%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG054+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 18:29:06 EDT 2022 % Result : Theorem 19.57s 19.77s % Output : Proof 19.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : ALG054+1 : TPTP v8.1.0. Released v2.7.0. % 0.04/0.13 % Command : run_zenon %s %d % 0.13/0.35 % Computer : n021.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Thu Jun 9 03:03:52 EDT 2022 % 0.13/0.35 % CPUTime : % 19.57/19.77 (* PROOF-FOUND *) % 19.57/19.77 % SZS status Theorem % 19.57/19.77 (* BEGIN-PROOF *) % 19.57/19.77 % SZS output start Proof % 19.57/19.77 Theorem co1 : (~((((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/(((op (e3) (e3)) = (e0))\/((op (e4) (e4)) = (e0))))))/\((((op (e0) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/(((op (e3) (e3)) = (e1))\/((op (e4) (e4)) = (e1))))))/\((((op (e0) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/(((op (e3) (e3)) = (e2))\/((op (e4) (e4)) = (e2))))))/\((((op (e0) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/(((op (e3) (e3)) = (e3))\/((op (e4) (e4)) = (e3))))))/\((((op (e0) (e0)) = (e4))\/(((op (e1) (e1)) = (e4))\/(((op (e2) (e2)) = (e4))\/(((op (e3) (e3)) = (e4))\/((op (e4) (e4)) = (e4))))))/\(((~((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))))))))))))))))))))))))))))))))). % 19.57/19.77 Proof. % 19.57/19.77 assert (zenon_L1_ : (~((e1) = (e1))) -> False). % 19.57/19.77 do 0 intro. intros zenon_H7. % 19.57/19.77 apply zenon_H7. apply refl_equal. % 19.57/19.77 (* end of lemma zenon_L1_ *) % 19.57/19.77 assert (zenon_L2_ : (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((unit) = (e0)) -> ((op (e1) (e4)) = (e1)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H8 zenon_H9 zenon_Ha zenon_Hb. % 19.57/19.77 cut (((op (e1) (unit)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e4)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H8. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H9. % 19.57/19.77 cut (((e1) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hc]. % 19.57/19.77 cut (((op (e1) (unit)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd]. % 19.57/19.77 congruence. % 19.57/19.77 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_He | zenon_intro zenon_Hf ]. % 19.57/19.77 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (unit)) = (op (e1) (e0)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_Hd. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_He. % 19.57/19.77 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 19.57/19.77 cut (((op (e1) (e0)) = (op (e1) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H10]. % 19.57/19.77 congruence. % 19.57/19.77 cut (((e0) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 19.57/19.77 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 19.57/19.77 congruence. % 19.57/19.77 apply zenon_H7. apply refl_equal. % 19.57/19.77 apply zenon_H11. apply sym_equal. exact zenon_Ha. % 19.57/19.77 apply zenon_Hf. apply refl_equal. % 19.57/19.77 apply zenon_Hf. apply refl_equal. % 19.57/19.77 apply zenon_Hc. apply sym_equal. exact zenon_Hb. % 19.57/19.77 (* end of lemma zenon_L2_ *) % 19.57/19.77 assert (zenon_L3_ : (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (unit) (e1)) = (e1)) -> ((unit) = (e1)) -> ((op (e1) (e4)) = (e1)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H12 zenon_H13 zenon_H14 zenon_Hb. % 19.57/19.77 cut (((op (unit) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e4)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H12. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H13. % 19.57/19.77 cut (((e1) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hc]. % 19.57/19.77 cut (((op (unit) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 19.57/19.77 congruence. % 19.57/19.77 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H16 | zenon_intro zenon_H17 ]. % 19.57/19.77 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (unit) (e1)) = (op (e1) (e1)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H15. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H16. % 19.57/19.77 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 19.57/19.77 cut (((op (e1) (e1)) = (op (unit) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 19.57/19.77 congruence. % 19.57/19.77 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 19.57/19.77 cut (((e1) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 19.57/19.77 congruence. % 19.57/19.77 apply zenon_H19. apply sym_equal. exact zenon_H14. % 19.57/19.77 apply zenon_H7. apply refl_equal. % 19.57/19.77 apply zenon_H17. apply refl_equal. % 19.57/19.77 apply zenon_H17. apply refl_equal. % 19.57/19.77 apply zenon_Hc. apply sym_equal. exact zenon_Hb. % 19.57/19.77 (* end of lemma zenon_L3_ *) % 19.57/19.77 assert (zenon_L4_ : (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((unit) = (e2)) -> ((op (e1) (e4)) = (e1)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H1a zenon_H9 zenon_H1b zenon_Hb. % 19.57/19.77 cut (((op (e1) (unit)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e4)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H1a. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H9. % 19.57/19.77 cut (((e1) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hc]. % 19.57/19.77 cut (((op (e1) (unit)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 19.57/19.77 congruence. % 19.57/19.77 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H1d | zenon_intro zenon_H1e ]. % 19.57/19.77 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (unit)) = (op (e1) (e2)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H1c. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H1d. % 19.57/19.77 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 19.57/19.77 cut (((op (e1) (e2)) = (op (e1) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H1f]. % 19.57/19.77 congruence. % 19.57/19.77 cut (((e2) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 19.57/19.77 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 19.57/19.77 congruence. % 19.57/19.77 apply zenon_H7. apply refl_equal. % 19.57/19.77 apply zenon_H20. apply sym_equal. exact zenon_H1b. % 19.57/19.77 apply zenon_H1e. apply refl_equal. % 19.57/19.77 apply zenon_H1e. apply refl_equal. % 19.57/19.77 apply zenon_Hc. apply sym_equal. exact zenon_Hb. % 19.57/19.77 (* end of lemma zenon_L4_ *) % 19.57/19.77 assert (zenon_L5_ : (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> ((unit) = (e3)) -> ((op (e1) (e4)) = (e1)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H21 zenon_H9 zenon_H22 zenon_Hb. % 19.57/19.77 cut (((op (e1) (unit)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e4)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H21. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H9. % 19.57/19.77 cut (((e1) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_Hc]. % 19.57/19.77 cut (((op (e1) (unit)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 19.57/19.77 congruence. % 19.57/19.77 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H24 | zenon_intro zenon_H25 ]. % 19.57/19.77 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (unit)) = (op (e1) (e3)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H23. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H24. % 19.57/19.77 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H25]. % 19.57/19.77 cut (((op (e1) (e3)) = (op (e1) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 19.57/19.77 congruence. % 19.57/19.77 cut (((e3) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 19.57/19.77 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 19.57/19.77 congruence. % 19.57/19.77 apply zenon_H7. apply refl_equal. % 19.57/19.77 apply zenon_H27. apply sym_equal. exact zenon_H22. % 19.57/19.77 apply zenon_H25. apply refl_equal. % 19.57/19.77 apply zenon_H25. apply refl_equal. % 19.57/19.77 apply zenon_Hc. apply sym_equal. exact zenon_Hb. % 19.57/19.77 (* end of lemma zenon_L5_ *) % 19.57/19.77 assert (zenon_L6_ : (~((e0) = (e0))) -> False). % 19.57/19.77 do 0 intro. intros zenon_H28. % 19.57/19.77 apply zenon_H28. apply refl_equal. % 19.57/19.77 (* end of lemma zenon_L6_ *) % 19.57/19.77 assert (zenon_L7_ : ((op (e0) (unit)) = (e0)) -> ((unit) = (e4)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e0) (e4)))) -> False). % 19.57/19.77 do 0 intro. intros zenon_H29 zenon_H2a zenon_H2b zenon_H2c. % 19.57/19.77 elim (classic ((op (e0) (e4)) = (op (e0) (e4)))); [ zenon_intro zenon_H2d | zenon_intro zenon_H2e ]. % 19.57/19.77 cut (((op (e0) (e4)) = (op (e0) (e4))) = ((op (e0) (e3)) = (op (e0) (e4)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H2c. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H2d. % 19.57/19.77 cut (((op (e0) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 19.57/19.77 cut (((op (e0) (e4)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 19.57/19.77 congruence. % 19.57/19.77 cut (((op (e0) (unit)) = (e0)) = ((op (e0) (e4)) = (op (e0) (e3)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H2f. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H29. % 19.57/19.77 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 19.57/19.77 cut (((op (e0) (unit)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 19.57/19.77 congruence. % 19.57/19.77 elim (classic ((op (e0) (e4)) = (op (e0) (e4)))); [ zenon_intro zenon_H2d | zenon_intro zenon_H2e ]. % 19.57/19.77 cut (((op (e0) (e4)) = (op (e0) (e4))) = ((op (e0) (unit)) = (op (e0) (e4)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H31. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H2d. % 19.57/19.77 cut (((op (e0) (e4)) = (op (e0) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 19.57/19.77 cut (((op (e0) (e4)) = (op (e0) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 19.57/19.77 congruence. % 19.57/19.77 cut (((e4) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 19.57/19.77 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 19.57/19.77 congruence. % 19.57/19.77 apply zenon_H28. apply refl_equal. % 19.57/19.77 apply zenon_H33. apply sym_equal. exact zenon_H2a. % 19.57/19.77 apply zenon_H2e. apply refl_equal. % 19.57/19.77 apply zenon_H2e. apply refl_equal. % 19.57/19.77 apply zenon_H30. apply sym_equal. exact zenon_H2b. % 19.57/19.77 apply zenon_H2e. apply refl_equal. % 19.57/19.77 apply zenon_H2e. apply refl_equal. % 19.57/19.77 (* end of lemma zenon_L7_ *) % 19.57/19.77 assert (zenon_L8_ : (~((op (e1) (e4)) = (op (e1) (unit)))) -> ((unit) = (e4)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H34 zenon_H2a. % 19.57/19.77 cut (((e4) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 19.57/19.77 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 19.57/19.77 congruence. % 19.57/19.77 apply zenon_H7. apply refl_equal. % 19.57/19.77 apply zenon_H33. apply sym_equal. exact zenon_H2a. % 19.57/19.77 (* end of lemma zenon_L8_ *) % 19.57/19.77 assert (zenon_L9_ : ((op (e1) (unit)) = (e1)) -> ((unit) = (e4)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> False). % 19.57/19.77 do 0 intro. intros zenon_H9 zenon_H2a zenon_H35 zenon_H21. % 19.57/19.77 elim (classic ((op (e1) (e4)) = (op (e1) (e4)))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 19.57/19.77 cut (((op (e1) (e4)) = (op (e1) (e4))) = ((op (e1) (e3)) = (op (e1) (e4)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H21. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H36. % 19.57/19.77 cut (((op (e1) (e4)) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 19.57/19.77 cut (((op (e1) (e4)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 19.57/19.77 congruence. % 19.57/19.77 cut (((op (e1) (unit)) = (e1)) = ((op (e1) (e4)) = (op (e1) (e3)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H38. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H9. % 19.57/19.77 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 19.57/19.77 cut (((op (e1) (unit)) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 19.57/19.77 congruence. % 19.57/19.77 elim (classic ((op (e1) (e4)) = (op (e1) (e4)))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 19.57/19.77 cut (((op (e1) (e4)) = (op (e1) (e4))) = ((op (e1) (unit)) = (op (e1) (e4)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H3a. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H36. % 19.57/19.77 cut (((op (e1) (e4)) = (op (e1) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 19.57/19.77 cut (((op (e1) (e4)) = (op (e1) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 19.57/19.77 congruence. % 19.57/19.77 apply (zenon_L8_); trivial. % 19.57/19.77 apply zenon_H37. apply refl_equal. % 19.57/19.77 apply zenon_H37. apply refl_equal. % 19.57/19.77 apply zenon_H39. apply sym_equal. exact zenon_H35. % 19.57/19.77 apply zenon_H37. apply refl_equal. % 19.57/19.77 apply zenon_H37. apply refl_equal. % 19.57/19.77 (* end of lemma zenon_L9_ *) % 19.57/19.77 assert (zenon_L10_ : ((~((op (e1) (e1)) = (e4)))\/((op (e1) (e4)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (e3)) = (e1)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e4) = (op (e1) (e1))) -> False). % 19.57/19.77 do 0 intro. intros zenon_H3b zenon_H8 zenon_H9 zenon_H12 zenon_H13 zenon_H1a zenon_H21 zenon_H35 zenon_H3c zenon_H3d. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H3e | zenon_intro zenon_Hb ]. % 19.57/19.77 apply zenon_H3e. apply sym_equal. exact zenon_H3d. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_Ha | zenon_intro zenon_H3f ]. % 19.57/19.77 apply (zenon_L2_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H14 | zenon_intro zenon_H40 ]. % 19.57/19.77 apply (zenon_L3_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H1b | zenon_intro zenon_H41 ]. % 19.57/19.77 apply (zenon_L4_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H22 | zenon_intro zenon_H2a ]. % 19.57/19.77 apply (zenon_L5_); trivial. % 19.57/19.77 apply (zenon_L9_); trivial. % 19.57/19.77 (* end of lemma zenon_L10_ *) % 19.57/19.77 assert (zenon_L11_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((e4) = (op (e1) (e1))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((~((op (e1) (e1)) = (e4)))\/((op (e1) (e4)) = (e1))) -> ((op (e1) (e1)) = (e3)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H42 zenon_H3d zenon_H3c zenon_H21 zenon_H1a zenon_H13 zenon_H12 zenon_H9 zenon_H8 zenon_H3b zenon_H43. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H35 ]. % 19.57/19.77 exact (zenon_H44 zenon_H43). % 19.57/19.77 apply (zenon_L10_); trivial. % 19.57/19.77 (* end of lemma zenon_L11_ *) % 19.57/19.77 assert (zenon_L12_ : (~((e2) = (e2))) -> False). % 19.57/19.77 do 0 intro. intros zenon_H45. % 19.57/19.77 apply zenon_H45. apply refl_equal. % 19.57/19.77 (* end of lemma zenon_L12_ *) % 19.57/19.77 assert (zenon_L13_ : (~((op (e2) (e4)) = (op (e2) (unit)))) -> ((unit) = (e4)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H46 zenon_H2a. % 19.57/19.77 cut (((e4) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 19.57/19.77 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 19.57/19.77 congruence. % 19.57/19.77 apply zenon_H45. apply refl_equal. % 19.57/19.77 apply zenon_H33. apply sym_equal. exact zenon_H2a. % 19.57/19.77 (* end of lemma zenon_L13_ *) % 19.57/19.77 assert (zenon_L14_ : ((op (e2) (unit)) = (e2)) -> ((unit) = (e4)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> False). % 19.57/19.77 do 0 intro. intros zenon_H47 zenon_H2a zenon_H48 zenon_H49. % 19.57/19.77 elim (classic ((op (e2) (e4)) = (op (e2) (e4)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 19.57/19.77 cut (((op (e2) (e4)) = (op (e2) (e4))) = ((op (e2) (e3)) = (op (e2) (e4)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H49. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H4a. % 19.57/19.77 cut (((op (e2) (e4)) = (op (e2) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 19.57/19.77 cut (((op (e2) (e4)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 19.57/19.77 congruence. % 19.57/19.77 cut (((op (e2) (unit)) = (e2)) = ((op (e2) (e4)) = (op (e2) (e3)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H4c. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H47. % 19.57/19.77 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 19.57/19.77 cut (((op (e2) (unit)) = (op (e2) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 19.57/19.77 congruence. % 19.57/19.77 elim (classic ((op (e2) (e4)) = (op (e2) (e4)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 19.57/19.77 cut (((op (e2) (e4)) = (op (e2) (e4))) = ((op (e2) (unit)) = (op (e2) (e4)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H4e. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H4a. % 19.57/19.77 cut (((op (e2) (e4)) = (op (e2) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 19.57/19.77 cut (((op (e2) (e4)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 19.57/19.77 congruence. % 19.57/19.77 apply (zenon_L13_); trivial. % 19.57/19.77 apply zenon_H4b. apply refl_equal. % 19.57/19.77 apply zenon_H4b. apply refl_equal. % 19.57/19.77 apply zenon_H4d. apply sym_equal. exact zenon_H48. % 19.57/19.77 apply zenon_H4b. apply refl_equal. % 19.57/19.77 apply zenon_H4b. apply refl_equal. % 19.57/19.77 (* end of lemma zenon_L14_ *) % 19.57/19.77 assert (zenon_L15_ : (((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)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (e1) (e4)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e2) (unit)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> False). % 19.57/19.77 do 0 intro. intros zenon_H3c zenon_H8 zenon_H13 zenon_H12 zenon_H1a zenon_Hb zenon_H9 zenon_H21 zenon_H47 zenon_H48 zenon_H49. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_Ha | zenon_intro zenon_H3f ]. % 19.57/19.77 apply (zenon_L2_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H14 | zenon_intro zenon_H40 ]. % 19.57/19.77 apply (zenon_L3_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H1b | zenon_intro zenon_H41 ]. % 19.57/19.77 apply (zenon_L4_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H22 | zenon_intro zenon_H2a ]. % 19.57/19.77 apply (zenon_L5_); trivial. % 19.57/19.77 apply (zenon_L14_); trivial. % 19.57/19.77 (* end of lemma zenon_L15_ *) % 19.57/19.77 assert (zenon_L16_ : ((~((op (e1) (e1)) = (e4)))\/((op (e1) (e4)) = (e1))) -> ((op (e2) (e2)) = (e3)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((op (e2) (unit)) = (e2)) -> (~((op (e2) (e3)) = (op (e2) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((e4) = (op (e1) (e1))) -> False). % 19.57/19.77 do 0 intro. intros zenon_H3b zenon_H4f zenon_H3c zenon_H47 zenon_H49 zenon_H21 zenon_H1a zenon_H13 zenon_H12 zenon_H9 zenon_H8 zenon_H50 zenon_H3d. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H3e | zenon_intro zenon_Hb ]. % 19.57/19.77 apply zenon_H3e. apply sym_equal. exact zenon_H3d. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H51 | zenon_intro zenon_H48 ]. % 19.57/19.77 exact (zenon_H51 zenon_H4f). % 19.57/19.77 apply (zenon_L15_); trivial. % 19.57/19.77 (* end of lemma zenon_L16_ *) % 19.57/19.77 assert (zenon_L17_ : (~((e3) = (e3))) -> False). % 19.57/19.77 do 0 intro. intros zenon_H52. % 19.57/19.77 apply zenon_H52. apply refl_equal. % 19.57/19.77 (* end of lemma zenon_L17_ *) % 19.57/19.77 assert (zenon_L18_ : (~((op (e3) (e0)) = (op (e3) (unit)))) -> ((unit) = (e0)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H53 zenon_Ha. % 19.57/19.77 cut (((e0) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 19.57/19.77 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 19.57/19.77 congruence. % 19.57/19.77 apply zenon_H52. apply refl_equal. % 19.57/19.77 apply zenon_H11. apply sym_equal. exact zenon_Ha. % 19.57/19.77 (* end of lemma zenon_L18_ *) % 19.57/19.77 assert (zenon_L19_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> ((unit) = (e0)) -> ((op (e3) (e3)) = (e3)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H54 zenon_H55 zenon_Ha zenon_H56. % 19.57/19.77 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e3)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H54. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H55. % 19.57/19.77 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 19.57/19.77 cut (((op (e3) (unit)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 19.57/19.77 congruence. % 19.57/19.77 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H59 | zenon_intro zenon_H5a ]. % 19.57/19.77 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e3) (unit)) = (op (e3) (e0)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H58. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H59. % 19.57/19.77 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 19.57/19.77 cut (((op (e3) (e0)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 19.57/19.77 congruence. % 19.57/19.77 apply (zenon_L18_); trivial. % 19.57/19.77 apply zenon_H5a. apply refl_equal. % 19.57/19.77 apply zenon_H5a. apply refl_equal. % 19.57/19.77 apply zenon_H57. apply sym_equal. exact zenon_H56. % 19.57/19.77 (* end of lemma zenon_L19_ *) % 19.57/19.77 assert (zenon_L20_ : (~((op (e3) (e1)) = (op (e3) (unit)))) -> ((unit) = (e1)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H5b zenon_H14. % 19.57/19.77 cut (((e1) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 19.57/19.77 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 19.57/19.77 congruence. % 19.57/19.77 apply zenon_H52. apply refl_equal. % 19.57/19.77 apply zenon_H19. apply sym_equal. exact zenon_H14. % 19.57/19.77 (* end of lemma zenon_L20_ *) % 19.57/19.77 assert (zenon_L21_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> ((unit) = (e1)) -> ((op (e3) (e3)) = (e3)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H5c zenon_H55 zenon_H14 zenon_H56. % 19.57/19.77 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e3)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H5c. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H55. % 19.57/19.77 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 19.57/19.77 cut (((op (e3) (unit)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 19.57/19.77 congruence. % 19.57/19.77 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H5e | zenon_intro zenon_H5f ]. % 19.57/19.77 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (unit)) = (op (e3) (e1)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H5d. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H5e. % 19.57/19.77 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 19.57/19.77 cut (((op (e3) (e1)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 19.57/19.77 congruence. % 19.57/19.77 apply (zenon_L20_); trivial. % 19.57/19.77 apply zenon_H5f. apply refl_equal. % 19.57/19.77 apply zenon_H5f. apply refl_equal. % 19.57/19.77 apply zenon_H57. apply sym_equal. exact zenon_H56. % 19.57/19.77 (* end of lemma zenon_L21_ *) % 19.57/19.77 assert (zenon_L22_ : (~((op (e3) (e2)) = (op (e3) (unit)))) -> ((unit) = (e2)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H60 zenon_H1b. % 19.57/19.77 cut (((e2) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 19.57/19.77 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 19.57/19.77 congruence. % 19.57/19.77 apply zenon_H52. apply refl_equal. % 19.57/19.77 apply zenon_H20. apply sym_equal. exact zenon_H1b. % 19.57/19.77 (* end of lemma zenon_L22_ *) % 19.57/19.77 assert (zenon_L23_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> ((unit) = (e2)) -> ((op (e3) (e3)) = (e3)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H61 zenon_H55 zenon_H1b zenon_H56. % 19.57/19.77 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e3)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H61. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H55. % 19.57/19.77 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 19.57/19.77 cut (((op (e3) (unit)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 19.57/19.77 congruence. % 19.57/19.77 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ]. % 19.57/19.77 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (unit)) = (op (e3) (e2)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H62. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H63. % 19.57/19.77 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 19.57/19.77 cut (((op (e3) (e2)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 19.57/19.77 congruence. % 19.57/19.77 apply (zenon_L22_); trivial. % 19.57/19.77 apply zenon_H64. apply refl_equal. % 19.57/19.77 apply zenon_H64. apply refl_equal. % 19.57/19.77 apply zenon_H57. apply sym_equal. exact zenon_H56. % 19.57/19.77 (* end of lemma zenon_L23_ *) % 19.57/19.77 assert (zenon_L24_ : (~((op (e3) (e4)) = (op (e3) (unit)))) -> ((unit) = (e4)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H65 zenon_H2a. % 19.57/19.77 cut (((e4) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 19.57/19.77 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 19.57/19.77 congruence. % 19.57/19.77 apply zenon_H52. apply refl_equal. % 19.57/19.77 apply zenon_H33. apply sym_equal. exact zenon_H2a. % 19.57/19.77 (* end of lemma zenon_L24_ *) % 19.57/19.77 assert (zenon_L25_ : ((op (e3) (unit)) = (e3)) -> ((unit) = (e4)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> False). % 19.57/19.77 do 0 intro. intros zenon_H55 zenon_H2a zenon_H56 zenon_H66. % 19.57/19.77 elim (classic ((op (e3) (e4)) = (op (e3) (e4)))); [ zenon_intro zenon_H67 | zenon_intro zenon_H68 ]. % 19.57/19.77 cut (((op (e3) (e4)) = (op (e3) (e4))) = ((op (e3) (e3)) = (op (e3) (e4)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H66. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H67. % 19.57/19.77 cut (((op (e3) (e4)) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H68]. % 19.57/19.77 cut (((op (e3) (e4)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 19.57/19.77 congruence. % 19.57/19.77 cut (((op (e3) (unit)) = (e3)) = ((op (e3) (e4)) = (op (e3) (e3)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H69. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H55. % 19.57/19.77 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 19.57/19.77 cut (((op (e3) (unit)) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 19.57/19.77 congruence. % 19.57/19.77 elim (classic ((op (e3) (e4)) = (op (e3) (e4)))); [ zenon_intro zenon_H67 | zenon_intro zenon_H68 ]. % 19.57/19.77 cut (((op (e3) (e4)) = (op (e3) (e4))) = ((op (e3) (unit)) = (op (e3) (e4)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H6a. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H67. % 19.57/19.77 cut (((op (e3) (e4)) = (op (e3) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H68]. % 19.57/19.77 cut (((op (e3) (e4)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 19.57/19.77 congruence. % 19.57/19.77 apply (zenon_L24_); trivial. % 19.57/19.77 apply zenon_H68. apply refl_equal. % 19.57/19.77 apply zenon_H68. apply refl_equal. % 19.57/19.77 apply zenon_H57. apply sym_equal. exact zenon_H56. % 19.57/19.77 apply zenon_H68. apply refl_equal. % 19.57/19.77 apply zenon_H68. apply refl_equal. % 19.57/19.77 (* end of lemma zenon_L25_ *) % 19.57/19.77 assert (zenon_L26_ : (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e4)) = (e1)) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e3) (unit)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> False). % 19.57/19.77 do 0 intro. intros zenon_H3c zenon_H54 zenon_H5c zenon_H61 zenon_Hb zenon_H9 zenon_H21 zenon_H55 zenon_H56 zenon_H66. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_Ha | zenon_intro zenon_H3f ]. % 19.57/19.77 apply (zenon_L19_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H14 | zenon_intro zenon_H40 ]. % 19.57/19.77 apply (zenon_L21_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H1b | zenon_intro zenon_H41 ]. % 19.57/19.77 apply (zenon_L23_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H22 | zenon_intro zenon_H2a ]. % 19.57/19.77 apply (zenon_L5_); trivial. % 19.57/19.77 apply (zenon_L25_); trivial. % 19.57/19.77 (* end of lemma zenon_L26_ *) % 19.57/19.77 assert (zenon_L27_ : ((~((op (e1) (e1)) = (e4)))\/((op (e1) (e4)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (unit)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e3) (e3)) = (op (e3) (e4)))) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e4) = (op (e1) (e1))) -> False). % 19.57/19.77 do 0 intro. intros zenon_H3b zenon_H54 zenon_H55 zenon_H56 zenon_H5c zenon_H61 zenon_H21 zenon_H9 zenon_H66 zenon_H3c zenon_H3d. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H3e | zenon_intro zenon_Hb ]. % 19.57/19.77 apply zenon_H3e. apply sym_equal. exact zenon_H3d. % 19.57/19.77 apply (zenon_L26_); trivial. % 19.57/19.77 (* end of lemma zenon_L27_ *) % 19.57/19.77 assert (zenon_L28_ : (~((op (e4) (e3)) = (op (unit) (e3)))) -> ((unit) = (e4)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H6b zenon_H2a. % 19.57/19.77 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 19.57/19.77 cut (((e4) = (unit))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 19.57/19.77 congruence. % 19.57/19.77 apply zenon_H33. apply sym_equal. exact zenon_H2a. % 19.57/19.77 apply zenon_H52. apply refl_equal. % 19.57/19.77 (* end of lemma zenon_L28_ *) % 19.57/19.77 assert (zenon_L29_ : (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((unit) = (e4)) -> ((op (e4) (e4)) = (e3)) -> False). % 19.57/19.77 do 0 intro. intros zenon_H6c zenon_H6d zenon_H2a zenon_H6e. % 19.57/19.77 cut (((op (unit) (e3)) = (e3)) = ((op (e4) (e3)) = (op (e4) (e4)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H6c. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H6d. % 19.57/19.77 cut (((e3) = (op (e4) (e4)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 19.57/19.77 cut (((op (unit) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 19.57/19.77 congruence. % 19.57/19.77 elim (classic ((op (e4) (e3)) = (op (e4) (e3)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 19.57/19.77 cut (((op (e4) (e3)) = (op (e4) (e3))) = ((op (unit) (e3)) = (op (e4) (e3)))). % 19.57/19.77 intro zenon_D_pnotp. % 19.57/19.77 apply zenon_H70. % 19.57/19.77 rewrite <- zenon_D_pnotp. % 19.57/19.77 exact zenon_H71. % 19.57/19.77 cut (((op (e4) (e3)) = (op (e4) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 19.57/19.77 cut (((op (e4) (e3)) = (op (unit) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 19.57/19.77 congruence. % 19.57/19.77 apply (zenon_L28_); trivial. % 19.57/19.77 apply zenon_H72. apply refl_equal. % 19.57/19.77 apply zenon_H72. apply refl_equal. % 19.57/19.77 apply zenon_H6f. apply sym_equal. exact zenon_H6e. % 19.57/19.77 (* end of lemma zenon_L29_ *) % 19.57/19.77 assert (zenon_L30_ : ((~((op (e1) (e1)) = (e4)))\/((op (e1) (e4)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e4)))) -> ((op (e1) (unit)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e4)))) -> ((op (unit) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e4)))) -> (~((op (e1) (e3)) = (op (e1) (e4)))) -> (~((op (e4) (e3)) = (op (e4) (e4)))) -> ((op (unit) (e3)) = (e3)) -> ((op (e4) (e4)) = (e3)) -> (((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/(((unit) = (e3))\/((unit) = (e4)))))) -> ((e4) = (op (e1) (e1))) -> False). % 19.57/19.77 do 0 intro. intros zenon_H3b zenon_H8 zenon_H9 zenon_H12 zenon_H13 zenon_H1a zenon_H21 zenon_H6c zenon_H6d zenon_H6e zenon_H3c zenon_H3d. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H3e | zenon_intro zenon_Hb ]. % 19.57/19.77 apply zenon_H3e. apply sym_equal. exact zenon_H3d. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_Ha | zenon_intro zenon_H3f ]. % 19.57/19.77 apply (zenon_L2_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H14 | zenon_intro zenon_H40 ]. % 19.57/19.77 apply (zenon_L3_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H1b | zenon_intro zenon_H41 ]. % 19.57/19.77 apply (zenon_L4_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H22 | zenon_intro zenon_H2a ]. % 19.57/19.77 apply (zenon_L5_); trivial. % 19.57/19.77 apply (zenon_L29_); trivial. % 19.57/19.77 (* end of lemma zenon_L30_ *) % 19.57/19.77 apply NNPP. intro zenon_G. % 19.57/19.77 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H74. zenon_intro zenon_H73. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H73). zenon_intro zenon_H29. zenon_intro zenon_H75. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H13. zenon_intro zenon_H76. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H76). zenon_intro zenon_H9. zenon_intro zenon_H77. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H77). zenon_intro zenon_H79. zenon_intro zenon_H78. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H78). zenon_intro zenon_H47. zenon_intro zenon_H7a. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H7a). zenon_intro zenon_H6d. zenon_intro zenon_H7b. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H7b). zenon_intro zenon_H55. zenon_intro zenon_H7c. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H7c). zenon_intro zenon_H7e. zenon_intro zenon_H7d. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H7d). zenon_intro zenon_H7f. zenon_intro zenon_H3c. % 19.57/19.77 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H81. zenon_intro zenon_H80. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H82). zenon_intro zenon_H85. zenon_intro zenon_H84. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H84). zenon_intro zenon_H87. zenon_intro zenon_H86. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H86). zenon_intro zenon_H89. zenon_intro zenon_H88. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H8a). zenon_intro zenon_H8d. zenon_intro zenon_H8c. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H93. zenon_intro zenon_H92. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H92). zenon_intro zenon_H95. zenon_intro zenon_H94. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H94). zenon_intro zenon_H97. zenon_intro zenon_H96. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H96). zenon_intro zenon_H99. zenon_intro zenon_H98. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H98). zenon_intro zenon_H9b. zenon_intro zenon_H9a. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9f. zenon_intro zenon_H9e. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H9e). zenon_intro zenon_Ha1. zenon_intro zenon_Ha0. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Ha0). zenon_intro zenon_Ha3. zenon_intro zenon_Ha2. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Ha2). zenon_intro zenon_Ha5. zenon_intro zenon_Ha4. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Ha4). zenon_intro zenon_Ha7. zenon_intro zenon_Ha6. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Ha6). zenon_intro zenon_Ha9. zenon_intro zenon_Ha8. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Ha8). zenon_intro zenon_Hab. zenon_intro zenon_Haa. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Haa). zenon_intro zenon_Had. zenon_intro zenon_Hac. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hac). zenon_intro zenon_Haf. zenon_intro zenon_Hae. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Hb1. zenon_intro zenon_Hb0. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hb0). zenon_intro zenon_Hb3. zenon_intro zenon_Hb2. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hb2). zenon_intro zenon_Hb5. zenon_intro zenon_Hb4. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hb4). zenon_intro zenon_Hb7. zenon_intro zenon_Hb6. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_Hb9. zenon_intro zenon_Hb8. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hb8). zenon_intro zenon_Hbb. zenon_intro zenon_Hba. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hba). zenon_intro zenon_Hbd. zenon_intro zenon_Hbc. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbf. zenon_intro zenon_Hbe. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hbe). zenon_intro zenon_Hc1. zenon_intro zenon_Hc0. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc3. zenon_intro zenon_Hc2. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_Hc5. zenon_intro zenon_Hc4. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_Hc7. zenon_intro zenon_Hc6. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc9. zenon_intro zenon_Hc8. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hcb. zenon_intro zenon_Hca. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_Hcd. zenon_intro zenon_Hcc. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_Hcf. zenon_intro zenon_Hce. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_Hd1. zenon_intro zenon_Hd0. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hd0). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hd2). zenon_intro zenon_Hd5. zenon_intro zenon_Hd4. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_Hd7. zenon_intro zenon_Hd6. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd9. zenon_intro zenon_Hd8. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Hdb. zenon_intro zenon_Hda. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hda). zenon_intro zenon_Hdd. zenon_intro zenon_Hdc. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hdc). zenon_intro zenon_Hdf. zenon_intro zenon_Hde. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hde). zenon_intro zenon_He1. zenon_intro zenon_He0. % 19.57/19.77 apply (zenon_and_s _ _ zenon_He0). zenon_intro zenon_He3. zenon_intro zenon_He2. % 19.57/19.77 apply (zenon_and_s _ _ zenon_He2). zenon_intro zenon_He5. zenon_intro zenon_He4. % 19.57/19.77 apply (zenon_and_s _ _ zenon_He4). zenon_intro zenon_He7. zenon_intro zenon_He6. % 19.57/19.77 apply (zenon_and_s _ _ zenon_He6). zenon_intro zenon_He9. zenon_intro zenon_He8. % 19.57/19.77 apply (zenon_and_s _ _ zenon_He8). zenon_intro zenon_Heb. zenon_intro zenon_Hea. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hed. zenon_intro zenon_Hec. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hec). zenon_intro zenon_Hef. zenon_intro zenon_Hee. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hee). zenon_intro zenon_Hf1. zenon_intro zenon_Hf0. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hf0). zenon_intro zenon_Hf3. zenon_intro zenon_Hf2. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Hf5. zenon_intro zenon_Hf4. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hf4). zenon_intro zenon_H2c. zenon_intro zenon_Hf6. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hf6). zenon_intro zenon_Hf8. zenon_intro zenon_Hf7. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hf7). zenon_intro zenon_Hfa. zenon_intro zenon_Hf9. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfc. zenon_intro zenon_Hfb. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hfb). zenon_intro zenon_H8. zenon_intro zenon_Hfd. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hfd). zenon_intro zenon_Hff. zenon_intro zenon_Hfe. % 19.57/19.77 apply (zenon_and_s _ _ zenon_Hfe). zenon_intro zenon_H101. zenon_intro zenon_H100. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H100). zenon_intro zenon_H12. zenon_intro zenon_H102. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H102). zenon_intro zenon_H104. zenon_intro zenon_H103. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H103). zenon_intro zenon_H1a. zenon_intro zenon_H105. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H105). zenon_intro zenon_H21. zenon_intro zenon_H106. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_H108. zenon_intro zenon_H107. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H107). zenon_intro zenon_H10a. zenon_intro zenon_H109. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H109). zenon_intro zenon_H10c. zenon_intro zenon_H10b. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H10b). zenon_intro zenon_H10e. zenon_intro zenon_H10d. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H10d). zenon_intro zenon_H110. zenon_intro zenon_H10f. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H10f). zenon_intro zenon_H112. zenon_intro zenon_H111. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H111). zenon_intro zenon_H114. zenon_intro zenon_H113. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H113). zenon_intro zenon_H116. zenon_intro zenon_H115. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H115). zenon_intro zenon_H118. zenon_intro zenon_H117. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H117). zenon_intro zenon_H49. zenon_intro zenon_H119. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H119). zenon_intro zenon_H11b. zenon_intro zenon_H11a. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H11a). zenon_intro zenon_H11d. zenon_intro zenon_H11c. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H11c). zenon_intro zenon_H54. zenon_intro zenon_H11e. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H11e). zenon_intro zenon_H120. zenon_intro zenon_H11f. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H11f). zenon_intro zenon_H122. zenon_intro zenon_H121. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H121). zenon_intro zenon_H5c. zenon_intro zenon_H123. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H123). zenon_intro zenon_H125. zenon_intro zenon_H124. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H124). zenon_intro zenon_H61. zenon_intro zenon_H126. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H126). zenon_intro zenon_H128. zenon_intro zenon_H127. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H127). zenon_intro zenon_H66. zenon_intro zenon_H129. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H129). zenon_intro zenon_H12b. zenon_intro zenon_H12a. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H12a). zenon_intro zenon_H12d. zenon_intro zenon_H12c. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H12c). zenon_intro zenon_H12f. zenon_intro zenon_H12e. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H12e). zenon_intro zenon_H131. zenon_intro zenon_H130. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H130). zenon_intro zenon_H133. zenon_intro zenon_H132. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H132). zenon_intro zenon_H135. zenon_intro zenon_H134. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H134). zenon_intro zenon_H137. zenon_intro zenon_H136. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H136). zenon_intro zenon_H139. zenon_intro zenon_H138. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H138). zenon_intro zenon_H13a. zenon_intro zenon_H6c. % 19.57/19.77 apply (zenon_and_s _ _ ax6). zenon_intro zenon_H13c. zenon_intro zenon_H13b. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H13b). zenon_intro zenon_H13e. zenon_intro zenon_H13d. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H3d. % 19.57/19.77 apply zenon_G. zenon_intro zenon_H140. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H146. zenon_intro zenon_H145. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H145). zenon_intro zenon_H148. zenon_intro zenon_H147. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H147). zenon_intro zenon_H14a. zenon_intro zenon_H149. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H149). zenon_intro zenon_H14c. zenon_intro zenon_H14b. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H14b). zenon_intro zenon_H14e. zenon_intro zenon_H14d. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H14d). zenon_intro zenon_H150. zenon_intro zenon_H14f. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H14f). zenon_intro zenon_H152. zenon_intro zenon_H151. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H151). zenon_intro zenon_H154. zenon_intro zenon_H153. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H153). zenon_intro zenon_H156. zenon_intro zenon_H155. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H155). zenon_intro zenon_H158. zenon_intro zenon_H157. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H157). zenon_intro zenon_H15a. zenon_intro zenon_H159. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H159). zenon_intro zenon_H42. zenon_intro zenon_H15b. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_H3b. zenon_intro zenon_H15c. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H15c). zenon_intro zenon_H15e. zenon_intro zenon_H15d. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H15d). zenon_intro zenon_H160. zenon_intro zenon_H15f. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H15f). zenon_intro zenon_H162. zenon_intro zenon_H161. % 19.57/19.77 apply (zenon_and_s _ _ zenon_H161). zenon_intro zenon_H50. zenon_intro zenon_H163. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H165 | zenon_intro zenon_H164 ]. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H166 | zenon_intro zenon_H2b ]. % 19.57/19.77 exact (zenon_H166 zenon_H165). % 19.57/19.77 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H3e | zenon_intro zenon_Hb ]. % 19.57/19.77 apply zenon_H3e. apply sym_equal. exact zenon_H3d. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_Ha | zenon_intro zenon_H3f ]. % 19.57/19.77 apply (zenon_L2_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H14 | zenon_intro zenon_H40 ]. % 19.57/19.77 apply (zenon_L3_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H1b | zenon_intro zenon_H41 ]. % 19.57/19.77 apply (zenon_L4_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H22 | zenon_intro zenon_H2a ]. % 19.57/19.77 apply (zenon_L5_); trivial. % 19.57/19.77 apply (zenon_L7_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H43 | zenon_intro zenon_H167 ]. % 19.57/19.77 apply (zenon_L11_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H4f | zenon_intro zenon_H168 ]. % 19.57/19.77 apply (zenon_L16_); trivial. % 19.57/19.77 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H56 | zenon_intro zenon_H6e ]. % 19.57/19.77 apply (zenon_L27_); trivial. % 19.57/19.77 apply (zenon_L30_); trivial. % 19.57/19.77 Qed. % 19.57/19.77 % SZS output end Proof % 19.57/19.77 (* END-PROOF *) % 19.57/19.77 nodes searched: 84825 % 19.57/19.77 max branch formulas: 526 % 19.57/19.77 proof nodes created: 10919 % 19.57/19.77 formulas created: 61702 % 19.57/19.77 %------------------------------------------------------------------------------