) = (e4)))))\/(((~((op (e0) (e3)) = (op (e3) (e0))))/\(((op (op (e3) (e0)) (e0)) = (e3))/\(~((op (op (e3) (e0)) (e3)) = (e0)))))\/(((~((op (e1) (e3)) = (op (e3) (e1))))/\(((op (op (e3) (e1)) (e1)) = (e3))/\(~((op (op (e3) (e1)) (e3)) = (e1)))))\/(((~((op (e2) (e3)) = (op (e3) (e2))))/\(((op (op (e3) (e2)) (e2)) = (e3))/\(~((op (op (e3) (e2)) (e3)) = (e2)))))\/(((~((op (e3) (e3)) = (op (e3) (e3))))/\(((op (op (e3) (e3)) (e3)) = (e3))/\(~((op (op (e3) (e3)) (e3)) = (e3)))))\/(((~((op (e4) (e3)) = (op (e3) (e4))))/\(((op (op (e3) (e4)) (e4)) = (e3))/\(~((op (op (e3) (e4)) (e3)) = (e4)))))\/(((~((op (e0) (e4)) = (op (e4) (e0))))/\(((op (op (e4) (e0)) (e0)) = (e4))/\(~((op (op (e4) (e0)) (e4)) = (e0)))))\/(((~((op (e1) (e4)) = (op (e4) (e1))))/\(((op (op (e4) (e1)) (e1)) = (e4))/\(~((op (op (e4) (e1)) (e4)) = (e1)))))\/(((~((op (e2) (e4)) = (op (e4) (e2))))/\(((op (op (e4) (e2)) (e2)) = (e4))/\(~((op (op (e4) (e2)) (e4)) = (e2)))))\/(((~((op (e3) (e4)) = (op (e4) (e3))))/\(((op (op (e4) (e3)) (e3)) = (e4))/\(~((op (op (e4) (e3)) (e4)) = (e3)))))\/((~((op (e4) (e4)) = (op (e4) (e4))))/\(((op (op (e4) (e4)) (e4)) = (e4))/\(~((op (op (e4) (e4)) (e4)) = (e4))))))))))))))))))))))))))))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> False). % 41.04/41.24 do 0 intro. intros zenon_H2ac zenon_H17e zenon_H17 zenon_He0 zenon_He1 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_H91 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_H136 zenon_H49 zenon_Hb zenon_Hc zenon_H18 zenon_H16 zenon_H1f zenon_H20 zenon_H22 zenon_H2d zenon_H2c zenon_H32 zenon_H34 zenon_H3b zenon_H51 zenon_H168 zenon_H17d zenon_H16d zenon_H50 zenon_H42 zenon_H41 zenon_H1c8 zenon_H8e zenon_H89 zenon_Hc2 zenon_H1b9 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H11f zenon_Hb6 zenon_H10b zenon_H1d5 zenon_Ha1 zenon_H60 zenon_H9a zenon_H9f zenon_Hb9 zenon_H1c9 zenon_H116 zenon_H115 zenon_H112 zenon_H18e zenon_H19a zenon_H14d zenon_H152 zenon_H157 zenon_H15b zenon_Haa zenon_Hbb zenon_H1fe zenon_H1fb zenon_H1ff zenon_H161 zenon_H169 zenon_H1f4 zenon_H1e5 zenon_H20c zenon_H20f zenon_H223 zenon_H220 zenon_H21a zenon_H217 zenon_H23c zenon_Hf6 zenon_Hf7 zenon_H22d zenon_H237 zenon_H236 zenon_H111 zenon_H240 zenon_H24e zenon_H246 zenon_H256 zenon_H260 zenon_H261 zenon_H267 zenon_H26a zenon_H26e zenon_H275 zenon_H279 zenon_H285 zenon_H299 zenon_H29c zenon_H2a0 zenon_H2a4 zenon_H2ad zenon_Hf1. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H146 | zenon_intro zenon_Ha5 ]. % 41.04/41.24 apply (zenon_L583_); trivial. % 41.04/41.24 apply (zenon_L584_); trivial. % 41.04/41.24 (* end of lemma zenon_L585_ *) % 41.04/41.24 assert (zenon_L586_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 41.04/41.24 do 0 intro. intros zenon_H3b zenon_H8d zenon_H61 zenon_H8e zenon_H5f zenon_H68 zenon_H60 zenon_H20 zenon_H32 zenon_H16 zenon_H34. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.24 apply (zenon_L101_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.24 apply (zenon_L24_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.24 apply (zenon_L42_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.24 apply (zenon_L26_); trivial. % 41.04/41.24 apply (zenon_L11_); trivial. % 41.04/41.24 (* end of lemma zenon_L586_ *) % 41.04/41.24 assert (zenon_L587_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 41.04/41.24 do 0 intro. intros zenon_H3b zenon_H61 zenon_H8e zenon_H60 zenon_H5f zenon_H77 zenon_H76 zenon_H20 zenon_H32 zenon_H16 zenon_H34. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.24 apply (zenon_L83_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.24 apply (zenon_L24_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.24 apply (zenon_L42_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.24 apply (zenon_L32_); trivial. % 41.04/41.24 apply (zenon_L11_); trivial. % 41.04/41.24 (* end of lemma zenon_L587_ *) % 41.04/41.24 assert (zenon_L588_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (((~((op (e0) (e0)) = (op (e0) (e0))))/\(((op (op (e0) (e0)) (e0)) = (e0))/\(~((op (op (e0) (e0)) (e0)) = (e0)))))\/(((~((op (e1) (e0)) = (op (e0) (e1))))/\(((op (op (e0) (e1)) (e1)) = (e0))/\(~((op (op (e0) (e1)) (e0)) = (e1)))))\/(((~((op (e2) (e0)) = (op (e0) (e2))))/\(((op (op (e0) (e2)) (e2)) = (e0))/\(~((op (op (e0) (e2)) (e0)) = (e2)))))\/(((~((op (e3) (e0)) = (op (e0) (e3))))/\(((op (op (e0) (e3)) (e3)) = (e0))/\(~((op (op (e0) (e3)) (e0)) = (e3)))))\/(((~((op (e4) (e0)) = (op (e0) (e4))))/\(((op (op (e0) (e4)) (e4)) = (e0))/\(~((op (op (e0) (e4)) (e0)) = (e4)))))\/(((~((op (e0) (e1)) = (op (e1) (e0))))/\(((op (op (e1) (e0)) (e0)) = (e1))/\(~((op (op (e1) (e0)) (e1)) = (e0)))))\/(((~((op (e1) (e1)) = (op (e1) (e1))))/\(((op (op (e1) (e1)) (e1)) = (e1))/\(~((op (op (e1) (e1)) (e1)) = (e1)))))\/(((~((op (e2) (e1)) = (op (e1) (e2))))/\(((op (op (e1) (e2)) (e2)) = (e1))/\(~((op (op (e1) (e2)) (e1)) = (e2)))))\/(((~((op (e3) (e1)) = (op (e1) (e3))))/\(((op (op (e1) (e3)) (e3)) = (e1))/\(~((op (op (e1) (e3)) (e1)) = (e3)))))\/(((~((op (e4) (e1)) = (op (e1) (e4))))/\(((op (op (e1) (e4)) (e4)) = (e1))/\(~((op (op (e1) (e4)) (e1)) = (e4)))))\/(((~((op (e0) (e2)) = (op (e2) (e0))))/\(((op (op (e2) (e0)) (e0)) = (e2))/\(~((op (op (e2) (e0)) (e2)) = (e0)))))\/(((~((op (e1) (e2)) = (op (e2) (e1))))/\(((op (op (e2) (e1)) (e1)) = (e2))/\(~((op (op (e2) (e1)) (e2)) = (e1)))))\/(((~((op (e2) (e2)) = (op (e2) (e2))))/\(((op (op (e2) (e2)) (e2)) = (e2))/\(~((op (op (e2) (e2)) (e2)) = (e2)))))\/(((~((op (e3) (e2)) = (op (e2) (e3))))/\(((op (op (e2) (e3)) (e3)) = (e2))/\(~((op (op (e2) (e3)) (e2)) = (e3)))))\/(((~((op (e4) (e2)) = (op (e2) (e4))))/\(((op (op (e2) (e4)) (e4)) = (e2))/\(~((op (op (e2) (e4)) (e2)) = (e4)))))\/(((~((op (e0) (e3)) = (op (e3) (e0))))/\(((op (op (e3) (e0)) (e0)) = (e3))/\(~((op (op (e3) (e0)) (e3)) = (e0)))))\/(((~((op (e1) (e3)) = (op (e3) (e1))))/\(((op (op (e3) (e1)) (e1)) = (e3))/\(~((op (op (e3) (e1)) (e3)) = (e1)))))\/(((~((op (e2) (e3)) = (op (e3) (e2))))/\(((op (op (e3) (e2)) (e2)) = (e3))/\(~((op (op (e3) (e2)) (e3)) = (e2)))))\/(((~((op (e3) (e3)) = (op (e3) (e3))))/\(((op (op (e3) (e3)) (e3)) = (e3))/\(~((op (op (e3) (e3)) (e3)) = (e3)))))\/(((~((op (e4) (e3)) = (op (e3) (e4))))/\(((op (op (e3) (e4)) (e4)) = (e3))/\(~((op (op (e3) (e4)) (e3)) = (e4)))))\/(((~((op (e0) (e4)) = (op (e4) (e0))))/\(((op (op (e4) (e0)) (e0)) = (e4))/\(~((op (op (e4) (e0)) (e4)) = (e0)))))\/(((~((op (e1) (e4)) = (op (e4) (e1))))/\(((op (op (e4) (e1)) (e1)) = (e4))/\(~((op (op (e4) (e1)) (e4)) = (e1)))))\/(((~((op (e2) (e4)) = (op (e4) (e2))))/\(((op (op (e4) (e2)) (e2)) = (e4))/\(~((op (op (e4) (e2)) (e4)) = (e2)))))\/(((~((op (e3) (e4)) = (op (e4) (e3))))/\(((op (op (e4) (e3)) (e3)) = (e4))/\(~((op (op (e4) (e3)) (e4)) = (e3)))))\/((~((op (e4) (e4)) = (op (e4) (e4))))/\(((op (op (e4) (e4)) (e4)) = (e4))/\(~((op (op (e4) (e4)) (e4)) = (e4))))))))))))))))))))))))))))) -> (((op (e0) (e3)) = (e4))\/(((op (e1) (e3)) = (e4))\/(((op (e2) (e3)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e4) (e3)) = (e0))\/(((op (e4) (e3)) = (e1))\/(((op (e4) (e3)) = (e2))\/(((op (e4) (e3)) = (e3))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e3)) = (op (e4) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e4) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e3)) = (e1))\/((op (e0) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e4) (e4)) = (e1)))\/((op (e4) (e1)) = (e4))) -> ((~((op (e3) (e3)) = (e4)))\/((op (e3) (e4)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 41.04/41.24 do 0 intro. intros zenon_H301 zenon_H14a zenon_Hf1 zenon_H2ad zenon_H2a4 zenon_H2a0 zenon_H29c zenon_H299 zenon_H285 zenon_H279 zenon_H275 zenon_H26e zenon_H260 zenon_H261 zenon_H267 zenon_H26a zenon_H256 zenon_H24e zenon_H246 zenon_H240 zenon_H111 zenon_H236 zenon_H22d zenon_Hf7 zenon_Hf6 zenon_H23c zenon_H217 zenon_H21a zenon_H220 zenon_H223 zenon_H20f zenon_H20c zenon_H1fe zenon_H1fb zenon_H161 zenon_H1f4 zenon_H1e5 zenon_H169 zenon_Haa zenon_H15b zenon_H157 zenon_H152 zenon_H14d zenon_H19a zenon_H18e zenon_H112 zenon_H115 zenon_H116 zenon_H1c9 zenon_Hb9 zenon_H9f zenon_H60 zenon_H10b zenon_H1d5 zenon_H1c4 zenon_Hbb zenon_Hc2 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_H1b9 zenon_Hb6 zenon_H8e zenon_Ha1 zenon_H1a9 zenon_H11f zenon_H165 zenon_H1c8 zenon_H41 zenon_H42 zenon_H50 zenon_H16d zenon_H17d zenon_H168 zenon_H51 zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H49 zenon_H136 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_He0 zenon_H17 zenon_H17e zenon_H2ac zenon_H302 zenon_Hf0. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H237 | zenon_intro zenon_H72 ]. % 41.04/41.24 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_He1 | zenon_intro zenon_H76 ]. % 41.04/41.24 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1ff | zenon_intro zenon_H7c ]. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H13e | zenon_intro zenon_H9a ]. % 41.04/41.24 apply (zenon_L526_); trivial. % 41.04/41.24 apply (zenon_L585_); trivial. % 41.04/41.24 apply (zenon_L40_); trivial. % 41.04/41.24 apply (zenon_L586_); trivial. % 41.04/41.24 apply (zenon_L587_); trivial. % 41.04/41.24 apply (zenon_L274_); trivial. % 41.04/41.24 (* end of lemma zenon_L588_ *) % 41.04/41.24 assert (zenon_L589_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 41.04/41.24 do 0 intro. intros zenon_He0 zenon_Hb zenon_H116 zenon_Hab zenon_H81 zenon_H197 zenon_H6e zenon_He1 zenon_Hd9 zenon_H61 zenon_Hc3 zenon_H9b zenon_Hbb zenon_H83 zenon_Hb6 zenon_Hb9 zenon_H9f zenon_H5f zenon_H73 zenon_H72 zenon_H16 zenon_H34 zenon_Haa zenon_Ha1 zenon_H18 zenon_H2d zenon_H17 zenon_H2c zenon_Hc2 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_Hc8 zenon_Hd4 zenon_Hd3 zenon_H58 zenon_Hba zenon_H57 zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 41.04/41.24 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.24 apply (zenon_L12_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.24 apply (zenon_L278_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.24 apply (zenon_L286_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.24 exact (zenon_He1 zenon_He5). % 41.04/41.24 apply (zenon_L82_); trivial. % 41.04/41.24 (* end of lemma zenon_L589_ *) % 41.04/41.24 assert (zenon_L590_ : (~((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e4)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.24 do 0 intro. intros zenon_Hda zenon_Hcc zenon_Hb1 zenon_H99 zenon_H91 zenon_H57 zenon_Hba zenon_Hd4 zenon_Hc8 zenon_Hc2 zenon_H17 zenon_H2d zenon_H18 zenon_Ha1 zenon_Haa zenon_H72 zenon_H73 zenon_H5f zenon_H9f zenon_Hbb zenon_H9b zenon_H61 zenon_Hd9 zenon_He1 zenon_H6e zenon_H197 zenon_H81 zenon_H116 zenon_Hb zenon_He0 zenon_H58 zenon_Hb9 zenon_Hb6 zenon_H34 zenon_H16 zenon_H32 zenon_H83 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H49 zenon_H4a zenon_H1b9 zenon_H115 zenon_H11f zenon_H2c zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_Hd3 zenon_H3b zenon_Hc3. % 41.04/41.24 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.24 apply (zenon_L277_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.24 apply (zenon_L589_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.24 apply (zenon_L123_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.24 apply (zenon_L285_); trivial. % 41.04/41.24 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.24 (* end of lemma zenon_L590_ *) % 41.04/41.24 assert (zenon_L591_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((e1) = (e3))) -> (~((op (e4) (e4)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.24 do 0 intro. intros zenon_H19a zenon_H168 zenon_Hee zenon_He9 zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H77 zenon_H87 zenon_H7b zenon_H88 zenon_H18e zenon_Hc3 zenon_H3b zenon_Hd3 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H2c zenon_H11f zenon_H115 zenon_H1b9 zenon_H4a zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_Hc zenon_H83 zenon_H32 zenon_H16 zenon_H34 zenon_Hb6 zenon_Hb9 zenon_H58 zenon_He0 zenon_Hb zenon_H116 zenon_H81 zenon_H6e zenon_He1 zenon_Hd9 zenon_H61 zenon_H9b zenon_Hbb zenon_H9f zenon_H5f zenon_H73 zenon_H72 zenon_Haa zenon_Ha1 zenon_H18 zenon_H2d zenon_H17 zenon_Hc2 zenon_Hc8 zenon_Hd4 zenon_Hba zenon_H57 zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_Hda zenon_H146. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.24 apply (zenon_L264_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.24 apply (zenon_L178_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.24 apply (zenon_L266_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.24 apply (zenon_L590_); trivial. % 41.04/41.24 exact (zenon_H146 zenon_H144). % 41.04/41.24 (* end of lemma zenon_L591_ *) % 41.04/41.24 assert (zenon_L592_ : (~((op (e4) (e4)) = (e1))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 41.04/41.24 do 0 intro. intros zenon_H146 zenon_H116 zenon_Hb zenon_He0 zenon_H49 zenon_H1b9 zenon_H115 zenon_H11f zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_H18e zenon_Hed zenon_He6 zenon_He8 zenon_He9 zenon_Hee zenon_H168 zenon_H19a zenon_H87 zenon_H81 zenon_H7b zenon_H89 zenon_H6e zenon_H77 zenon_H68 zenon_H88 zenon_He1 zenon_Hd9 zenon_H61 zenon_Hc3 zenon_H9b zenon_Hbb zenon_H83 zenon_Hb6 zenon_Hb9 zenon_H9f zenon_H5f zenon_H73 zenon_H72 zenon_H16 zenon_H34 zenon_Haa zenon_Ha1 zenon_H18 zenon_H2d zenon_H17 zenon_H2c zenon_Hc2 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_Hc8 zenon_Hd4 zenon_Hd3 zenon_H58 zenon_Hba zenon_H57 zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 41.04/41.24 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.24 apply (zenon_L12_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.24 apply (zenon_L591_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.24 apply (zenon_L41_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.24 exact (zenon_He1 zenon_He5). % 41.04/41.24 apply (zenon_L82_); trivial. % 41.04/41.24 (* end of lemma zenon_L592_ *) % 41.04/41.24 assert (zenon_L593_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.24 do 0 intro. intros zenon_H19a zenon_H17 zenon_H2d zenon_H49 zenon_Hc zenon_H4a zenon_H168 zenon_H116 zenon_H2c zenon_H115 zenon_H112 zenon_H18e zenon_H34 zenon_H16 zenon_H32 zenon_H81 zenon_H1f zenon_H20 zenon_H22 zenon_H50 zenon_H16d zenon_H41 zenon_H193 zenon_H51 zenon_H3b zenon_H146. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.24 apply (zenon_L262_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.24 apply (zenon_L167_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.24 apply (zenon_L266_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.24 apply (zenon_L271_); trivial. % 41.04/41.24 exact (zenon_H146 zenon_H144). % 41.04/41.24 (* end of lemma zenon_L593_ *) % 41.04/41.24 assert (zenon_L594_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e1)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 41.04/41.24 do 0 intro. intros zenon_H3b zenon_H8e zenon_H5f zenon_H9f zenon_H22 zenon_H1f zenon_H77 zenon_H76 zenon_H20 zenon_H1bf zenon_Hb1. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.24 apply (zenon_L83_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.24 apply (zenon_L89_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.24 apply (zenon_L8_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.24 apply (zenon_L32_); trivial. % 41.04/41.24 apply (zenon_L290_); trivial. % 41.04/41.24 (* end of lemma zenon_L594_ *) % 41.04/41.24 assert (zenon_L595_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 41.04/41.24 do 0 intro. intros zenon_H1c8 zenon_H146 zenon_H51 zenon_H41 zenon_H16d zenon_H50 zenon_H81 zenon_H18e zenon_H112 zenon_H115 zenon_H2c zenon_H116 zenon_H168 zenon_H4a zenon_Hc zenon_H49 zenon_H2d zenon_H17 zenon_H19a zenon_H1c9 zenon_Hb9 zenon_H34 zenon_H16 zenon_H32 zenon_H3b zenon_H8e zenon_H5f zenon_H9f zenon_H22 zenon_H1f zenon_H77 zenon_H76 zenon_H20 zenon_Hb1. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 41.04/41.24 apply (zenon_L593_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 41.04/41.24 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.24 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 41.04/41.24 apply (zenon_L273_); trivial. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 41.04/41.24 apply (zenon_L196_); trivial. % 41.04/41.24 apply (zenon_L594_); trivial. % 41.04/41.24 (* end of lemma zenon_L595_ *) % 41.04/41.24 assert (zenon_L596_ : ((~((op (e4) (e4)) = (e1)))\/((op (e4) (e1)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> False). % 41.04/41.24 do 0 intro. intros zenon_H2ac zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H17 zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H1c8 zenon_Hb1 zenon_H8e zenon_H5f zenon_H76 zenon_H9f zenon_H77 zenon_Hb9 zenon_H1c9 zenon_H49 zenon_H168 zenon_H116 zenon_H115 zenon_H112 zenon_H18e zenon_H81 zenon_H16d zenon_H50 zenon_H41 zenon_H51 zenon_H19a zenon_Hee zenon_Hd9 zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H87 zenon_H83 zenon_H7b zenon_H88 zenon_Hba zenon_Hc2 zenon_Hb6 zenon_Haa zenon_Ha1 zenon_He0 zenon_Hf1. % 41.04/41.24 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H146 | zenon_intro zenon_Ha5 ]. % 41.04/41.24 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.25 apply (zenon_L12_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.25 apply (zenon_L595_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.25 apply (zenon_L132_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.25 apply (zenon_L116_); trivial. % 41.04/41.25 apply (zenon_L92_); trivial. % 41.04/41.25 apply (zenon_L99_); trivial. % 41.04/41.25 apply (zenon_L117_); trivial. % 41.04/41.25 apply (zenon_L113_); trivial. % 41.04/41.25 (* end of lemma zenon_L596_ *) % 41.04/41.25 assert (zenon_L597_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (((~((op (e0) (e0)) = (op (e0) (e0))))/\(((op (op (e0) (e0)) (e0)) = (e0))/\(~((op (op (e0) (e0)) (e0)) = (e0)))))\/(((~((op (e1) (e0)) = (op (e0) (e1))))/\(((op (op (e0) (e1)) (e1)) = (e0))/\(~((op (op (e0) (e1)) (e0)) = (e1)))))\/(((~((op (e2) (e0)) = (op (e0) (e2))))/\(((op (op (e0) (e2)) (e2)) = (e0))/\(~((op (op (e0) (e2)) (e0)) = (e2)))))\/(((~((op (e3) (e0)) = (op (e0) (e3))))/\(((op (op (e0) (e3)) (e3)) = (e0))/\(~((op (op (e0) (e3)) (e0)) = (e3)))))\/(((~((op (e4) (e0)) = (op (e0) (e4))))/\(((op (op (e0) (e4)) (e4)) = (e0))/\(~((op (op (e0) (e4)) (e0)) = (e4)))))\/(((~((op (e0) (e1)) = (op (e1) (e0))))/\(((op (op (e1) (e0)) (e0)) = (e1))/\(~((op (op (e1) (e0)) (e1)) = (e0)))))\/(((~((op (e1) (e1)) = (op (e1) (e1))))/\(((op (op (e1) (e1)) (e1)) = (e1))/\(~((op (op (e1) (e1)) (e1)) = (e1)))))\/(((~((op (e2) (e1)) = (op (e1) (e2))))/\(((op (op (e1) (e2)) (e2)) = (e1))/\(~((op (op (e1) (e2)) (e1)) = (e2)))))\/(((~((op (e3) (e1)) = (op (e1) (e3))))/\(((op (op (e1) (e3)) (e3)) = (e1))/\(~((op (op (e1) (e3)) (e1)) = (e3)))))\/(((~((op (e4) (e1)) = (op (e1) (e4))))/\(((op (op (e1) (e4)) (e4)) = (e1))/\(~((op (op (e1) (e4)) (e1)) = (e4)))))\/(((~((op (e0) (e2)) = (op (e2) (e0))))/\(((op (op (e2) (e0)) (e0)) = (e2))/\(~((op (op (e2) (e0)) (e2)) = (e0)))))\/(((~((op (e1) (e2)) = (op (e2) (e1))))/\(((op (op (e2) (e1)) (e1)) = (e2))/\(~((op (op (e2) (e1)) (e2)) = (e1)))))\/(((~((op (e2) (e2)) = (op (e2) (e2))))/\(((op (op (e2) (e2)) (e2)) = (e2))/\(~((op (op (e2) (e2)) (e2)) = (e2)))))\/(((~((op (e3) (e2)) = (op (e2) (e3))))/\(((op (op (e2) (e3)) (e3)) = (e2))/\(~((op (op (e2) (e3)) (e2)) = (e3)))))\/(((~((op (e4) (e2)) = (op (e2) (e4))))/\(((op (op (e2) (e4)) (e4)) = (e2))/\(~((op (op (e2) (e4)) (e2)) = (e4)))))\/(((~((op (e0) (e3)) = (op (e3) (e0))))/\(((op (op (e3) (e0)) (e0)) = (e3))/\(~((op (op (e3) (e0)) (e3)) = (e0)))))\/(((~((op (e1) (e3)) = (op (e3) (e1))))/\(((op (op (e3) (e1)) (e1)) = (e3))/\(~((op (op (e3) (e1)) (e3)) = (e1)))))\/(((~((op (e2) (e3)) = (op (e3) (e2))))/\(((op (op (e3) (e2)) (e2)) = (e3))/\(~((op (op (e3) (e2)) (e3)) = (e2)))))\/(((~((op (e3) (e3)) = (op (e3) (e3))))/\(((op (op (e3) (e3)) (e3)) = (e3))/\(~((op (op (e3) (e3)) (e3)) = (e3)))))\/(((~((op (e4) (e3)) = (op (e3) (e4))))/\(((op (op (e3) (e4)) (e4)) = (e3))/\(~((op (op (e3) (e4)) (e3)) = (e4)))))\/(((~((op (e0) (e4)) = (op (e4) (e0))))/\(((op (op (e4) (e0)) (e0)) = (e4))/\(~((op (op (e4) (e0)) (e4)) = (e0)))))\/(((~((op (e1) (e4)) = (op (e4) (e1))))/\(((op (op (e4) (e1)) (e1)) = (e4))/\(~((op (op (e4) (e1)) (e4)) = (e1)))))\/(((~((op (e2) (e4)) = (op (e4) (e2))))/\(((op (op (e4) (e2)) (e2)) = (e4))/\(~((op (op (e4) (e2)) (e4)) = (e2)))))\/(((~((op (e3) (e4)) = (op (e4) (e3))))/\(((op (op (e4) (e3)) (e3)) = (e4))/\(~((op (op (e4) (e3)) (e4)) = (e3)))))\/((~((op (e4) (e4)) = (op (e4) (e4))))/\(((op (op (e4) (e4)) (e4)) = (e4))/\(~((op (op (e4) (e4)) (e4)) = (e4))))))))))))))))))))))))))))) -> (((op (e0) (e3)) = (e4))\/(((op (e1) (e3)) = (e4))\/(((op (e2) (e3)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e4) (e3)) = (e0))\/(((op (e4) (e3)) = (e1))\/(((op (e4) (e3)) = (e2))\/(((op (e4) (e3)) = (e3))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e3)) = (op (e4) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e4) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e3)) = (e1))\/((op (e0) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e4) (e4)) = (e1)))\/((op (e4) (e1)) = (e4))) -> ((~((op (e3) (e3)) = (e4)))\/((op (e3) (e4)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.25 do 0 intro. intros zenon_H301 zenon_H14a zenon_Hf1 zenon_H2ad zenon_H2a4 zenon_H2a0 zenon_H29c zenon_H299 zenon_H285 zenon_H279 zenon_H275 zenon_H26e zenon_H260 zenon_H261 zenon_H267 zenon_H26a zenon_H256 zenon_H24e zenon_H246 zenon_H240 zenon_H111 zenon_H236 zenon_H22d zenon_Hf7 zenon_Hf6 zenon_H23c zenon_H217 zenon_H21a zenon_H220 zenon_H223 zenon_H20f zenon_H20c zenon_H1fe zenon_H1fb zenon_H161 zenon_H1f4 zenon_H1e5 zenon_H169 zenon_Haa zenon_H15b zenon_H157 zenon_H152 zenon_H14d zenon_H19a zenon_H18e zenon_H112 zenon_H115 zenon_H116 zenon_H1c9 zenon_Hb9 zenon_H9f zenon_H10b zenon_H1d5 zenon_H1c4 zenon_Hbb zenon_Hc2 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_H1b9 zenon_Hb6 zenon_H8e zenon_Ha1 zenon_H1a9 zenon_H11f zenon_H165 zenon_H1c8 zenon_H41 zenon_H42 zenon_H50 zenon_H16d zenon_H17d zenon_H168 zenon_H51 zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H49 zenon_H136 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_He0 zenon_H17 zenon_H17e zenon_H2ac zenon_H302 zenon_Hf0 zenon_H89 zenon_He1 zenon_Hc3 zenon_H146. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H60 | zenon_intro zenon_H8a ]. % 41.04/41.25 apply (zenon_L588_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H72 | zenon_intro zenon_H8b ]. % 41.04/41.25 apply (zenon_L592_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H8b); [ zenon_intro zenon_H76 | zenon_intro zenon_H8c ]. % 41.04/41.25 apply (zenon_L596_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H8d | zenon_intro zenon_H7c ]. % 41.04/41.25 exact (zenon_H89 zenon_H8d). % 41.04/41.25 apply (zenon_L40_); trivial. % 41.04/41.25 apply (zenon_L99_); trivial. % 41.04/41.25 (* end of lemma zenon_L597_ *) % 41.04/41.25 assert (zenon_L598_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> ((op (e3) (e4)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e4) (e2)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> False). % 41.04/41.25 do 0 intro. intros zenon_H3b zenon_Hc8 zenon_H99 zenon_H32 zenon_H9f zenon_H72 zenon_H5f zenon_H197 zenon_H16 zenon_H81 zenon_Hd3 zenon_Hc9 zenon_He9. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.25 apply (zenon_L70_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.25 apply (zenon_L71_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.25 apply (zenon_L50_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.25 apply (zenon_L270_); trivial. % 41.04/41.25 apply (zenon_L107_); trivial. % 41.04/41.25 (* end of lemma zenon_L598_ *) % 41.04/41.25 assert (zenon_L599_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (e4) (e2)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e3) (unit)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.25 do 0 intro. intros zenon_H19a zenon_H17 zenon_H2d zenon_H49 zenon_Hc zenon_H4a zenon_H168 zenon_H34 zenon_H58 zenon_Hba zenon_H57 zenon_H1f zenon_H20 zenon_Hbb zenon_H112 zenon_H2c zenon_H18e zenon_H22 zenon_He9 zenon_Hc9 zenon_Hd3 zenon_H81 zenon_H16 zenon_H5f zenon_H72 zenon_H9f zenon_H32 zenon_H99 zenon_Hc8 zenon_H3b zenon_H146. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.25 apply (zenon_L262_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.25 apply (zenon_L178_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.25 apply (zenon_L266_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.25 apply (zenon_L598_); trivial. % 41.04/41.25 exact (zenon_H146 zenon_H144). % 41.04/41.25 (* end of lemma zenon_L599_ *) % 41.04/41.25 assert (zenon_L600_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((e1) = (e3))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e4) (e2)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> False). % 41.04/41.25 do 0 intro. intros zenon_He0 zenon_H18 zenon_Hb zenon_H146 zenon_H9f zenon_H72 zenon_H81 zenon_H18e zenon_H2c zenon_H112 zenon_Hbb zenon_Hba zenon_H168 zenon_H49 zenon_H2d zenon_H17 zenon_H19a zenon_He9 zenon_Hd3 zenon_H83 zenon_H5f zenon_H89 zenon_H57 zenon_H58 zenon_H6e zenon_H77 zenon_H16 zenon_H34 zenon_H73 zenon_H61 zenon_H68 zenon_H88 zenon_He1 zenon_H3b zenon_Hc8 zenon_H32 zenon_H22 zenon_H20 zenon_H1f zenon_Hc9 zenon_H99 zenon_H91 zenon_Hc. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.25 apply (zenon_L12_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.25 apply (zenon_L599_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.25 apply (zenon_L212_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.25 exact (zenon_He1 zenon_He5). % 41.04/41.25 apply (zenon_L73_); trivial. % 41.04/41.25 (* end of lemma zenon_L600_ *) % 41.04/41.25 assert (zenon_L601_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 41.04/41.25 do 0 intro. intros zenon_H3b zenon_H68 zenon_H8d zenon_H9f zenon_H5f zenon_H73 zenon_H72 zenon_H20 zenon_H32 zenon_H16 zenon_H34. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.25 apply (zenon_L101_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.25 apply (zenon_L104_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.25 apply (zenon_L50_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.25 apply (zenon_L30_); trivial. % 41.04/41.25 apply (zenon_L11_); trivial. % 41.04/41.25 (* end of lemma zenon_L601_ *) % 41.04/41.25 assert (zenon_L602_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((e1) = (e3))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e4) (e4)) = (e1)))\/((op (e4) (e1)) = (e4))) -> False). % 41.04/41.25 do 0 intro. intros zenon_Hf0 zenon_H14a zenon_Hf1 zenon_He0 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_H91 zenon_Hd4 zenon_Hba zenon_Hd9 zenon_Hee zenon_H168 zenon_H49 zenon_Hbb zenon_H112 zenon_H18e zenon_H1b9 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H11f zenon_H115 zenon_H116 zenon_Haa zenon_Hb9 zenon_Hb6 zenon_Hc2 zenon_H72 zenon_H9f zenon_Ha1 zenon_H19a zenon_Hb zenon_Hc zenon_H18 zenon_H16 zenon_H17 zenon_H1f zenon_H20 zenon_H22 zenon_H2d zenon_H2c zenon_H32 zenon_H34 zenon_H3b zenon_H1c4 zenon_H1a9 zenon_H165 zenon_H42 zenon_H8e zenon_H2ac. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_He1 | zenon_intro zenon_H76 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H13e | zenon_intro zenon_H9a ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H146 | zenon_intro zenon_Ha5 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 41.04/41.25 apply (zenon_L592_); trivial. % 41.04/41.25 apply (zenon_L99_); trivial. % 41.04/41.25 apply (zenon_L600_); trivial. % 41.04/41.25 apply (zenon_L525_); trivial. % 41.04/41.25 apply (zenon_L51_); trivial. % 41.04/41.25 apply (zenon_L601_); trivial. % 41.04/41.25 apply (zenon_L196_); trivial. % 41.04/41.25 (* end of lemma zenon_L602_ *) % 41.04/41.25 assert (zenon_L603_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (((~((op (e0) (e0)) = (op (e0) (e0))))/\(((op (op (e0) (e0)) (e0)) = (e0))/\(~((op (op (e0) (e0)) (e0)) = (e0)))))\/(((~((op (e1) (e0)) = (op (e0) (e1))))/\(((op (op (e0) (e1)) (e1)) = (e0))/\(~((op (op (e0) (e1)) (e0)) = (e1)))))\/(((~((op (e2) (e0)) = (op (e0) (e2))))/\(((op (op (e0) (e2)) (e2)) = (e0))/\(~((op (op (e0) (e2)) (e0)) = (e2)))))\/(((~((op (e3) (e0)) = (op (e0) (e3))))/\(((op (op (e0) (e3)) (e3)) = (e0))/\(~((op (op (e0) (e3)) (e0)) = (e3)))))\/(((~((op (e4) (e0)) = (op (e0) (e4))))/\(((op (op (e0) (e4)) (e4)) = (e0))/\(~((op (op (e0) (e4)) (e0)) = (e4)))))\/(((~((op (e0) (e1)) = (op (e1) (e0))))/\(((op (op (e1) (e0)) (e0)) = (e1))/\(~((op (op (e1) (e0)) (e1)) = (e0)))))\/(((~((op (e1) (e1)) = (op (e1) (e1))))/\(((op (op (e1) (e1)) (e1)) = (e1))/\(~((op (op (e1) (e1)) (e1)) = (e1)))))\/(((~((op (e2) (e1)) = (op (e1) (e2))))/\(((op (op (e1) (e2)) (e2)) = (e1))/\(~((op (op (e1) (e2)) (e1)) = (e2)))))\/(((~((op (e3) (e1)) = (op (e1) (e3))))/\(((op (op (e1) (e3)) (e3)) = (e1))/\(~((op (op (e1) (e3)) (e1)) = (e3)))))\/(((~((op (e4) (e1)) = (op (e1) (e4))))/\(((op (op (e1) (e4)) (e4)) = (e1))/\(~((op (op (e1) (e4)) (e1)) = (e4)))))\/(((~((op (e0) (e2)) = (op (e2) (e0))))/\(((op (op (e2) (e0)) (e0)) = (e2))/\(~((op (op (e2) (e0)) (e2)) = (e0)))))\/(((~((op (e1) (e2)) = (op (e2) (e1))))/\(((op (op (e2) (e1)) (e1)) = (e2))/\(~((op (op (e2) (e1)) (e2)) = (e1)))))\/(((~((op (e2) (e2)) = (op (e2) (e2))))/\(((op (op (e2) (e2)) (e2)) = (e2))/\(~((op (op (e2) (e2)) (e2)) = (e2)))))\/(((~((op (e3) (e2)) = (op (e2) (e3))))/\(((op (op (e2) (e3)) (e3)) = (e2))/\(~((op (op (e2) (e3)) (e2)) = (e3)))))\/(((~((op (e4) (e2)) = (op (e2) (e4))))/\(((op (op (e2) (e4)) (e4)) = (e2))/\(~((op (op (e2) (e4)) (e2)) = (e4)))))\/(((~((op (e0) (e3)) = (op (e3) (e0))))/\(((op (op (e3) (e0)) (e0)) = (e3))/\(~((op (op (e3) (e0)) (e3)) = (e0)))))\/(((~((op (e1) (e3)) = (op (e3) (e1))))/\(((op (op (e3) (e1)) (e1)) = (e3))/\(~((op (op (e3) (e1)) (e3)) = (e1)))))\/(((~((op (e2) (e3)) = (op (e3) (e2))))/\(((op (op (e3) (e2)) (e2)) = (e3))/\(~((op (op (e3) (e2)) (e3)) = (e2)))))\/(((~((op (e3) (e3)) = (op (e3) (e3))))/\(((op (op (e3) (e3)) (e3)) = (e3))/\(~((op (op (e3) (e3)) (e3)) = (e3)))))\/(((~((op (e4) (e3)) = (op (e3) (e4))))/\(((op (op (e3) (e4)) (e4)) = (e3))/\(~((op (op (e3) (e4)) (e3)) = (e4)))))\/(((~((op (e0) (e4)) = (op (e4) (e0))))/\(((op (op (e4) (e0)) (e0)) = (e4))/\(~((op (op (e4) (e0)) (e4)) = (e0)))))\/(((~((op (e1) (e4)) = (op (e4) (e1))))/\(((op (op (e4) (e1)) (e1)) = (e4))/\(~((op (op (e4) (e1)) (e4)) = (e1)))))\/(((~((op (e2) (e4)) = (op (e4) (e2))))/\(((op (op (e4) (e2)) (e2)) = (e4))/\(~((op (op (e4) (e2)) (e4)) = (e2)))))\/(((~((op (e3) (e4)) = (op (e4) (e3))))/\(((op (op (e4) (e3)) (e3)) = (e4))/\(~((op (op (e4) (e3)) (e4)) = (e3)))))\/((~((op (e4) (e4)) = (op (e4) (e4))))/\(((op (op (e4) (e4)) (e4)) = (e4))/\(~((op (op (e4) (e4)) (e4)) = (e4))))))))))))))))))))))))))))) -> (((op (e0) (e3)) = (e4))\/(((op (e1) (e3)) = (e4))\/(((op (e2) (e3)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e4) (e3)) = (e0))\/(((op (e4) (e3)) = (e1))\/(((op (e4) (e3)) = (e2))\/(((op (e4) (e3)) = (e3))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e3)) = (op (e4) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e4) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e3)) = (e1))\/((op (e0) (e4)) = (e1)))))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e4) (e4)) = (e1)))\/((op (e4) (e1)) = (e4))) -> ((~((op (e3) (e3)) = (e4)))\/((op (e3) (e4)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 41.04/41.25 do 0 intro. intros zenon_H101 zenon_Hfc zenon_Hfe zenon_Hff zenon_H301 zenon_H14a zenon_Hf1 zenon_H2ad zenon_H2a4 zenon_H2a0 zenon_H29c zenon_H299 zenon_H285 zenon_H279 zenon_H275 zenon_H26e zenon_H260 zenon_H261 zenon_H267 zenon_H26a zenon_H256 zenon_H24e zenon_H246 zenon_H240 zenon_H111 zenon_H236 zenon_H22d zenon_Hf6 zenon_H23c zenon_H217 zenon_H21a zenon_H220 zenon_H223 zenon_H20f zenon_H20c zenon_H1fe zenon_H1fb zenon_H161 zenon_H1f4 zenon_H1e5 zenon_H169 zenon_Haa zenon_H15b zenon_H157 zenon_H152 zenon_H14d zenon_H19a zenon_H18e zenon_H112 zenon_H115 zenon_H116 zenon_H1c9 zenon_Hb9 zenon_H9f zenon_H10b zenon_H1d5 zenon_H1c4 zenon_Hbb zenon_Hc2 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_H1b9 zenon_Hb6 zenon_H8e zenon_Ha1 zenon_H1a9 zenon_H11f zenon_H165 zenon_H1c8 zenon_H41 zenon_H42 zenon_H50 zenon_H16d zenon_H17d zenon_H168 zenon_H51 zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H49 zenon_H136 zenon_Hee zenon_Hd9 zenon_Hba zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_He0 zenon_H17 zenon_H17e zenon_H2ac zenon_H302 zenon_Hf0. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hfb ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H237 | zenon_intro zenon_H72 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_He1 | zenon_intro zenon_H76 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1ff | zenon_intro zenon_H7c ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H13e | zenon_intro zenon_H9a ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H146 | zenon_intro zenon_Ha5 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 41.04/41.25 apply (zenon_L597_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H60 | zenon_intro zenon_H8a ]. % 41.04/41.25 apply (zenon_L526_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H72 | zenon_intro zenon_H8b ]. % 41.04/41.25 apply (zenon_L600_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H8b); [ zenon_intro zenon_H76 | zenon_intro zenon_H8c ]. % 41.04/41.25 apply (zenon_L596_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H8d | zenon_intro zenon_H7c ]. % 41.04/41.25 exact (zenon_H89 zenon_H8d). % 41.04/41.25 apply (zenon_L40_); trivial. % 41.04/41.25 apply (zenon_L525_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H146 | zenon_intro zenon_Ha5 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 41.04/41.25 apply (zenon_L597_); trivial. % 41.04/41.25 apply (zenon_L246_); trivial. % 41.04/41.25 apply (zenon_L584_); trivial. % 41.04/41.25 apply (zenon_L40_); trivial. % 41.04/41.25 apply (zenon_L110_); trivial. % 41.04/41.25 apply (zenon_L596_); trivial. % 41.04/41.25 apply (zenon_L602_); trivial. % 41.04/41.25 apply (zenon_L139_); trivial. % 41.04/41.25 (* end of lemma zenon_L603_ *) % 41.04/41.25 assert (zenon_L604_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> False). % 41.04/41.25 do 0 intro. intros zenon_Hf0 zenon_H8e zenon_H9f zenon_H72 zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H17 zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H50 zenon_H49 zenon_H10c zenon_H42 zenon_H10b zenon_Hee zenon_Hd9 zenon_Hf2 zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_He0. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_He1 | zenon_intro zenon_H76 ]. % 41.04/41.25 apply (zenon_L153_); trivial. % 41.04/41.25 apply (zenon_L196_); trivial. % 41.04/41.25 (* end of lemma zenon_L604_ *) % 41.04/41.25 assert (zenon_L605_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (e0)) = (e4)) -> ((op (e4) (unit)) = (e4)) -> ((op (e3) (e4)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e4) (e3)) = (e2)) -> False). % 41.04/41.25 do 0 intro. intros zenon_H3b zenon_H72 zenon_H5f zenon_H61 zenon_H9b zenon_Hc8 zenon_H9a zenon_H99 zenon_Hbf zenon_H83 zenon_H91 zenon_Hc zenon_H92. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.25 apply (zenon_L46_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.25 apply (zenon_L49_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.25 apply (zenon_L84_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.25 apply (zenon_L67_); trivial. % 41.04/41.25 apply (zenon_L44_); trivial. % 41.04/41.25 (* end of lemma zenon_L605_ *) % 41.04/41.25 assert (zenon_L606_ : (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e3) (e4)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e4) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 41.04/41.25 do 0 intro. intros zenon_Hd9 zenon_Hbf zenon_H61 zenon_H5f zenon_H72 zenon_Hc3 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_H83 zenon_He8 zenon_Hb6 zenon_Hb9 zenon_H34 zenon_Haa zenon_Ha1 zenon_H2d zenon_H2c zenon_Hc2 zenon_H92 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_Hc8 zenon_Hd4 zenon_Hd3 zenon_H58 zenon_Hf2 zenon_H6e zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_H9a | zenon_intro zenon_Hdb ]. % 41.04/41.25 apply (zenon_L605_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hdc ]. % 41.04/41.25 apply (zenon_L126_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hdd ]. % 41.04/41.25 apply (zenon_L73_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hde ]. % 41.04/41.25 apply (zenon_L127_); trivial. % 41.04/41.25 exact (zenon_Hda zenon_Hde). % 41.04/41.25 (* end of lemma zenon_L606_ *) % 41.04/41.25 assert (zenon_L607_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e3) (e4)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> False). % 41.04/41.25 do 0 intro. intros zenon_He0 zenon_Hb zenon_H49 zenon_H1b9 zenon_H115 zenon_H11f zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_H88 zenon_H7b zenon_H81 zenon_H87 zenon_H77 zenon_H73 zenon_H57 zenon_H68 zenon_Hed zenon_He6 zenon_He9 zenon_Hee zenon_He1 zenon_Hd9 zenon_Hbf zenon_H61 zenon_H5f zenon_H72 zenon_Hc3 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_H83 zenon_He8 zenon_Hb6 zenon_Hb9 zenon_H34 zenon_Haa zenon_Ha1 zenon_H2d zenon_H2c zenon_Hc2 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_Hc8 zenon_Hd4 zenon_Hd3 zenon_H58 zenon_Hf2 zenon_H6e zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.25 apply (zenon_L12_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.25 apply (zenon_L285_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.25 apply (zenon_L152_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.25 exact (zenon_He1 zenon_He5). % 41.04/41.25 apply (zenon_L606_); trivial. % 41.04/41.25 (* end of lemma zenon_L607_ *) % 41.04/41.25 assert (zenon_L608_ : (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (unit) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> (~((op (e4) (e4)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e2)) = (e2)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e4) (e4)) = (e2))) -> False). % 41.04/41.25 do 0 intro. intros zenon_H116 zenon_H4a zenon_H8e zenon_H42 zenon_H125 zenon_Hda zenon_H3b zenon_Hcc zenon_Hb1 zenon_H99 zenon_H91 zenon_H6e zenon_Hf2 zenon_H58 zenon_Hd3 zenon_Hd4 zenon_Hc8 zenon_H32 zenon_H22 zenon_H20 zenon_H1f zenon_Hc zenon_Hc2 zenon_H2c zenon_H2d zenon_Ha1 zenon_Haa zenon_H34 zenon_Hb9 zenon_Hb6 zenon_He8 zenon_H83 zenon_H16 zenon_H17 zenon_H18 zenon_H9b zenon_H72 zenon_H5f zenon_H61 zenon_Hd9 zenon_He1 zenon_Hee zenon_He9 zenon_He6 zenon_Hed zenon_H68 zenon_H57 zenon_H73 zenon_H77 zenon_H87 zenon_H81 zenon_H7b zenon_H88 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H11f zenon_H115 zenon_H1b9 zenon_H49 zenon_Hb zenon_He0 zenon_Hc3. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hc4 ]. % 41.04/41.25 apply (zenon_L317_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc5 ]. % 41.04/41.25 apply (zenon_L278_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc6 ]. % 41.04/41.25 apply (zenon_L214_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc7 ]. % 41.04/41.25 apply (zenon_L607_); trivial. % 41.04/41.25 exact (zenon_Hc3 zenon_Hc7). % 41.04/41.25 (* end of lemma zenon_L608_ *) % 41.04/41.25 assert (zenon_L609_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e4) (e2)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e4) (e4)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e4))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((e1) = (op (e4) (e2))) -> (~((e0) = (e1))) -> False). % 41.04/41.25 do 0 intro. intros zenon_H12d zenon_H10b zenon_H50 zenon_H9f zenon_Hf0 zenon_H109 zenon_H12e zenon_Hc3 zenon_He0 zenon_Hb zenon_H49 zenon_H1b9 zenon_H115 zenon_H11f zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_H88 zenon_H7b zenon_H81 zenon_H87 zenon_H77 zenon_H73 zenon_H57 zenon_H68 zenon_Hed zenon_He6 zenon_He9 zenon_Hee zenon_He1 zenon_Hd9 zenon_H61 zenon_H5f zenon_H72 zenon_H9b zenon_H18 zenon_H17 zenon_H16 zenon_H83 zenon_He8 zenon_Hb6 zenon_Hb9 zenon_Haa zenon_Ha1 zenon_H2d zenon_H2c zenon_Hc2 zenon_Hc zenon_H1f zenon_H20 zenon_H22 zenon_H32 zenon_Hc8 zenon_Hd4 zenon_Hd3 zenon_H58 zenon_Hf2 zenon_H6e zenon_H91 zenon_H99 zenon_Hb1 zenon_Hcc zenon_H3b zenon_Hda zenon_H42 zenon_H8e zenon_H4a zenon_H116 zenon_H34 zenon_H129. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H10c | zenon_intro zenon_H12f ]. % 41.04/41.25 apply (zenon_L604_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H120 | zenon_intro zenon_H130 ]. % 41.04/41.25 apply (zenon_L170_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H132 | zenon_intro zenon_H131 ]. % 41.04/41.25 exact (zenon_H12e zenon_H132). % 41.04/41.25 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H125 | zenon_intro zenon_H128 ]. % 41.04/41.25 apply (zenon_L608_); trivial. % 41.04/41.25 apply (zenon_L174_); trivial. % 41.04/41.25 (* end of lemma zenon_L609_ *) % 41.04/41.25 assert (zenon_L610_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e1) (e4)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (e3)) = (e2)) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (unit)) = (e2)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 41.04/41.25 do 0 intro. intros zenon_H3b zenon_H113 zenon_H2c zenon_H112 zenon_H4a zenon_Hc zenon_H49 zenon_H22 zenon_H20 zenon_H1f zenon_H6e zenon_Hf2 zenon_H58 zenon_H32 zenon_H16 zenon_H34. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H9 | zenon_intro zenon_H3c ]. % 41.04/41.25 apply (zenon_L164_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3d ]. % 41.04/41.25 apply (zenon_L17_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H21 | zenon_intro zenon_H3e ]. % 41.04/41.25 apply (zenon_L8_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 41.04/41.25 apply (zenon_L120_); trivial. % 41.04/41.25 apply (zenon_L11_); trivial. % 41.04/41.25 (* end of lemma zenon_L610_ *) % 41.04/41.25 assert (zenon_L611_ : (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((e1) = (op (e4) (e2))) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e2)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((e1) = (e3))) -> ((e3) = (op (e2) (e4))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (e4) (e2)) = (e4)) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e3) (unit)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e4) (e4)) = (e1))) -> False). % 41.04/41.25 do 0 intro. intros zenon_H19a zenon_H17 zenon_H2d zenon_H168 zenon_H34 zenon_H58 zenon_Hf2 zenon_H6e zenon_H1f zenon_H20 zenon_H49 zenon_Hc zenon_H4a zenon_H112 zenon_H2c zenon_H18e zenon_H22 zenon_He9 zenon_Hc9 zenon_Hd3 zenon_H81 zenon_H16 zenon_H5f zenon_H72 zenon_H9f zenon_H32 zenon_H99 zenon_Hc8 zenon_H3b zenon_H146. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H17a | zenon_intro zenon_H19b ]. % 41.04/41.25 apply (zenon_L262_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H113 | zenon_intro zenon_H19c ]. % 41.04/41.25 apply (zenon_L610_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18d | zenon_intro zenon_H19d ]. % 41.04/41.25 apply (zenon_L266_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H144 ]. % 41.04/41.25 apply (zenon_L598_); trivial. % 41.04/41.25 exact (zenon_H146 zenon_H144). % 41.04/41.25 (* end of lemma zenon_L611_ *) % 41.04/41.25 assert (zenon_L612_ : ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e4) (e2)) = (e0)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> False). % 41.04/41.25 do 0 intro. intros zenon_Hf1 zenon_H19a zenon_H146 zenon_H18e zenon_H168 zenon_Hbb zenon_H89 zenon_Hf0 zenon_H8e zenon_H9f zenon_H72 zenon_H50 zenon_H49 zenon_H42 zenon_H10b zenon_Hee zenon_Hd9 zenon_Hf2 zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_He0 zenon_H109 zenon_H11f zenon_H12e zenon_H115 zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_H1b9 zenon_He1 zenon_Haa zenon_Hc2 zenon_Hb6 zenon_Hb9 zenon_H116 zenon_Ha1 zenon_H129 zenon_H12d zenon_Hb zenon_Hc zenon_H18 zenon_H16 zenon_H17 zenon_H1f zenon_H20 zenon_H22 zenon_H2d zenon_H2c zenon_H32 zenon_H34 zenon_H3b. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.25 apply (zenon_L12_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.25 apply (zenon_L609_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.25 apply (zenon_L41_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.25 exact (zenon_He1 zenon_He5). % 41.04/41.25 apply (zenon_L128_); trivial. % 41.04/41.25 apply (zenon_L99_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.25 apply (zenon_L12_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.25 apply (zenon_L611_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.25 apply (zenon_L212_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.25 exact (zenon_He1 zenon_He5). % 41.04/41.25 apply (zenon_L73_); trivial. % 41.04/41.25 (* end of lemma zenon_L612_ *) % 41.04/41.25 assert (zenon_L613_ : ((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e4) (e2)) = (e0)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((e1) = (op (e4) (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> ((~((op (e4) (e4)) = (e1)))\/((op (e4) (e1)) = (e4))) -> False). % 41.04/41.25 do 0 intro. intros zenon_H14a zenon_Hf1 zenon_H19a zenon_H18e zenon_H168 zenon_Hbb zenon_Hf0 zenon_H8e zenon_H9f zenon_H72 zenon_H50 zenon_H49 zenon_H42 zenon_H10b zenon_Hee zenon_Hd9 zenon_Hf2 zenon_Hd4 zenon_H91 zenon_He9 zenon_Hd3 zenon_Hb1 zenon_H9b zenon_H99 zenon_Hc8 zenon_Hcc zenon_He8 zenon_He6 zenon_Hed zenon_H68 zenon_H5f zenon_H61 zenon_H58 zenon_H57 zenon_H73 zenon_H6e zenon_H77 zenon_H87 zenon_H83 zenon_H81 zenon_H7b zenon_H88 zenon_He0 zenon_H109 zenon_H11f zenon_H12e zenon_H115 zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_H1b9 zenon_Haa zenon_Hc2 zenon_Hb6 zenon_Hb9 zenon_H116 zenon_Ha1 zenon_H129 zenon_H12d zenon_Hb zenon_Hc zenon_H18 zenon_H16 zenon_H17 zenon_H1f zenon_H20 zenon_H22 zenon_H2d zenon_H2c zenon_H32 zenon_H34 zenon_H3b zenon_H1c4 zenon_H1a9 zenon_H165 zenon_H2ac. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_He1 | zenon_intro zenon_H76 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H13e | zenon_intro zenon_H9a ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H146 | zenon_intro zenon_Ha5 ]. % 41.04/41.25 apply (zenon_L612_); trivial. % 41.04/41.25 apply (zenon_L525_); trivial. % 41.04/41.25 apply (zenon_L121_); trivial. % 41.04/41.25 apply (zenon_L130_); trivial. % 41.04/41.25 apply (zenon_L196_); trivial. % 41.04/41.25 (* end of lemma zenon_L613_ *) % 41.04/41.25 assert (zenon_L614_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e4) (e4)) = (e4))) -> (~((op (e4) (e4)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e4) (e4)) = (e1)))\/((op (e4) (e1)) = (e4))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e4) (e2)) = (e0)))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e2) (e2)) = (e0))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (unit)) = (e0)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((e1) = (e3))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> ((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (unit) (e3)) = (e3)) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> False). % 41.04/41.25 do 0 intro. intros zenon_H1c8 zenon_Hda zenon_Hc3 zenon_H89 zenon_H16d zenon_H41 zenon_H51 zenon_H146 zenon_H1c9 zenon_H2ac zenon_H165 zenon_H1a9 zenon_H1c4 zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H17 zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H12d zenon_H129 zenon_Ha1 zenon_H116 zenon_Hb9 zenon_Hb6 zenon_Hc2 zenon_Haa zenon_H1b9 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H115 zenon_H12e zenon_H11f zenon_H109 zenon_He0 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hd3 zenon_He9 zenon_H91 zenon_Hd4 zenon_Hf2 zenon_Hd9 zenon_Hee zenon_H10b zenon_H42 zenon_H49 zenon_H50 zenon_Hf0 zenon_Hbb zenon_H168 zenon_H18e zenon_H19a zenon_Hf1 zenon_H14a zenon_H3b zenon_H8e zenon_H5f zenon_H9f zenon_H22 zenon_H1f zenon_H77 zenon_H76 zenon_H20 zenon_Hb1. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H193 | zenon_intro zenon_H1ca ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd | zenon_intro zenon_He2 ]. % 41.04/41.25 apply (zenon_L12_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H4a | zenon_intro zenon_He3 ]. % 41.04/41.25 apply (zenon_L593_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H59 | zenon_intro zenon_He4 ]. % 41.04/41.25 apply (zenon_L41_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_He5 | zenon_intro zenon_H92 ]. % 41.04/41.25 apply (zenon_L133_); trivial. % 41.04/41.25 apply (zenon_L128_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cb ]. % 41.04/41.25 exact (zenon_H1c9 zenon_H1cc). % 41.04/41.25 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H19e | zenon_intro zenon_H1cd ]. % 41.04/41.25 apply (zenon_L273_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H72 | zenon_intro zenon_H1bf ]. % 41.04/41.25 apply (zenon_L613_); trivial. % 41.04/41.25 apply (zenon_L594_); trivial. % 41.04/41.25 (* end of lemma zenon_L614_ *) % 41.04/41.25 assert (zenon_L615_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> ((~((op (e4) (e4)) = (e1)))\/((op (e4) (e1)) = (e4))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e4) (e2)) = (e0)))))) -> (~((e0) = (e1))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e2) (e2)) = (e0))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (unit) (e0)) = (e0)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> ((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4))) -> (~((op (e1) (e1)) = (e3))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e1) = (op (e4) (e2))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e1) (e0)) = (e1)) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((op (e4) (e4)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (unit)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> False). % 41.04/41.25 do 0 intro. intros zenon_H1c8 zenon_H2ac zenon_H165 zenon_H1a9 zenon_H1c4 zenon_H12d zenon_H129 zenon_H1b9 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H12e zenon_H11f zenon_H109 zenon_Hed zenon_He6 zenon_Hee zenon_H10b zenon_H42 zenon_Hf0 zenon_Hf1 zenon_H14a zenon_H1c9 zenon_H3b zenon_H34 zenon_H32 zenon_H2c zenon_H2d zenon_H22 zenon_H20 zenon_H1f zenon_H17 zenon_H16 zenon_H18 zenon_Hc zenon_Hb zenon_H19a zenon_H146 zenon_H51 zenon_H41 zenon_H50 zenon_H16d zenon_H81 zenon_H18e zenon_H112 zenon_H115 zenon_H116 zenon_H168 zenon_H49 zenon_H88 zenon_H7b zenon_H83 zenon_H87 zenon_H89 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H58 zenon_H61 zenon_H5f zenon_H68 zenon_Hd9 zenon_Hcc zenon_Hb1 zenon_H91 zenon_Hf2 zenon_Hd4 zenon_He9 zenon_Hd3 zenon_H9f zenon_H8e zenon_H76 zenon_H9b zenon_H99 zenon_Hc8 zenon_Ha1 zenon_Haa zenon_Hb9 zenon_Hb6 zenon_He8 zenon_Hc2 zenon_Hbb zenon_He0. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hda | zenon_intro zenon_Hde ]. % 41.04/41.25 apply (zenon_L614_); trivial. % 41.04/41.25 apply (zenon_L99_); trivial. % 41.04/41.25 apply (zenon_L117_); trivial. % 41.04/41.25 (* end of lemma zenon_L615_ *) % 41.04/41.25 assert (zenon_L616_ : ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> ((~((op (e4) (e4)) = (e1)))\/((op (e4) (e1)) = (e4))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> (~((e0) = (e3))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e4) (e2)) = (e0)))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e2) (e2)) = (e0))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (unit) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> (~((e1) = (e3))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> ((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((e3) = (op (e2) (e4))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> False). % 41.04/41.25 do 0 intro. intros zenon_H16d zenon_H41 zenon_H51 zenon_H1c9 zenon_H1c8 zenon_H2ac zenon_H165 zenon_H1a9 zenon_H1c4 zenon_H2c zenon_H2d zenon_H17 zenon_H18 zenon_Hc zenon_Hb zenon_H12d zenon_H129 zenon_Ha1 zenon_H116 zenon_Hb9 zenon_Hb6 zenon_Hc2 zenon_Haa zenon_H1b9 zenon_H1b3 zenon_H1ae zenon_H1ad zenon_H112 zenon_H115 zenon_H12e zenon_H11f zenon_H109 zenon_He0 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H73 zenon_H57 zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_H91 zenon_Hd4 zenon_Hd9 zenon_Hee zenon_H10b zenon_H42 zenon_H49 zenon_H50 zenon_H9f zenon_H8e zenon_Hf0 zenon_H168 zenon_H18e zenon_H19a zenon_Hf1 zenon_H14a zenon_Hbb zenon_H58 zenon_Hf2 zenon_H61 zenon_H5f zenon_H1f zenon_H20 zenon_H22 zenon_H6e zenon_H32 zenon_H16 zenon_H34 zenon_H3b. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_He1 | zenon_intro zenon_H76 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H13e | zenon_intro zenon_H9a ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H146 | zenon_intro zenon_Ha5 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H60 | zenon_intro zenon_H8a ]. % 41.04/41.25 apply (zenon_L181_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H72 | zenon_intro zenon_H8b ]. % 41.04/41.25 apply (zenon_L613_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H8b); [ zenon_intro zenon_H76 | zenon_intro zenon_H8c ]. % 41.04/41.25 apply (zenon_L615_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H8d | zenon_intro zenon_H7c ]. % 41.04/41.25 exact (zenon_H89 zenon_H8d). % 41.04/41.25 apply (zenon_L40_); trivial. % 41.04/41.25 apply (zenon_L525_); trivial. % 41.04/41.25 apply (zenon_L121_); trivial. % 41.04/41.25 apply (zenon_L130_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H146 | zenon_intro zenon_Ha5 ]. % 41.04/41.25 apply (zenon_L615_); trivial. % 41.04/41.25 apply (zenon_L113_); trivial. % 41.04/41.25 apply (zenon_L225_); trivial. % 41.04/41.25 (* end of lemma zenon_L616_ *) % 41.04/41.25 assert (zenon_L617_ : ((~((op (e3) (e3)) = (e4)))\/((op (e3) (e4)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e3)) = (e1))\/((op (e0) (e4)) = (e1)))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e2)) = (e4)))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e4) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e3) (e1)) = (e0))\/((op (e4) (e1)) = (e0)))))) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> (~((op (e3) (e0)) = (op (e4) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/(((op (e0) (e3)) = (e3))\/((op (e0) (e3)) = (e4)))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e4)) = (op (e3) (e4)))) -> (((op (e3) (e0)) = (e4))\/(((op (e3) (e1)) = (e4))\/(((op (e3) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e3) (e4)) = (e4)))))) -> (~((op (e0) (e4)) = (op (e2) (e4)))) -> (((op (e0) (e4)) = (e4))\/(((op (e1) (e4)) = (e4))\/(((op (e2) (e4)) = (e4))\/(((op (e3) (e4)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e4)) = (e3)))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e4) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/(((op (e1) (e3)) = (e3))\/((op (e1) (e3)) = (e4)))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e4)) = (e2)))))) -> (~((op (e2) (e3)) = (op (e4) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e3)) = (e1)))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e4)) = (op (e3) (e4)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e1)) = (e3))\/((op (e2) (e1)) = (e4)))))) -> (~((op (e1) (e3)) = (op (e4) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e4)) = (e2)))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e4) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e4) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e2)) = (e4)))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e4) (e3)))) -> (((op (e4) (e3)) = (e0))\/(((op (e4) (e3)) = (e1))\/(((op (e4) (e3)) = (e2))\/(((op (e4) (e3)) = (e3))\/((op (e4) (e3)) = (e4)))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e4))\/(((op (e1) (e3)) = (e4))\/(((op (e2) (e3)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e4) (e3)) = (e4)))))) -> (((~((op (e0) (e0)) = (op (e0) (e0))))/\(((op (op (e0) (e0)) (e0)) = (e0))/\(~((op (op (e0) (e0)) (e0)) = (e0)))))\/(((~((op (e1) (e0)) = (op (e0) (e1))))/\(((op (op (e0) (e1)) (e1)) = (e0))/\(~((op (op (e0) (e1)) (e0)) = (e1)))))\/(((~((op (e2) (e0)) = (op (e0) (e2))))/\(((op (op (e0) (e2)) (e2)) = (e0))/\(~((op (op (e0) (e2)) (e0)) = (e2)))))\/(((~((op (e3) (e0)) = (op (e0) (e3))))/\(((op (op (e0) (e3)) (e3)) = (e0))/\(~((op (op (e0) (e3)) (e0)) = (e3)))))\/(((~((op (e4) (e0)) = (op (e0) (e4))))/\(((op (op (e0) (e4)) (e4)) = (e0))/\(~((op (op (e0) (e4)) (e0)) = (e4)))))\/(((~((op (e0) (e1)) = (op (e1) (e0))))/\(((op (op (e1) (e0)) (e0)) = (e1))/\(~((op (op (e1) (e0)) (e1)) = (e0)))))\/(((~((op (e1) (e1)) = (op (e1) (e1))))/\(((op (op (e1) (e1)) (e1)) = (e1))/\(~((op (op (e1) (e1)) (e1)) = (e1)))))\/(((~((op (e2) (e1)) = (op (e1) (e2))))/\(((op (op (e1) (e2)) (e2)) = (e1))/\(~((op (op (e1) (e2)) (e1)) = (e2)))))\/(((~((op (e3) (e1)) = (op (e1) (e3))))/\(((op (op (e1) (e3)) (e3)) = (e1))/\(~((op (op (e1) (e3)) (e1)) = (e3)))))\/(((~((op (e4) (e1)) = (op (e1) (e4))))/\(((op (op (e1) (e4)) (e4)) = (e1))/\(~((op (op (e1) (e4)) (e1)) = (e4)))))\/(((~((op (e0) (e2)) = (op (e2) (e0))))/\(((op (op (e2) (e0)) (e0)) = (e2))/\(~((op (op (e2) (e0)) (e2)) = (e0)))))\/(((~((op (e1) (e2)) = (op (e2) (e1))))/\(((op (op (e2) (e1)) (e1)) = (e2))/\(~((op (op (e2) (e1)) (e2)) = (e1)))))\/(((~((op (e2) (e2)) = (op (e2) (e2))))/\(((op (op (e2) (e2)) (e2)) = (e2))/\(~((op (op (e2) (e2)) (e2)) = (e2)))))\/(((~((op (e3) (e2)) = (op (e2) (e3))))/\(((op (op (e2) (e3)) (e3)) = (e2))/\(~((op (op (e2) (e3)) (e2)) = (e3)))))\/(((~((op (e4) (e2)) = (op (e2) (e4))))/\(((op (op (e2) (e4)) (e4)) = (e2))/\(~((op (op (e2) (e4)) (e2)) = (e4)))))\/(((~((op (e0) (e3)) = (op (e3) (e0))))/\(((op (op (e3) (e0)) (e0)) = (e3))/\(~((op (op (e3) (e0)) (e3)) = (e0)))))\/(((~((op (e1) (e3)) = (op (e3) (e1))))/\(((op (op (e3) (e1)) (e1)) = (e3))/\(~((op (op (e3) (e1)) (e3)) = (e1)))))\/(((~((op (e2) (e3)) = (op (e3) (e2))))/\(((op (op (e3) (e2)) (e2)) = (e3))/\(~((op (op (e3) (e2)) (e3)) = (e2)))))\/(((~((op (e3) (e3)) = (op (e3) (e3))))/\(((op (op (e3) (e3)) (e3)) = (e3))/\(~((op (op (e3) (e3)) (e3)) = (e3)))))\/(((~((op (e4) (e3)) = (op (e3) (e4))))/\(((op (op (e3) (e4)) (e4)) = (e3))/\(~((op (op (e3) (e4)) (e3)) = (e4)))))\/(((~((op (e0) (e4)) = (op (e4) (e0))))/\(((op (op (e4) (e0)) (e0)) = (e4))/\(~((op (op (e4) (e0)) (e4)) = (e0)))))\/(((~((op (e1) (e4)) = (op (e4) (e1))))/\(((op (op (e4) (e1)) (e1)) = (e4))/\(~((op (op (e4) (e1)) (e4)) = (e1)))))\/(((~((op (e2) (e4)) = (op (e4) (e2))))/\(((op (op (e4) (e2)) (e2)) = (e4))/\(~((op (op (e4) (e2)) (e4)) = (e2)))))\/(((~((op (e3) (e4)) = (op (e4) (e3))))/\(((op (op (e4) (e3)) (e3)) = (e4))/\(~((op (op (e4) (e3)) (e4)) = (e3)))))\/((~((op (e4) (e4)) = (op (e4) (e4))))/\(((op (op (e4) (e4)) (e4)) = (e4))/\(~((op (op (e4) (e4)) (e4)) = (e4))))))))))))))))))))))))))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e4) (e4)) = (e0)))\/((op (e4) (e0)) = (e4))) -> ((~((op (e4) (e4)) = (e2)))\/((op (e4) (e2)) = (e4))) -> (((op (e0) (e4)) = (e1))\/(((op (e1) (e4)) = (e1))\/(((op (e2) (e4)) = (e1))\/(((op (e3) (e4)) = (e1))\/((op (e4) (e4)) = (e1)))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e4)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (unit)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e3)) = (e2)))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((e0) = (op (op (e4) (e2)) (op (e4) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> (~((op (e1) (e4)) = (op (e3) (e4)))) -> (~((op (e1) (e4)) = (op (e2) (e4)))) -> (~((op (e0) (e4)) = (op (e1) (e4)))) -> (((op (e1) (e4)) = (e0))\/(((op (e1) (e4)) = (e1))\/(((op (e1) (e4)) = (e2))\/(((op (e1) (e4)) = (e3))\/((op (e1) (e4)) = (e4)))))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (((op (e0) (e4)) = (e2))\/(((op (e1) (e4)) = (e2))\/(((op (e2) (e4)) = (e2))\/(((op (e3) (e4)) = (e2))\/((op (e4) (e4)) = (e2)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e0) (e2)) = (op (e0) (e4)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e4) (e2)) = (e0)))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (unit) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e4)) = (e0))\/(((op (e1) (e4)) = (e0))\/(((op (e2) (e4)) = (e0))\/(((op (e3) (e4)) = (e0))\/((op (e4) (e4)) = (e0)))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e4)))) -> ((~((op (e4) (e4)) = (e1)))\/((op (e4) (e1)) = (e4))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e3) (e1)) = (e3))\/((op (e4) (e1)) = (e3)))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e3) (e4)) = (e3)))))) -> (~((op (e3) (e0)) = (op (e3) (e4)))) -> (~((op (e3) (e1)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e4)))) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (unit)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e4) (e4)) = (e4)))\/((op (e4) (e4)) = (e4))) -> (~((op (e4) (e0)) = (op (e4) (e4)))) -> (~((op (e4) (e1)) = (op (e4) (e4)))) -> (~((op (e4) (e0)) = (op (e4) (e3)))) -> (~((op (e4) (e0)) = (op (e4) (e2)))) -> ((op (e4) (unit)) = (e4)) -> (~((op (e4) (e0)) = (op (e4) (e1)))) -> (~((op (e4) (e1)) = (op (e4) (e3)))) -> ((op (unit) (e4)) = (e4)) -> (~((op (e4) (e2)) = (op (e4) (e4)))) -> (~((op (e4) (e2)) = (op (e4) (e3)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e4) (e0)) = (e4))\/(((op (e4) (e1)) = (e4))\/(((op (e4) (e2)) = (e4))\/(((op (e4) (e3)) = (e4))\/((op (e4) (e4)) = (e4)))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e2) (e0)) = (op (e2) (e4)))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e4)))) -> ((e3) = (op (e2) (e4))) -> ((op (unit) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> ((op (e3) (e2)) = (e0)) -> ((op (unit) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e4) (e1)) = (op (e4) (e2)))) -> ((op (unit) (e1)) = (e1)) -> ((e1) = (op (e4) (e2))) -> False). % 41.04/41.25 do 0 intro. intros zenon_H302 zenon_H17e zenon_H136 zenon_H17d zenon_H1d5 zenon_H14d zenon_H152 zenon_H157 zenon_H15b zenon_H169 zenon_H1e5 zenon_H1f4 zenon_H161 zenon_H1fb zenon_H1fe zenon_H20c zenon_H20f zenon_H223 zenon_H220 zenon_H21a zenon_H217 zenon_H23c zenon_Hf6 zenon_H22d zenon_H236 zenon_H111 zenon_H240 zenon_H246 zenon_H24e zenon_H256 zenon_H26a zenon_H267 zenon_H261 zenon_H260 zenon_H26e zenon_H275 zenon_H279 zenon_H285 zenon_H299 zenon_H29c zenon_H2a0 zenon_H2a4 zenon_H2ad zenon_H301 zenon_Hff zenon_Hfe zenon_Hfc zenon_H101 zenon_Hbb zenon_H14a zenon_Hf1 zenon_H19a zenon_H18e zenon_H168 zenon_Hf0 zenon_H9f zenon_H50 zenon_H49 zenon_H10b zenon_He0 zenon_H109 zenon_H11f zenon_H12e zenon_H115 zenon_H112 zenon_H1ad zenon_H1ae zenon_H1b3 zenon_H1b9 zenon_Haa zenon_Hc2 zenon_H116 zenon_Ha1 zenon_H129 zenon_H12d zenon_Hb zenon_Hc zenon_H18 zenon_H1c4 zenon_H1a9 zenon_H165 zenon_H2ac zenon_H1c8 zenon_H1c9 zenon_H51 zenon_H41 zenon_H16d zenon_Hf7 zenon_H88 zenon_H7b zenon_H81 zenon_H83 zenon_H87 zenon_H77 zenon_H6e zenon_H73 zenon_H57 zenon_H61 zenon_H5f zenon_H68 zenon_Hed zenon_He6 zenon_He8 zenon_Hcc zenon_Hc8 zenon_H99 zenon_H9b zenon_Hb1 zenon_Hd3 zenon_He9 zenon_H91 zenon_Hd4 zenon_H17 zenon_H2c zenon_H2d zenon_Hd9 zenon_Hee zenon_H3b zenon_Hb6 zenon_H58 zenon_Hb9 zenon_H22 zenon_H20 zenon_H1f zenon_H125 zenon_H42 zenon_H8e zenon_H32 zenon_H16 zenon_H34. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hba | zenon_intro zenon_Hf8 ]. % 41.04/41.25 apply (zenon_L603_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf9 ]. % 41.04/41.25 apply (zenon_L616_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hfa ]. % 41.04/41.25 exact (zenon_Hf7 zenon_Hfb). % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H59 | zenon_intro zenon_Hb7 ]. % 41.04/41.25 apply (zenon_L132_); trivial. % 41.04/41.25 apply (zenon_L214_); trivial. % 41.04/41.25 (* end of lemma zenon_L617_ *) % 41.04/41.25 apply NNPP. intro zenon_G. % 41.04/41.25 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H304. zenon_intro zenon_H303. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H303). zenon_intro zenon_H306. zenon_intro zenon_H305. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H305). zenon_intro zenon_H1d5. zenon_intro zenon_H307. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H307). zenon_intro zenon_H1f4. zenon_intro zenon_H308. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H308). zenon_intro zenon_H30a. zenon_intro zenon_H309. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H309). zenon_intro zenon_H30c. zenon_intro zenon_H30b. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H30b). zenon_intro zenon_H30e. zenon_intro zenon_H30d. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H30d). zenon_intro zenon_H310. zenon_intro zenon_H30f. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H30f). zenon_intro zenon_H23c. zenon_intro zenon_H311. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H311). zenon_intro zenon_H1b9. zenon_intro zenon_H312. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H312). zenon_intro zenon_H314. zenon_intro zenon_H313. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H313). zenon_intro zenon_H24e. zenon_intro zenon_H315. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H315). zenon_intro zenon_H317. zenon_intro zenon_H316. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H316). zenon_intro zenon_H319. zenon_intro zenon_H318. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H318). zenon_intro zenon_H31b. zenon_intro zenon_H31a. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H31a). zenon_intro zenon_H31d. zenon_intro zenon_H31c. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H31c). zenon_intro zenon_H31f. zenon_intro zenon_H31e. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H31e). zenon_intro zenon_H279. zenon_intro zenon_H320. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H320). zenon_intro zenon_H322. zenon_intro zenon_H321. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H321). zenon_intro zenon_H324. zenon_intro zenon_H323. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H323). zenon_intro zenon_H326. zenon_intro zenon_H325. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H325). zenon_intro zenon_H328. zenon_intro zenon_H327. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H327). zenon_intro zenon_H32a. zenon_intro zenon_H329. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H329). zenon_intro zenon_H29c. zenon_intro zenon_H140. % 41.04/41.25 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H42. zenon_intro zenon_H32b. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H32b). zenon_intro zenon_H50. zenon_intro zenon_H32c. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H32c). zenon_intro zenon_H16. zenon_intro zenon_H32d. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H32d). zenon_intro zenon_H2c. zenon_intro zenon_H32e. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H32e). zenon_intro zenon_Hc. zenon_intro zenon_H32f. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H32f). zenon_intro zenon_H58. zenon_intro zenon_H330. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H330). zenon_intro zenon_H20. zenon_intro zenon_H331. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H331). zenon_intro zenon_H5f. zenon_intro zenon_H332. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H332). zenon_intro zenon_Hd3. zenon_intro zenon_H333. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H333). zenon_intro zenon_H99. zenon_intro zenon_H3b. % 41.04/41.25 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H16a. zenon_intro zenon_H334. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H334). zenon_intro zenon_H336. zenon_intro zenon_H335. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H335). zenon_intro zenon_H17d. zenon_intro zenon_H337. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H337). zenon_intro zenon_H339. zenon_intro zenon_H338. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H338). zenon_intro zenon_H33b. zenon_intro zenon_H33a. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H33a). zenon_intro zenon_H33d. zenon_intro zenon_H33c. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H33c). zenon_intro zenon_H33f. zenon_intro zenon_H33e. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H33e). zenon_intro zenon_H341. zenon_intro zenon_H340. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H340). zenon_intro zenon_H343. zenon_intro zenon_H342. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H342). zenon_intro zenon_H345. zenon_intro zenon_H344. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H344). zenon_intro zenon_H347. zenon_intro zenon_H346. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H346). zenon_intro zenon_H15b. zenon_intro zenon_H348. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H348). zenon_intro zenon_H117. zenon_intro zenon_H349. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H349). zenon_intro zenon_H34b. zenon_intro zenon_H34a. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H34a). zenon_intro zenon_H34d. zenon_intro zenon_H34c. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H34c). zenon_intro zenon_H34f. zenon_intro zenon_H34e. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H34e). zenon_intro zenon_H223. zenon_intro zenon_H350. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H350). zenon_intro zenon_H1c8. zenon_intro zenon_H351. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H351). zenon_intro zenon_H353. zenon_intro zenon_H352. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H352). zenon_intro zenon_H355. zenon_intro zenon_H354. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H354). zenon_intro zenon_H357. zenon_intro zenon_H356. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H356). zenon_intro zenon_H12d. zenon_intro zenon_H358. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H358). zenon_intro zenon_H35a. zenon_intro zenon_H359. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H359). zenon_intro zenon_H35c. zenon_intro zenon_H35b. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H35b). zenon_intro zenon_Hf6. zenon_intro zenon_H35d. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H35d). zenon_intro zenon_H35f. zenon_intro zenon_H35e. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H35e). zenon_intro zenon_H361. zenon_intro zenon_H360. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H360). zenon_intro zenon_H363. zenon_intro zenon_H362. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H362). zenon_intro zenon_H365. zenon_intro zenon_H364. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H364). zenon_intro zenon_H367. zenon_intro zenon_H366. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H366). zenon_intro zenon_H369. zenon_intro zenon_H368. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H368). zenon_intro zenon_H36b. zenon_intro zenon_H36a. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H36a). zenon_intro zenon_H36d. zenon_intro zenon_H36c. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H36c). zenon_intro zenon_H236. zenon_intro zenon_H36e. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H36e). zenon_intro zenon_H26a. zenon_intro zenon_H36f. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H36f). zenon_intro zenon_He0. zenon_intro zenon_H370. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H370). zenon_intro zenon_H88. zenon_intro zenon_H371. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H371). zenon_intro zenon_H373. zenon_intro zenon_H372. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H372). zenon_intro zenon_H1fe. zenon_intro zenon_H374. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H374). zenon_intro zenon_H2a4. zenon_intro zenon_H375. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H375). zenon_intro zenon_H377. zenon_intro zenon_H376. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H376). zenon_intro zenon_H1c4. zenon_intro zenon_H378. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H378). zenon_intro zenon_H37a. zenon_intro zenon_H379. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H379). zenon_intro zenon_H19a. zenon_intro zenon_H37b. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H37b). zenon_intro zenon_H37d. zenon_intro zenon_H37c. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H37c). zenon_intro zenon_Hc2. zenon_intro zenon_H37e. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H37e). zenon_intro zenon_H380. zenon_intro zenon_H37f. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H37f). zenon_intro zenon_H382. zenon_intro zenon_H381. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H381). zenon_intro zenon_Hd9. zenon_intro zenon_H20f. % 41.04/41.25 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H384. zenon_intro zenon_H383. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H383). zenon_intro zenon_H386. zenon_intro zenon_H385. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H385). zenon_intro zenon_H388. zenon_intro zenon_H387. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H387). zenon_intro zenon_H38a. zenon_intro zenon_H389. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H389). zenon_intro zenon_H38c. zenon_intro zenon_H38b. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H38b). zenon_intro zenon_H217. zenon_intro zenon_H38d. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H38d). zenon_intro zenon_H38f. zenon_intro zenon_H38e. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H38e). zenon_intro zenon_H260. zenon_intro zenon_H390. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H390). zenon_intro zenon_H392. zenon_intro zenon_H391. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H391). zenon_intro zenon_H1e5. zenon_intro zenon_H393. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H393). zenon_intro zenon_H395. zenon_intro zenon_H394. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H394). zenon_intro zenon_H246. zenon_intro zenon_H396. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H396). zenon_intro zenon_H398. zenon_intro zenon_H397. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H397). zenon_intro zenon_H39a. zenon_intro zenon_H399. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H399). zenon_intro zenon_H14d. zenon_intro zenon_H39b. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H39b). zenon_intro zenon_H152. zenon_intro zenon_H39c. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H39c). zenon_intro zenon_H157. zenon_intro zenon_H39d. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H39d). zenon_intro zenon_H285. zenon_intro zenon_H39e. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H39e). zenon_intro zenon_H261. zenon_intro zenon_H39f. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H39f). zenon_intro zenon_H3a1. zenon_intro zenon_H3a0. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3a0). zenon_intro zenon_H26e. zenon_intro zenon_H3a2. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3a2). zenon_intro zenon_H3a4. zenon_intro zenon_H3a3. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3a3). zenon_intro zenon_H267. zenon_intro zenon_H3a5. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3a5). zenon_intro zenon_H3a7. zenon_intro zenon_H3a6. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3a6). zenon_intro zenon_H3a9. zenon_intro zenon_H3a8. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3a8). zenon_intro zenon_H3ab. zenon_intro zenon_H3aa. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3aa). zenon_intro zenon_H275. zenon_intro zenon_H3ac. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3ac). zenon_intro zenon_H3ae. zenon_intro zenon_H3ad. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3ad). zenon_intro zenon_H3b0. zenon_intro zenon_H3af. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3af). zenon_intro zenon_H21a. zenon_intro zenon_H3b1. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3b1). zenon_intro zenon_H220. zenon_intro zenon_H3b2. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3b2). zenon_intro zenon_H2a0. zenon_intro zenon_H3b3. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3b3). zenon_intro zenon_H3b5. zenon_intro zenon_H3b4. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3b4). zenon_intro zenon_H299. zenon_intro zenon_H3b6. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3b6). zenon_intro zenon_H3b8. zenon_intro zenon_H3b7. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3b7). zenon_intro zenon_H3ba. zenon_intro zenon_H3b9. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3b9). zenon_intro zenon_H256. zenon_intro zenon_H3bb. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3bb). zenon_intro zenon_H3bd. zenon_intro zenon_H3bc. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3bc). zenon_intro zenon_H22d. zenon_intro zenon_H3be. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3be). zenon_intro zenon_H3c0. zenon_intro zenon_H3bf. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3bf). zenon_intro zenon_H1b3. zenon_intro zenon_H3c1. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3c1). zenon_intro zenon_H20c. zenon_intro zenon_H3c2. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3c2). zenon_intro zenon_H1fb. zenon_intro zenon_H3c3. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3c3). zenon_intro zenon_H3c5. zenon_intro zenon_H3c4. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3c4). zenon_intro zenon_H1ae. zenon_intro zenon_H3c6. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3c6). zenon_intro zenon_H1ad. zenon_intro zenon_H3c7. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3c7). zenon_intro zenon_H3c9. zenon_intro zenon_H3c8. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H240. zenon_intro zenon_H3ca. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H3cc. zenon_intro zenon_H3cb. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3cb). zenon_intro zenon_H3ce. zenon_intro zenon_H3cd. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3cd). zenon_intro zenon_H41. zenon_intro zenon_H3cf. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3cf). zenon_intro zenon_H10b. zenon_intro zenon_H3d0. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3d0). zenon_intro zenon_H161. zenon_intro zenon_H3d1. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3d1). zenon_intro zenon_H165. zenon_intro zenon_H3d2. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3d2). zenon_intro zenon_H136. zenon_intro zenon_H3d3. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3d3). zenon_intro zenon_H51. zenon_intro zenon_H3d4. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3d4). zenon_intro zenon_H168. zenon_intro zenon_H3d5. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3d5). zenon_intro zenon_Hb. zenon_intro zenon_H3d6. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3d6). zenon_intro zenon_Ha1. zenon_intro zenon_H3d7. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3d7). zenon_intro zenon_H169. zenon_intro zenon_H3d8. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3d8). zenon_intro zenon_H18. zenon_intro zenon_H3d9. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3d9). zenon_intro zenon_H103. zenon_intro zenon_H3da. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3da). zenon_intro zenon_H2d. zenon_intro zenon_H3db. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3db). zenon_intro zenon_H112. zenon_intro zenon_H3dc. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3dc). zenon_intro zenon_H109. zenon_intro zenon_H3dd. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H111. zenon_intro zenon_H3de. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3de). zenon_intro zenon_H115. zenon_intro zenon_H3df. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3df). zenon_intro zenon_H49. zenon_intro zenon_H3e0. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3e0). zenon_intro zenon_Haa. zenon_intro zenon_H3e1. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3e1). zenon_intro zenon_H116. zenon_intro zenon_H3e2. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3e2). zenon_intro zenon_Hbb. zenon_intro zenon_H3e3. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3e3). zenon_intro zenon_Hfc. zenon_intro zenon_H3e4. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3e4). zenon_intro zenon_H57. zenon_intro zenon_H3e5. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3e5). zenon_intro zenon_Hb6. zenon_intro zenon_H3e6. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3e6). zenon_intro zenon_Hfe. zenon_intro zenon_H3e7. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3e7). zenon_intro zenon_H6e. zenon_intro zenon_H3e8. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3e8). zenon_intro zenon_Hb9. zenon_intro zenon_H3e9. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3e9). zenon_intro zenon_Hff. zenon_intro zenon_H3ea. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_H3ec. zenon_intro zenon_H3eb. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3eb). zenon_intro zenon_H1f. zenon_intro zenon_H3ed. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3ed). zenon_intro zenon_H61. zenon_intro zenon_H3ee. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3ee). zenon_intro zenon_H8e. zenon_intro zenon_H3ef. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3ef). zenon_intro zenon_H68. zenon_intro zenon_H3f0. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3f0). zenon_intro zenon_H7b. zenon_intro zenon_H3f1. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3f1). zenon_intro zenon_H9f. zenon_intro zenon_H3f2. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3f2). zenon_intro zenon_H73. zenon_intro zenon_H3f3. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3f3). zenon_intro zenon_H81. zenon_intro zenon_H3f4. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3f4). zenon_intro zenon_H77. zenon_intro zenon_H3f5. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3f5). zenon_intro zenon_H83. zenon_intro zenon_H3f6. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3f6). zenon_intro zenon_H87. zenon_intro zenon_H3f7. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3f7). zenon_intro zenon_H9b. zenon_intro zenon_H3f8. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3f8). zenon_intro zenon_Hc8. zenon_intro zenon_H3f9. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3f9). zenon_intro zenon_Hcc. zenon_intro zenon_H3fa. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3fa). zenon_intro zenon_He6. zenon_intro zenon_H3fb. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3fb). zenon_intro zenon_H32. zenon_intro zenon_H3fc. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3fc). zenon_intro zenon_Hb1. zenon_intro zenon_H3fd. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3fd). zenon_intro zenon_He8. zenon_intro zenon_H3fe. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3fe). zenon_intro zenon_H91. zenon_intro zenon_H3ff. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H3ff). zenon_intro zenon_He9. zenon_intro zenon_Hd4. % 41.04/41.25 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H129. zenon_intro zenon_H400. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H400). zenon_intro zenon_H402. zenon_intro zenon_H401. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H401). zenon_intro zenon_H1a9. zenon_intro zenon_H403. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H403). zenon_intro zenon_H405. zenon_intro zenon_H404. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H404). zenon_intro zenon_H407. zenon_intro zenon_H406. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H406). zenon_intro zenon_H18e. zenon_intro zenon_H408. % 41.04/41.25 apply (zenon_and_s _ _ ax6). zenon_intro zenon_H11f. zenon_intro zenon_H409. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H409). zenon_intro zenon_H34. zenon_intro zenon_H22. % 41.04/41.25 apply zenon_G. zenon_intro zenon_H40a. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H40a). zenon_intro zenon_H40c. zenon_intro zenon_H40b. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H40b). zenon_intro zenon_H40e. zenon_intro zenon_H40d. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H40d). zenon_intro zenon_H410. zenon_intro zenon_H40f. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H40f). zenon_intro zenon_H412. zenon_intro zenon_H411. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H411). zenon_intro zenon_H414. zenon_intro zenon_H413. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H413). zenon_intro zenon_H164. zenon_intro zenon_H415. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H415). zenon_intro zenon_H13b. zenon_intro zenon_H416. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H416). zenon_intro zenon_H418. zenon_intro zenon_H417. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H417). zenon_intro zenon_H41a. zenon_intro zenon_H419. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H419). zenon_intro zenon_H41c. zenon_intro zenon_H41b. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H41b). zenon_intro zenon_H14b. zenon_intro zenon_H41d. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H41d). zenon_intro zenon_H41f. zenon_intro zenon_H41e. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H41e). zenon_intro zenon_H101. zenon_intro zenon_H420. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H420). zenon_intro zenon_H422. zenon_intro zenon_H421. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H421). zenon_intro zenon_H424. zenon_intro zenon_H423. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H423). zenon_intro zenon_H426. zenon_intro zenon_H425. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H425). zenon_intro zenon_H301. zenon_intro zenon_H427. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H427). zenon_intro zenon_Hf0. zenon_intro zenon_H428. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H428). zenon_intro zenon_Hee. zenon_intro zenon_H429. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H429). zenon_intro zenon_H302. zenon_intro zenon_H42a. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H42a). zenon_intro zenon_H14a. zenon_intro zenon_H42b. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H42b). zenon_intro zenon_H2ac. zenon_intro zenon_H42c. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H42c). zenon_intro zenon_Hf1. zenon_intro zenon_H42d. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H42d). zenon_intro zenon_H149. zenon_intro zenon_H42e. % 41.04/41.25 apply (zenon_and_s _ _ zenon_H42e). zenon_intro zenon_Hed. zenon_intro zenon_H2ad. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H40c); [ zenon_intro zenon_H16b | zenon_intro zenon_H16d ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H15c | zenon_intro zenon_H17 ]. % 41.04/41.25 apply (zenon_L219_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H118 | zenon_intro zenon_H11b ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H12e | zenon_intro zenon_Hba ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H16d | zenon_intro zenon_H16c ]. % 41.04/41.25 exact (zenon_H16b zenon_H16d). % 41.04/41.25 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H43 | zenon_intro zenon_H16e ]. % 41.04/41.25 apply (zenon_L176_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H10c | zenon_intro zenon_H16f ]. % 41.04/41.25 apply (zenon_L204_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H162 | zenon_intro zenon_H166 ]. % 41.04/41.25 apply (zenon_L230_); trivial. % 41.04/41.25 apply (zenon_L234_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_He1 | zenon_intro zenon_H76 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H89 | zenon_intro zenon_H8d ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H13e | zenon_intro zenon_H9a ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 41.04/41.25 apply (zenon_L235_); trivial. % 41.04/41.25 apply (zenon_L236_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc9 ]. % 41.04/41.25 apply (zenon_L245_); trivial. % 41.04/41.25 apply (zenon_L246_); trivial. % 41.04/41.25 apply (zenon_L111_); trivial. % 41.04/41.25 apply (zenon_L247_); trivial. % 41.04/41.25 apply (zenon_L248_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H40e); [ zenon_intro zenon_H17e | zenon_intro zenon_H43 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H15c | zenon_intro zenon_H17 ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H43 | zenon_intro zenon_H15d ]. % 41.04/41.25 apply (zenon_L250_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 41.04/41.25 exact (zenon_H15c zenon_H15f). % 41.04/41.25 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H14c | zenon_intro zenon_H160 ]. % 41.04/41.25 apply (zenon_L216_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H151 | zenon_intro zenon_H156 ]. % 41.04/41.25 apply (zenon_L217_); trivial. % 41.04/41.25 apply (zenon_L218_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H41a); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H10f ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H12e | zenon_intro zenon_Hba ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hfb ]. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H10c | zenon_intro zenon_H12f ]. % 41.04/41.25 apply (zenon_L204_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H120 | zenon_intro zenon_H130 ]. % 41.04/41.25 apply (zenon_L170_); trivial. % 41.04/41.25 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H132 | zenon_intro zenon_H131 ]. % 41.04/41.25 exact (zenon_H12e zenon_H132). % 41.04/41.25 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H125 | zenon_intro zenon_H128 ]. % 41.04/41.25 apply (zenon_L617_); trivial. % 41.04/41.25 apply (zenon_L174_); trivial. % 41.04/41.25 apply (zenon_L139_); trivial. % 41.04/41.25 apply (zenon_L603_); trivial. % 41.04/41.25 apply (zenon_L383_); trivial. % 41.04/41.25 apply (zenon_L250_); trivial. % 41.04/41.25 Qed. % 41.04/41.25 % SZS output end Proof % 41.04/41.25 (* END-PROOF *) % 41.04/41.25 nodes searched: 364679 % 41.04/41.25 max branch formulas: 812 % 41.04/41.25 proof nodes created: 34984 % 41.04/41.25 formulas created: 202464 % 41.04/41.25 %------------------------------------------------------------------------------