%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG117+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n026.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 18:29:30 EDT 2022 % Result : Theorem 21.03s 21.26s % Output : Proof 21.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : ALG117+1 : TPTP v8.1.0. Released v2.7.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n026.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 15:34:47 EDT 2022 % 0.12/0.34 % CPUTime : % 21.03/21.26 (* PROOF-FOUND *) % 21.03/21.26 % SZS status Theorem % 21.03/21.26 (* BEGIN-PROOF *) % 21.03/21.26 % SZS output start Proof % 21.03/21.26 Theorem co1 : ((((h1 (op1 (e10) (e10))) = (op2 (h1 (e10)) (h1 (e10))))/\(((h1 (op1 (e10) (e11))) = (op2 (h1 (e10)) (h1 (e11))))/\(((h1 (op1 (e10) (e12))) = (op2 (h1 (e10)) (h1 (e12))))/\(((h1 (op1 (e10) (e13))) = (op2 (h1 (e10)) (h1 (e13))))/\(((h1 (op1 (e11) (e10))) = (op2 (h1 (e11)) (h1 (e10))))/\(((h1 (op1 (e11) (e11))) = (op2 (h1 (e11)) (h1 (e11))))/\(((h1 (op1 (e11) (e12))) = (op2 (h1 (e11)) (h1 (e12))))/\(((h1 (op1 (e11) (e13))) = (op2 (h1 (e11)) (h1 (e13))))/\(((h1 (op1 (e12) (e10))) = (op2 (h1 (e12)) (h1 (e10))))/\(((h1 (op1 (e12) (e11))) = (op2 (h1 (e12)) (h1 (e11))))/\(((h1 (op1 (e12) (e12))) = (op2 (h1 (e12)) (h1 (e12))))/\(((h1 (op1 (e12) (e13))) = (op2 (h1 (e12)) (h1 (e13))))/\(((h1 (op1 (e13) (e10))) = (op2 (h1 (e13)) (h1 (e10))))/\(((h1 (op1 (e13) (e11))) = (op2 (h1 (e13)) (h1 (e11))))/\(((h1 (op1 (e13) (e12))) = (op2 (h1 (e13)) (h1 (e12))))/\(((h1 (op1 (e13) (e13))) = (op2 (h1 (e13)) (h1 (e13))))/\((((h1 (e10)) = (e20))\/(((h1 (e11)) = (e20))\/(((h1 (e12)) = (e20))\/((h1 (e13)) = (e20)))))/\((((h1 (e10)) = (e21))\/(((h1 (e11)) = (e21))\/(((h1 (e12)) = (e21))\/((h1 (e13)) = (e21)))))/\((((h1 (e10)) = (e22))\/(((h1 (e11)) = (e22))\/(((h1 (e12)) = (e22))\/((h1 (e13)) = (e22)))))/\(((h1 (e10)) = (e23))\/(((h1 (e11)) = (e23))\/(((h1 (e12)) = (e23))\/((h1 (e13)) = (e23))))))))))))))))))))))))\/((((h2 (op1 (e10) (e10))) = (op2 (h2 (e10)) (h2 (e10))))/\(((h2 (op1 (e10) (e11))) = (op2 (h2 (e10)) (h2 (e11))))/\(((h2 (op1 (e10) (e12))) = (op2 (h2 (e10)) (h2 (e12))))/\(((h2 (op1 (e10) (e13))) = (op2 (h2 (e10)) (h2 (e13))))/\(((h2 (op1 (e11) (e10))) = (op2 (h2 (e11)) (h2 (e10))))/\(((h2 (op1 (e11) (e11))) = (op2 (h2 (e11)) (h2 (e11))))/\(((h2 (op1 (e11) (e12))) = (op2 (h2 (e11)) (h2 (e12))))/\(((h2 (op1 (e11) (e13))) = (op2 (h2 (e11)) (h2 (e13))))/\(((h2 (op1 (e12) (e10))) = (op2 (h2 (e12)) (h2 (e10))))/\(((h2 (op1 (e12) (e11))) = (op2 (h2 (e12)) (h2 (e11))))/\(((h2 (op1 (e12) (e12))) = (op2 (h2 (e12)) (h2 (e12))))/\(((h2 (op1 (e12) (e13))) = (op2 (h2 (e12)) (h2 (e13))))/\(((h2 (op1 (e13) (e10))) = (op2 (h2 (e13)) (h2 (e10))))/\(((h2 (op1 (e13) (e11))) = (op2 (h2 (e13)) (h2 (e11))))/\(((h2 (op1 (e13) (e12))) = (op2 (h2 (e13)) (h2 (e12))))/\(((h2 (op1 (e13) (e13))) = (op2 (h2 (e13)) (h2 (e13))))/\((((h2 (e10)) = (e20))\/(((h2 (e11)) = (e20))\/(((h2 (e12)) = (e20))\/((h2 (e13)) = (e20)))))/\((((h2 (e10)) = (e21))\/(((h2 (e11)) = (e21))\/(((h2 (e12)) = (e21))\/((h2 (e13)) = (e21)))))/\((((h2 (e10)) = (e22))\/(((h2 (e11)) = (e22))\/(((h2 (e12)) = (e22))\/((h2 (e13)) = (e22)))))/\(((h2 (e10)) = (e23))\/(((h2 (e11)) = (e23))\/(((h2 (e12)) = (e23))\/((h2 (e13)) = (e23))))))))))))))))))))))))\/((((h3 (op1 (e10) (e10))) = (op2 (h3 (e10)) (h3 (e10))))/\(((h3 (op1 (e10) (e11))) = (op2 (h3 (e10)) (h3 (e11))))/\(((h3 (op1 (e10) (e12))) = (op2 (h3 (e10)) (h3 (e12))))/\(((h3 (op1 (e10) (e13))) = (op2 (h3 (e10)) (h3 (e13))))/\(((h3 (op1 (e11) (e10))) = (op2 (h3 (e11)) (h3 (e10))))/\(((h3 (op1 (e11) (e11))) = (op2 (h3 (e11)) (h3 (e11))))/\(((h3 (op1 (e11) (e12))) = (op2 (h3 (e11)) (h3 (e12))))/\(((h3 (op1 (e11) (e13))) = (op2 (h3 (e11)) (h3 (e13))))/\(((h3 (op1 (e12) (e10))) = (op2 (h3 (e12)) (h3 (e10))))/\(((h3 (op1 (e12) (e11))) = (op2 (h3 (e12)) (h3 (e11))))/\(((h3 (op1 (e12) (e12))) = (op2 (h3 (e12)) (h3 (e12))))/\(((h3 (op1 (e12) (e13))) = (op2 (h3 (e12)) (h3 (e13))))/\(((h3 (op1 (e13) (e10))) = (op2 (h3 (e13)) (h3 (e10))))/\(((h3 (op1 (e13) (e11))) = (op2 (h3 (e13)) (h3 (e11))))/\(((h3 (op1 (e13) (e12))) = (op2 (h3 (e13)) (h3 (e12))))/\(((h3 (op1 (e13) (e13))) = (op2 (h3 (e13)) (h3 (e13))))/\((((h3 (e10)) = (e20))\/(((h3 (e11)) = (e20))\/(((h3 (e12)) = (e20))\/((h3 (e13)) = (e20)))))/\((((h3 (e10)) = (e21))\/(((h3 (e11)) = (e21))\/(((h3 (e12)) = (e21))\/((h3 (e13)) = (e21)))))/\((((h3 (e10)) = (e22))\/(((h3 (e11)) = (e22))\/(((h3 (e12)) = (e22))\/((h3 (e13)) = (e22)))))/\(((h3 (e10)) = (e23))\/(((h3 (e11)) = (e23))\/(((h3 (e12)) = (e23))\/((h3 (e13)) = (e23))))))))))))))))))))))))\/(((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))/\(((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))/\(((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))/\(((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))/\(((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))/\(((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))/\(((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))/\(((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))/\(((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))/\(((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))/\(((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))/\(((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))/\(((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))/\(((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))/\(((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))/\(((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))/\((((h4 (e10)) = (e20))\/(((h4 (e11)) = (e20))\/(((h4 (e12)) = (e20))\/((h4 (e13)) = (e20)))))/\((((h4 (e10)) = (e21))\/(((h4 (e11)) = (e21))\/(((h4 (e12)) = (e21))\/((h4 (e13)) = (e21)))))/\((((h4 (e10)) = (e22))\/(((h4 (e11)) = (e22))\/(((h4 (e12)) = (e22))\/((h4 (e13)) = (e22)))))/\(((h4 (e10)) = (e23))\/(((h4 (e11)) = (e23))\/(((h4 (e12)) = (e23))\/((h4 (e13)) = (e23))))))))))))))))))))))))))). % 21.03/21.26 Proof. % 21.03/21.26 assert (zenon_L1_ : (~((h4 (e10)) = (e20))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H12 zenon_H13 zenon_H14. % 21.03/21.26 cut (((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) = ((h4 (e10)) = (e20))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H12. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H13. % 21.03/21.26 cut (((op2 (e23) (op2 (e23) (e23))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 21.03/21.26 cut (((h4 (e10)) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H16]. % 21.03/21.26 congruence. % 21.03/21.26 apply zenon_H16. apply refl_equal. % 21.03/21.26 apply zenon_H15. apply sym_equal. exact zenon_H14. % 21.03/21.26 (* end of lemma zenon_L1_ *) % 21.03/21.26 assert (zenon_L2_ : (((op1 (e11) (e11)) = (e11))/\(~((op1 (e11) (e11)) = (e11)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H17. % 21.03/21.26 apply (zenon_and_s _ _ zenon_H17). zenon_intro zenon_H19. zenon_intro zenon_H18. % 21.03/21.26 exact (zenon_H18 zenon_H19). % 21.03/21.26 (* end of lemma zenon_L2_ *) % 21.03/21.26 assert (zenon_L3_ : (~((e13) = (e13))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H1a. % 21.03/21.26 apply zenon_H1a. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L3_ *) % 21.03/21.26 assert (zenon_L4_ : (~((op1 (op1 (e13) (e13)) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H1b zenon_H1c. % 21.03/21.26 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 21.03/21.26 cut (((op1 (e13) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 21.03/21.26 congruence. % 21.03/21.26 apply zenon_H1d. apply sym_equal. exact zenon_H1c. % 21.03/21.26 apply zenon_H1a. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L4_ *) % 21.03/21.26 assert (zenon_L5_ : (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e12) (e12)) = (e11)) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H1e zenon_H1f zenon_H20 zenon_H1c. % 21.03/21.26 cut (((e11) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e12) (e12)) = (op1 (e12) (e13)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H1e. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H1f. % 21.03/21.26 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 21.03/21.26 cut (((e11) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H22 | zenon_intro zenon_H23 ]. % 21.03/21.26 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((e11) = (op1 (e12) (e12)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H21. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H22. % 21.03/21.26 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 21.03/21.26 cut (((op1 (e12) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H24 zenon_H20). % 21.03/21.26 apply zenon_H23. apply refl_equal. % 21.03/21.26 apply zenon_H23. apply refl_equal. % 21.03/21.26 apply (zenon_L4_); trivial. % 21.03/21.26 (* end of lemma zenon_L5_ *) % 21.03/21.26 assert (zenon_L6_ : (((op1 (e12) (e12)) = (e11))/\(~((op1 (e12) (e11)) = (e12)))) -> ((e12) = (op1 (e13) (e13))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H25 zenon_H1c zenon_H1f zenon_H1e. % 21.03/21.26 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H20. zenon_intro zenon_H26. % 21.03/21.26 apply (zenon_L5_); trivial. % 21.03/21.26 (* end of lemma zenon_L6_ *) % 21.03/21.26 assert (zenon_L7_ : (~((e12) = (e12))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H27. % 21.03/21.26 apply zenon_H27. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L7_ *) % 21.03/21.26 assert (zenon_L8_ : ((e12) = (op1 (e13) (e13))) -> ((op1 (e13) (e13)) = (e11)) -> (~((e11) = (e12))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H1c zenon_H28 zenon_H29. % 21.03/21.26 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H2a | zenon_intro zenon_H27 ]. % 21.03/21.26 cut (((e12) = (e12)) = ((e11) = (e12))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H29. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H2a. % 21.03/21.26 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 21.03/21.26 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((e12) = (op1 (e13) (e13))) = ((e12) = (e11))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H2b. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H1c. % 21.03/21.26 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 21.03/21.26 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 21.03/21.26 congruence. % 21.03/21.26 apply zenon_H27. apply refl_equal. % 21.03/21.26 exact (zenon_H2c zenon_H28). % 21.03/21.26 apply zenon_H27. apply refl_equal. % 21.03/21.26 apply zenon_H27. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L8_ *) % 21.03/21.26 assert (zenon_L9_ : (((op1 (e13) (e13)) = (e11))/\(~((op1 (e13) (e11)) = (e13)))) -> ((e12) = (op1 (e13) (e13))) -> (~((e11) = (e12))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H2d zenon_H1c zenon_H29. % 21.03/21.26 apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H28. zenon_intro zenon_H2e. % 21.03/21.26 apply (zenon_L8_); trivial. % 21.03/21.26 (* end of lemma zenon_L9_ *) % 21.03/21.26 assert (zenon_L10_ : (((op2 (e21) (e21)) = (e21))/\(~((op2 (e21) (e21)) = (e21)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H2f. % 21.03/21.26 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 21.03/21.26 exact (zenon_H30 zenon_H31). % 21.03/21.26 (* end of lemma zenon_L10_ *) % 21.03/21.26 assert (zenon_L11_ : (~((e23) = (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H32. % 21.03/21.26 apply zenon_H32. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L11_ *) % 21.03/21.26 assert (zenon_L12_ : (~((op2 (op2 (e23) (e23)) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (e23) (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H33 zenon_H34. % 21.03/21.26 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 21.03/21.26 cut (((op2 (e23) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 21.03/21.26 congruence. % 21.03/21.26 apply zenon_H35. apply sym_equal. exact zenon_H34. % 21.03/21.26 apply zenon_H32. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L12_ *) % 21.03/21.26 assert (zenon_L13_ : (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e22) (e22)) = (e21)) -> ((e22) = (op2 (e23) (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H36 zenon_H37 zenon_H38 zenon_H34. % 21.03/21.26 cut (((e21) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e22) (e22)) = (op2 (e22) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H36. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H37. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 21.03/21.26 cut (((e21) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 21.03/21.26 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((e21) = (op2 (e22) (e22)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H39. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H3a. % 21.03/21.26 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 21.03/21.26 cut (((op2 (e22) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H3c zenon_H38). % 21.03/21.26 apply zenon_H3b. apply refl_equal. % 21.03/21.26 apply zenon_H3b. apply refl_equal. % 21.03/21.26 apply (zenon_L12_); trivial. % 21.03/21.26 (* end of lemma zenon_L13_ *) % 21.03/21.26 assert (zenon_L14_ : (((op2 (e22) (e22)) = (e21))/\(~((op2 (e22) (e21)) = (e22)))) -> ((e22) = (op2 (e23) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H3d zenon_H34 zenon_H37 zenon_H36. % 21.03/21.26 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H38. zenon_intro zenon_H3e. % 21.03/21.26 apply (zenon_L13_); trivial. % 21.03/21.26 (* end of lemma zenon_L14_ *) % 21.03/21.26 assert (zenon_L15_ : (~((e22) = (e22))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H3f. % 21.03/21.26 apply zenon_H3f. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L15_ *) % 21.03/21.26 assert (zenon_L16_ : ((e22) = (op2 (e23) (e23))) -> ((op2 (e23) (e23)) = (e21)) -> (~((e21) = (e22))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H34 zenon_H40 zenon_H41. % 21.03/21.26 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H42 | zenon_intro zenon_H3f ]. % 21.03/21.26 cut (((e22) = (e22)) = ((e21) = (e22))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H41. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H42. % 21.03/21.26 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 21.03/21.26 cut (((e22) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H43]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((e22) = (op2 (e23) (e23))) = ((e22) = (e21))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H43. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H34. % 21.03/21.26 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 21.03/21.26 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 21.03/21.26 congruence. % 21.03/21.26 apply zenon_H3f. apply refl_equal. % 21.03/21.26 exact (zenon_H44 zenon_H40). % 21.03/21.26 apply zenon_H3f. apply refl_equal. % 21.03/21.26 apply zenon_H3f. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L16_ *) % 21.03/21.26 assert (zenon_L17_ : (((op2 (e23) (e23)) = (e21))/\(~((op2 (e23) (e21)) = (e23)))) -> ((e22) = (op2 (e23) (e23))) -> (~((e21) = (e22))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H45 zenon_H34 zenon_H41. % 21.03/21.26 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H40. zenon_intro zenon_H46. % 21.03/21.26 apply (zenon_L16_); trivial. % 21.03/21.26 (* end of lemma zenon_L17_ *) % 21.03/21.26 assert (zenon_L18_ : (((op2 (e20) (e20)) = (e20))/\(~((op2 (e20) (e20)) = (e20)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H47. % 21.03/21.26 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 21.03/21.26 exact (zenon_H48 zenon_H49). % 21.03/21.26 (* end of lemma zenon_L18_ *) % 21.03/21.26 assert (zenon_L19_ : (~((e21) = (e21))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H4a. % 21.03/21.26 apply zenon_H4a. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L19_ *) % 21.03/21.26 assert (zenon_L20_ : (~((e20) = (e21))) -> ((op2 (e20) (e20)) = (e21)) -> ((op2 (e20) (e20)) = (e20)) -> False). % 21.03/21.26 do 0 intro. intros zenon_H4b zenon_H4c zenon_H49. % 21.03/21.26 cut (((op2 (e20) (e20)) = (e21)) = ((e20) = (e21))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H4b. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H4c. % 21.03/21.26 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.03/21.26 cut (((op2 (e20) (e20)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H48 zenon_H49). % 21.03/21.26 apply zenon_H4a. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L20_ *) % 21.03/21.26 assert (zenon_L21_ : (~((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e22)))) -> ((e22) = (op2 (e23) (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H4d zenon_H34. % 21.03/21.26 cut (((op2 (e23) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 21.03/21.26 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 21.03/21.26 congruence. % 21.03/21.26 apply zenon_H32. apply refl_equal. % 21.03/21.26 apply zenon_H35. apply sym_equal. exact zenon_H34. % 21.03/21.26 (* end of lemma zenon_L21_ *) % 21.03/21.26 assert (zenon_L22_ : (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e20) (e22)) = (e20)) -> ((e22) = (op2 (e23) (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H4e zenon_H14 zenon_H4f zenon_H34. % 21.03/21.26 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e20) (e22)) = (op2 (e23) (e22)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H4e. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H14. % 21.03/21.26 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 21.03/21.26 cut (((e20) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e20) (e22)) = (op2 (e20) (e22)))); [ zenon_intro zenon_H51 | zenon_intro zenon_H52 ]. % 21.03/21.26 cut (((op2 (e20) (e22)) = (op2 (e20) (e22))) = ((e20) = (op2 (e20) (e22)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H50. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H51. % 21.03/21.26 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 21.03/21.26 cut (((op2 (e20) (e22)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H53 zenon_H4f). % 21.03/21.26 apply zenon_H52. apply refl_equal. % 21.03/21.26 apply zenon_H52. apply refl_equal. % 21.03/21.26 apply (zenon_L21_); trivial. % 21.03/21.26 (* end of lemma zenon_L22_ *) % 21.03/21.26 assert (zenon_L23_ : (((op2 (e20) (e20)) = (e23))/\(~((op2 (e20) (e23)) = (e20)))) -> (~((e20) = (e21))) -> ((op2 (e20) (e20)) = (e21)) -> (~((op2 (e20) (e21)) = (e20))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (e23))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H54 zenon_H4b zenon_H4c zenon_H55 zenon_H4e zenon_H14 zenon_H34 zenon_H56. % 21.03/21.26 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H58. zenon_intro zenon_H57. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H49 | zenon_intro zenon_H59 ]. % 21.03/21.26 apply (zenon_L20_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 21.03/21.26 exact (zenon_H55 zenon_H5b). % 21.03/21.26 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4f | zenon_intro zenon_H5c ]. % 21.03/21.26 apply (zenon_L22_); trivial. % 21.03/21.26 exact (zenon_H57 zenon_H5c). % 21.03/21.26 (* end of lemma zenon_L23_ *) % 21.03/21.26 assert (zenon_L24_ : (~((e20) = (e20))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H5d. % 21.03/21.26 apply zenon_H5d. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L24_ *) % 21.03/21.26 assert (zenon_L25_ : (((op2 (e21) (e21)) = (e23))/\(~((op2 (e21) (e23)) = (e21)))) -> ((op2 (e21) (e21)) = (e20)) -> (~((e20) = (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H5e zenon_H5f zenon_H60. % 21.03/21.26 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H62. zenon_intro zenon_H61. % 21.03/21.26 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H63 | zenon_intro zenon_H32 ]. % 21.03/21.26 cut (((e23) = (e23)) = ((e20) = (e23))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H60. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H63. % 21.03/21.26 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 21.03/21.26 cut (((e23) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op2 (e21) (e21)) = (e20)) = ((e23) = (e20))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H64. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H5f. % 21.03/21.26 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 21.03/21.26 cut (((op2 (e21) (e21)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H65 zenon_H62). % 21.03/21.26 apply zenon_H5d. apply refl_equal. % 21.03/21.26 apply zenon_H32. apply refl_equal. % 21.03/21.26 apply zenon_H32. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L25_ *) % 21.03/21.26 assert (zenon_L26_ : (((op1 (e10) (e10)) = (e10))/\(~((op1 (e10) (e10)) = (e10)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H66. % 21.03/21.26 apply (zenon_and_s _ _ zenon_H66). zenon_intro zenon_H68. zenon_intro zenon_H67. % 21.03/21.26 exact (zenon_H67 zenon_H68). % 21.03/21.26 (* end of lemma zenon_L26_ *) % 21.03/21.26 assert (zenon_L27_ : (~((e11) = (e11))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H69. % 21.03/21.26 apply zenon_H69. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L27_ *) % 21.03/21.26 assert (zenon_L28_ : ((op1 (e10) (e10)) = (e11)) -> ((op1 (e10) (e10)) = (e13)) -> (~((e11) = (e13))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H6a zenon_H6b zenon_H6c. % 21.03/21.26 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H6d | zenon_intro zenon_H1a ]. % 21.03/21.26 cut (((e13) = (e13)) = ((e11) = (e13))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H6c. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H6d. % 21.03/21.26 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 21.03/21.26 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op1 (e10) (e10)) = (e11)) = ((e13) = (e11))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H6e. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H6a. % 21.03/21.26 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 21.03/21.26 cut (((op1 (e10) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H6f zenon_H6b). % 21.03/21.26 apply zenon_H69. apply refl_equal. % 21.03/21.26 apply zenon_H1a. apply refl_equal. % 21.03/21.26 apply zenon_H1a. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L28_ *) % 21.03/21.26 assert (zenon_L29_ : (((op1 (e10) (e10)) = (e13))/\(~((op1 (e10) (e13)) = (e10)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((e11) = (e13))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H70 zenon_H6a zenon_H6c. % 21.03/21.26 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H6b. zenon_intro zenon_H71. % 21.03/21.26 apply (zenon_L28_); trivial. % 21.03/21.26 (* end of lemma zenon_L29_ *) % 21.03/21.26 assert (zenon_L30_ : (~((e10) = (e10))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H72. % 21.03/21.26 apply zenon_H72. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L30_ *) % 21.03/21.26 assert (zenon_L31_ : (((op1 (e11) (e11)) = (e13))/\(~((op1 (e11) (e13)) = (e11)))) -> ((op1 (e11) (e11)) = (e10)) -> (~((e10) = (e13))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H73 zenon_H74 zenon_H75. % 21.03/21.26 apply (zenon_and_s _ _ zenon_H73). zenon_intro zenon_H77. zenon_intro zenon_H76. % 21.03/21.26 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H6d | zenon_intro zenon_H1a ]. % 21.03/21.26 cut (((e13) = (e13)) = ((e10) = (e13))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H75. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H6d. % 21.03/21.26 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 21.03/21.26 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op1 (e11) (e11)) = (e10)) = ((e13) = (e10))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H78. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H74. % 21.03/21.26 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 21.03/21.26 cut (((op1 (e11) (e11)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H79 zenon_H77). % 21.03/21.26 apply zenon_H72. apply refl_equal. % 21.03/21.26 apply zenon_H1a. apply refl_equal. % 21.03/21.26 apply zenon_H1a. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L31_ *) % 21.03/21.26 assert (zenon_L32_ : ((op2 (e20) (e20)) = (e21)) -> ((op2 (e20) (e20)) = (e23)) -> (~((e21) = (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H4c zenon_H58 zenon_H7a. % 21.03/21.26 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H63 | zenon_intro zenon_H32 ]. % 21.03/21.26 cut (((e23) = (e23)) = ((e21) = (e23))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H7a. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H63. % 21.03/21.26 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 21.03/21.26 cut (((e23) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op2 (e20) (e20)) = (e21)) = ((e23) = (e21))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H7b. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H4c. % 21.03/21.26 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.03/21.26 cut (((op2 (e20) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H7c zenon_H58). % 21.03/21.26 apply zenon_H4a. apply refl_equal. % 21.03/21.26 apply zenon_H32. apply refl_equal. % 21.03/21.26 apply zenon_H32. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L32_ *) % 21.03/21.26 assert (zenon_L33_ : (~((e10) = (e11))) -> ((op1 (e10) (e10)) = (e11)) -> ((op1 (e10) (e10)) = (e10)) -> False). % 21.03/21.26 do 0 intro. intros zenon_H7d zenon_H6a zenon_H68. % 21.03/21.26 cut (((op1 (e10) (e10)) = (e11)) = ((e10) = (e11))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H7d. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H6a. % 21.03/21.26 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 21.03/21.26 cut (((op1 (e10) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H67 zenon_H68). % 21.03/21.26 apply zenon_H69. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L33_ *) % 21.03/21.26 assert (zenon_L34_ : (~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H7e zenon_H1c. % 21.03/21.26 cut (((op1 (e13) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 21.03/21.26 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 21.03/21.26 congruence. % 21.03/21.26 apply zenon_H1a. apply refl_equal. % 21.03/21.26 apply zenon_H1d. apply sym_equal. exact zenon_H1c. % 21.03/21.26 (* end of lemma zenon_L34_ *) % 21.03/21.26 assert (zenon_L35_ : (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e10) (e12)) = (e10)) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H7f zenon_H80 zenon_H81 zenon_H1c. % 21.03/21.26 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e10) (e12)) = (op1 (e13) (e12)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H7f. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H80. % 21.03/21.26 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 21.03/21.26 cut (((e10) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op1 (e10) (e12)) = (op1 (e10) (e12)))); [ zenon_intro zenon_H83 | zenon_intro zenon_H84 ]. % 21.03/21.26 cut (((op1 (e10) (e12)) = (op1 (e10) (e12))) = ((e10) = (op1 (e10) (e12)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H82. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H83. % 21.03/21.26 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 21.03/21.26 cut (((op1 (e10) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H85 zenon_H81). % 21.03/21.26 apply zenon_H84. apply refl_equal. % 21.03/21.26 apply zenon_H84. apply refl_equal. % 21.03/21.26 apply (zenon_L34_); trivial. % 21.03/21.26 (* end of lemma zenon_L35_ *) % 21.03/21.26 assert (zenon_L36_ : (~((h4 (e11)) = (e21))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H86 zenon_H87 zenon_H37. % 21.03/21.26 cut (((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) = ((h4 (e11)) = (e21))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H86. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H87. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 21.03/21.26 cut (((h4 (e11)) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 21.03/21.26 congruence. % 21.03/21.26 apply zenon_H89. apply refl_equal. % 21.03/21.26 apply zenon_H88. apply sym_equal. exact zenon_H37. % 21.03/21.26 (* end of lemma zenon_L36_ *) % 21.03/21.26 assert (zenon_L37_ : ((op1 (e12) (e12)) = (e13)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H8a zenon_H8b zenon_H8c. % 21.03/21.26 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H22 | zenon_intro zenon_H23 ]. % 21.03/21.26 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e10) (e12)) = (op1 (e12) (e12)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H8c. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H22. % 21.03/21.26 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 21.03/21.26 cut (((op1 (e12) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H8d]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op1 (e12) (e12)) = (e13)) = ((op1 (e12) (e12)) = (op1 (e10) (e12)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H8d. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H8a. % 21.03/21.26 cut (((e13) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 21.03/21.26 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 21.03/21.26 congruence. % 21.03/21.26 apply zenon_H23. apply refl_equal. % 21.03/21.26 apply zenon_H8e. apply sym_equal. exact zenon_H8b. % 21.03/21.26 apply zenon_H23. apply refl_equal. % 21.03/21.26 apply zenon_H23. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L37_ *) % 21.03/21.26 assert (zenon_L38_ : ((op1 (e10) (e13)) = (e10)) -> ((op1 (e10) (e13)) = (e13)) -> (~((e10) = (e13))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H8f zenon_H90 zenon_H75. % 21.03/21.26 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H6d | zenon_intro zenon_H1a ]. % 21.03/21.26 cut (((e13) = (e13)) = ((e10) = (e13))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H75. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H6d. % 21.03/21.26 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 21.03/21.26 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op1 (e10) (e13)) = (e10)) = ((e13) = (e10))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H78. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H8f. % 21.03/21.26 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 21.03/21.26 cut (((op1 (e10) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H91 zenon_H90). % 21.03/21.26 apply zenon_H72. apply refl_equal. % 21.03/21.26 apply zenon_H1a. apply refl_equal. % 21.03/21.26 apply zenon_H1a. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L38_ *) % 21.03/21.26 assert (zenon_L39_ : ((op2 (e22) (e22)) = (e23)) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H92 zenon_H93 zenon_H94. % 21.03/21.26 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 21.03/21.26 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e20) (e22)) = (op2 (e22) (e22)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H94. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H3a. % 21.03/21.26 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 21.03/21.26 cut (((op2 (e22) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H95]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op2 (e22) (e22)) = (e23)) = ((op2 (e22) (e22)) = (op2 (e20) (e22)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H95. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H92. % 21.03/21.26 cut (((e23) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 21.03/21.26 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 21.03/21.26 congruence. % 21.03/21.26 apply zenon_H3b. apply refl_equal. % 21.03/21.26 apply zenon_H96. apply sym_equal. exact zenon_H93. % 21.03/21.26 apply zenon_H3b. apply refl_equal. % 21.03/21.26 apply zenon_H3b. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L39_ *) % 21.03/21.26 assert (zenon_L40_ : ((op2 (e20) (e23)) = (e20)) -> ((op2 (e20) (e23)) = (e23)) -> (~((e20) = (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H5c zenon_H97 zenon_H60. % 21.03/21.26 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H63 | zenon_intro zenon_H32 ]. % 21.03/21.26 cut (((e23) = (e23)) = ((e20) = (e23))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H60. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H63. % 21.03/21.26 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 21.03/21.26 cut (((e23) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op2 (e20) (e23)) = (e20)) = ((e23) = (e20))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H64. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H5c. % 21.03/21.26 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 21.03/21.26 cut (((op2 (e20) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H98 zenon_H97). % 21.03/21.26 apply zenon_H5d. apply refl_equal. % 21.03/21.26 apply zenon_H32. apply refl_equal. % 21.03/21.26 apply zenon_H32. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L40_ *) % 21.03/21.26 assert (zenon_L41_ : (((op1 (e13) (e13)) = (e13))/\(~((op1 (e13) (e13)) = (e13)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H99. % 21.03/21.26 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H9b. zenon_intro zenon_H9a. % 21.03/21.26 exact (zenon_H9a zenon_H9b). % 21.03/21.26 (* end of lemma zenon_L41_ *) % 21.03/21.26 assert (zenon_L42_ : (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e12)) = (e10)) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H9c zenon_H80 zenon_H9d zenon_H1c. % 21.03/21.26 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e12) (e12)) = (op1 (e13) (e12)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H9c. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H80. % 21.03/21.26 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 21.03/21.26 cut (((e10) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H22 | zenon_intro zenon_H23 ]. % 21.03/21.26 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((e10) = (op1 (e12) (e12)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H9e. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H22. % 21.03/21.26 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 21.03/21.26 cut (((op1 (e12) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H9f zenon_H9d). % 21.03/21.26 apply zenon_H23. apply refl_equal. % 21.03/21.26 apply zenon_H23. apply refl_equal. % 21.03/21.26 apply (zenon_L34_); trivial. % 21.03/21.26 (* end of lemma zenon_L42_ *) % 21.03/21.26 assert (zenon_L43_ : (((op1 (e12) (e12)) = (e10))/\(~((op1 (e12) (e10)) = (e12)))) -> ((e12) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_Ha0 zenon_H1c zenon_H80 zenon_H9c. % 21.03/21.26 apply (zenon_and_s _ _ zenon_Ha0). zenon_intro zenon_H9d. zenon_intro zenon_Ha1. % 21.03/21.26 apply (zenon_L42_); trivial. % 21.03/21.26 (* end of lemma zenon_L43_ *) % 21.03/21.26 assert (zenon_L44_ : ((e12) = (op1 (e13) (e13))) -> ((op1 (e13) (e13)) = (e10)) -> (~((e10) = (e12))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H1c zenon_Ha2 zenon_Ha3. % 21.03/21.26 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H2a | zenon_intro zenon_H27 ]. % 21.03/21.26 cut (((e12) = (e12)) = ((e10) = (e12))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Ha3. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H2a. % 21.03/21.26 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 21.03/21.26 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((e12) = (op1 (e13) (e13))) = ((e12) = (e10))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Ha4. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H1c. % 21.03/21.26 cut (((op1 (e13) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 21.03/21.26 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 21.03/21.26 congruence. % 21.03/21.26 apply zenon_H27. apply refl_equal. % 21.03/21.26 exact (zenon_Ha5 zenon_Ha2). % 21.03/21.26 apply zenon_H27. apply refl_equal. % 21.03/21.26 apply zenon_H27. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L44_ *) % 21.03/21.26 assert (zenon_L45_ : (((op1 (e13) (e13)) = (e10))/\(~((op1 (e13) (e10)) = (e13)))) -> ((e12) = (op1 (e13) (e13))) -> (~((e10) = (e12))) -> False). % 21.03/21.26 do 0 intro. intros zenon_Ha6 zenon_H1c zenon_Ha3. % 21.03/21.26 apply (zenon_and_s _ _ zenon_Ha6). zenon_intro zenon_Ha2. zenon_intro zenon_Ha7. % 21.03/21.26 apply (zenon_L44_); trivial. % 21.03/21.26 (* end of lemma zenon_L45_ *) % 21.03/21.26 assert (zenon_L46_ : (((op2 (e23) (e23)) = (e23))/\(~((op2 (e23) (e23)) = (e23)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_Ha8. % 21.03/21.26 apply (zenon_and_s _ _ zenon_Ha8). zenon_intro zenon_Haa. zenon_intro zenon_Ha9. % 21.03/21.26 exact (zenon_Ha9 zenon_Haa). % 21.03/21.26 (* end of lemma zenon_L46_ *) % 21.03/21.26 assert (zenon_L47_ : (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e22)) = (e20)) -> ((e22) = (op2 (e23) (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_Hab zenon_H14 zenon_Hac zenon_H34. % 21.03/21.26 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e22) (e22)) = (op2 (e23) (e22)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hab. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H14. % 21.03/21.26 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 21.03/21.26 cut (((e20) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 21.03/21.26 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((e20) = (op2 (e22) (e22)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Had. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H3a. % 21.03/21.26 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 21.03/21.26 cut (((op2 (e22) (e22)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_Hae zenon_Hac). % 21.03/21.26 apply zenon_H3b. apply refl_equal. % 21.03/21.26 apply zenon_H3b. apply refl_equal. % 21.03/21.26 apply (zenon_L21_); trivial. % 21.03/21.26 (* end of lemma zenon_L47_ *) % 21.03/21.26 assert (zenon_L48_ : (((op2 (e22) (e22)) = (e20))/\(~((op2 (e22) (e20)) = (e22)))) -> ((e22) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_Haf zenon_H34 zenon_H14 zenon_Hab. % 21.03/21.26 apply (zenon_and_s _ _ zenon_Haf). zenon_intro zenon_Hac. zenon_intro zenon_Hb0. % 21.03/21.26 apply (zenon_L47_); trivial. % 21.03/21.26 (* end of lemma zenon_L48_ *) % 21.03/21.26 assert (zenon_L49_ : ((e22) = (op2 (e23) (e23))) -> ((op2 (e23) (e23)) = (e20)) -> (~((e20) = (e22))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H34 zenon_Hb1 zenon_Hb2. % 21.03/21.26 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H42 | zenon_intro zenon_H3f ]. % 21.03/21.26 cut (((e22) = (e22)) = ((e20) = (e22))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hb2. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H42. % 21.03/21.26 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 21.03/21.26 cut (((e22) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((e22) = (op2 (e23) (e23))) = ((e22) = (e20))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hb3. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H34. % 21.03/21.26 cut (((op2 (e23) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 21.03/21.26 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 21.03/21.26 congruence. % 21.03/21.26 apply zenon_H3f. apply refl_equal. % 21.03/21.26 exact (zenon_Hb4 zenon_Hb1). % 21.03/21.26 apply zenon_H3f. apply refl_equal. % 21.03/21.26 apply zenon_H3f. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L49_ *) % 21.03/21.26 assert (zenon_L50_ : (((op2 (e23) (e23)) = (e20))/\(~((op2 (e23) (e20)) = (e23)))) -> ((e22) = (op2 (e23) (e23))) -> (~((e20) = (e22))) -> False). % 21.03/21.26 do 0 intro. intros zenon_Hb5 zenon_H34 zenon_Hb2. % 21.03/21.26 apply (zenon_and_s _ _ zenon_Hb5). zenon_intro zenon_Hb1. zenon_intro zenon_Hb6. % 21.03/21.26 apply (zenon_L49_); trivial. % 21.03/21.26 (* end of lemma zenon_L50_ *) % 21.03/21.26 assert (zenon_L51_ : ((op2 (e20) (e20)) = (e21)) -> ((op2 (e20) (e20)) = (e22)) -> (~((e21) = (e22))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H4c zenon_Hb7 zenon_H41. % 21.03/21.26 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H42 | zenon_intro zenon_H3f ]. % 21.03/21.26 cut (((e22) = (e22)) = ((e21) = (e22))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H41. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H42. % 21.03/21.26 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 21.03/21.26 cut (((e22) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H43]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op2 (e20) (e20)) = (e21)) = ((e22) = (e21))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H43. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H4c. % 21.03/21.26 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.03/21.26 cut (((op2 (e20) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hb8]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_Hb8 zenon_Hb7). % 21.03/21.26 apply zenon_H4a. apply refl_equal. % 21.03/21.26 apply zenon_H3f. apply refl_equal. % 21.03/21.26 apply zenon_H3f. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L51_ *) % 21.03/21.26 assert (zenon_L52_ : ((op2 (e21) (e21)) = (e20)) -> ((op2 (e21) (e21)) = (e21)) -> (~((e20) = (e21))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H5f zenon_H31 zenon_H4b. % 21.03/21.26 elim (classic ((e21) = (e21))); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H4a ]. % 21.03/21.26 cut (((e21) = (e21)) = ((e20) = (e21))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H4b. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hb9. % 21.03/21.26 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.03/21.26 cut (((e21) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op2 (e21) (e21)) = (e20)) = ((e21) = (e20))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hba. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H5f. % 21.03/21.26 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 21.03/21.26 cut (((op2 (e21) (e21)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H30 zenon_H31). % 21.03/21.26 apply zenon_H5d. apply refl_equal. % 21.03/21.26 apply zenon_H4a. apply refl_equal. % 21.03/21.26 apply zenon_H4a. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L52_ *) % 21.03/21.26 assert (zenon_L53_ : (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e21) (e22)) = (e20)) -> ((e22) = (op2 (e23) (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_Hbb zenon_H14 zenon_Hbc zenon_H34. % 21.03/21.26 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e21) (e22)) = (op2 (e23) (e22)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hbb. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H14. % 21.03/21.26 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 21.03/21.26 cut (((e20) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hbf ]. % 21.03/21.26 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((e20) = (op2 (e21) (e22)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hbd. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hbe. % 21.03/21.26 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 21.03/21.26 cut (((op2 (e21) (e22)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_Hc0 zenon_Hbc). % 21.03/21.26 apply zenon_Hbf. apply refl_equal. % 21.03/21.26 apply zenon_Hbf. apply refl_equal. % 21.03/21.26 apply (zenon_L21_); trivial. % 21.03/21.26 (* end of lemma zenon_L53_ *) % 21.03/21.26 assert (zenon_L54_ : (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e20) (e23)) = (e21)) -> ((e22) = (op2 (e23) (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_Hc1 zenon_H37 zenon_Hc2 zenon_H34. % 21.03/21.26 cut (((e21) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e20) (e23)) = (op2 (e22) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hc1. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H37. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 21.03/21.26 cut (((e21) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 21.03/21.26 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((e21) = (op2 (e20) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hc3. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hc4. % 21.03/21.26 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 21.03/21.26 cut (((op2 (e20) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_Hc6 zenon_Hc2). % 21.03/21.26 apply zenon_Hc5. apply refl_equal. % 21.03/21.26 apply zenon_Hc5. apply refl_equal. % 21.03/21.26 apply (zenon_L12_); trivial. % 21.03/21.26 (* end of lemma zenon_L54_ *) % 21.03/21.26 assert (zenon_L55_ : (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e21) (e23)) = (e21)) -> ((e22) = (op2 (e23) (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_Hc7 zenon_H37 zenon_Hc8 zenon_H34. % 21.03/21.26 cut (((e21) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e21) (e23)) = (op2 (e22) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hc7. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H37. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 21.03/21.26 cut (((e21) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcb ]. % 21.03/21.26 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e21) = (op2 (e21) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hc9. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hca. % 21.03/21.26 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 21.03/21.26 cut (((op2 (e21) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H61 zenon_Hc8). % 21.03/21.26 apply zenon_Hcb. apply refl_equal. % 21.03/21.26 apply zenon_Hcb. apply refl_equal. % 21.03/21.26 apply (zenon_L12_); trivial. % 21.03/21.26 (* end of lemma zenon_L55_ *) % 21.03/21.26 assert (zenon_L56_ : (~((op2 (op2 (e23) (e23)) (e23)) = (op2 (e20) (e20)))) -> ((op2 (e22) (e23)) = (e21)) -> ((e22) = (op2 (e23) (e23))) -> ((op2 (e20) (e20)) = (e21)) -> False). % 21.03/21.26 do 0 intro. intros zenon_Hcc zenon_Hcd zenon_H34 zenon_H4c. % 21.03/21.26 cut (((op2 (e22) (e23)) = (e21)) = ((op2 (op2 (e23) (e23)) (e23)) = (op2 (e20) (e20)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hcc. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hcd. % 21.03/21.26 cut (((e21) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 21.03/21.26 cut (((op2 (e22) (e23)) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (op2 (e23) (e23)) (e23)) = (op2 (op2 (e23) (e23)) (e23)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e22) (e23)) = (op2 (op2 (e23) (e23)) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hcf. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hd0. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 21.03/21.26 congruence. % 21.03/21.26 apply (zenon_L12_); trivial. % 21.03/21.26 apply zenon_Hd1. apply refl_equal. % 21.03/21.26 apply zenon_Hd1. apply refl_equal. % 21.03/21.26 apply zenon_Hce. apply sym_equal. exact zenon_H4c. % 21.03/21.26 (* end of lemma zenon_L56_ *) % 21.03/21.26 assert (zenon_L57_ : ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e23) (e20)) = (e21)) -> ((op2 (e22) (e23)) = (e21)) -> ((op2 (e20) (e20)) = (e21)) -> ((e22) = (op2 (e23) (e23))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H37 zenon_Hd2 zenon_Hcd zenon_H4c zenon_H34 zenon_Hd3. % 21.03/21.26 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd5 ]. % 21.03/21.26 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((op2 (e20) (e20)) = (op2 (e23) (e20)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hd3. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hd4. % 21.03/21.26 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 21.03/21.26 cut (((op2 (e23) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((e21) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e23) (e20)) = (op2 (e20) (e20)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hd6. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H37. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 21.03/21.26 cut (((e21) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd5 ]. % 21.03/21.26 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((e21) = (op2 (e23) (e20)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hd7. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hd4. % 21.03/21.26 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 21.03/21.26 cut (((op2 (e23) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_Hd8 zenon_Hd2). % 21.03/21.26 apply zenon_Hd5. apply refl_equal. % 21.03/21.26 apply zenon_Hd5. apply refl_equal. % 21.03/21.26 apply (zenon_L56_); trivial. % 21.03/21.26 apply zenon_Hd5. apply refl_equal. % 21.03/21.26 apply zenon_Hd5. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L57_ *) % 21.03/21.26 assert (zenon_L58_ : (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e20) (e20)) = (e21)) -> ((op2 (e23) (e20)) = (e21)) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (e23) (e23))) -> (~((e21) = (e22))) -> False). % 21.03/21.26 do 0 intro. intros zenon_Hd9 zenon_Hc1 zenon_Hc7 zenon_Hd3 zenon_H4c zenon_Hd2 zenon_H37 zenon_H34 zenon_H41. % 21.03/21.26 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc2 | zenon_intro zenon_Hda ]. % 21.03/21.26 apply (zenon_L54_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hdb ]. % 21.03/21.26 apply (zenon_L55_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Hcd | zenon_intro zenon_H40 ]. % 21.03/21.26 apply (zenon_L57_); trivial. % 21.03/21.26 apply (zenon_L16_); trivial. % 21.03/21.26 (* end of lemma zenon_L58_ *) % 21.03/21.26 assert (zenon_L59_ : (~((op2 (e23) (op2 (e23) (e23))) = (op2 (e21) (e21)))) -> ((op2 (e23) (e22)) = (e20)) -> ((e22) = (op2 (e23) (e23))) -> ((op2 (e21) (e21)) = (e20)) -> False). % 21.03/21.26 do 0 intro. intros zenon_Hdc zenon_Hdd zenon_H34 zenon_H5f. % 21.03/21.26 cut (((op2 (e23) (e22)) = (e20)) = ((op2 (e23) (op2 (e23) (e23))) = (op2 (e21) (e21)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hdc. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hdd. % 21.03/21.26 cut (((e20) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 21.03/21.26 cut (((op2 (e23) (e22)) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (op2 (e23) (e23))))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ]. % 21.03/21.26 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e23) (e22)) = (op2 (e23) (op2 (e23) (e23))))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hdf. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_He0. % 21.03/21.26 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 21.03/21.26 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 21.03/21.26 congruence. % 21.03/21.26 apply (zenon_L21_); trivial. % 21.03/21.26 apply zenon_He1. apply refl_equal. % 21.03/21.26 apply zenon_He1. apply refl_equal. % 21.03/21.26 apply zenon_Hde. apply sym_equal. exact zenon_H5f. % 21.03/21.26 (* end of lemma zenon_L59_ *) % 21.03/21.26 assert (zenon_L60_ : ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e21)) = (e20)) -> ((op2 (e23) (e22)) = (e20)) -> ((op2 (e21) (e21)) = (e20)) -> ((e22) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H14 zenon_He2 zenon_Hdd zenon_H5f zenon_H34 zenon_He3. % 21.03/21.26 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_He4 | zenon_intro zenon_He5 ]. % 21.03/21.26 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((op2 (e21) (e21)) = (op2 (e22) (e21)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_He3. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_He4. % 21.03/21.26 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 21.03/21.26 cut (((op2 (e22) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e22) (e21)) = (op2 (e21) (e21)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_He6. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H14. % 21.03/21.26 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hdc]. % 21.03/21.26 cut (((e20) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_He4 | zenon_intro zenon_He5 ]. % 21.03/21.26 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((e20) = (op2 (e22) (e21)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_He7. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_He4. % 21.03/21.26 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 21.03/21.26 cut (((op2 (e22) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_He8 zenon_He2). % 21.03/21.26 apply zenon_He5. apply refl_equal. % 21.03/21.26 apply zenon_He5. apply refl_equal. % 21.03/21.26 apply (zenon_L59_); trivial. % 21.03/21.26 apply zenon_He5. apply refl_equal. % 21.03/21.26 apply zenon_He5. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L60_ *) % 21.03/21.26 assert (zenon_L61_ : (~((op2 (op2 (e23) (e23)) (e23)) = (op2 (e23) (e21)))) -> ((op2 (e22) (e23)) = (e21)) -> ((e22) = (op2 (e23) (e23))) -> ((op2 (e23) (e21)) = (e21)) -> False). % 21.03/21.26 do 0 intro. intros zenon_He9 zenon_Hcd zenon_H34 zenon_Hea. % 21.03/21.26 cut (((op2 (e22) (e23)) = (e21)) = ((op2 (op2 (e23) (e23)) (e23)) = (op2 (e23) (e21)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_He9. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hcd. % 21.03/21.26 cut (((e21) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 21.03/21.26 cut (((op2 (e22) (e23)) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (op2 (e23) (e23)) (e23)) = (op2 (op2 (e23) (e23)) (e23)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e22) (e23)) = (op2 (op2 (e23) (e23)) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hcf. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hd0. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 21.03/21.26 congruence. % 21.03/21.26 apply (zenon_L12_); trivial. % 21.03/21.26 apply zenon_Hd1. apply refl_equal. % 21.03/21.26 apply zenon_Hd1. apply refl_equal. % 21.03/21.26 apply zenon_Heb. apply sym_equal. exact zenon_Hea. % 21.03/21.26 (* end of lemma zenon_L61_ *) % 21.03/21.26 assert (zenon_L62_ : (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> ((op2 (e22) (e23)) = (e21)) -> ((op2 (e23) (e21)) = (e21)) -> ((e22) = (op2 (e23) (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_Hec zenon_H37 zenon_Hed zenon_Hcd zenon_Hea zenon_H34. % 21.03/21.26 cut (((e21) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e22) (e21)) = (op2 (e23) (e21)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hec. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H37. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_He9]. % 21.03/21.26 cut (((e21) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hee]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_He4 | zenon_intro zenon_He5 ]. % 21.03/21.26 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((e21) = (op2 (e22) (e21)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hee. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_He4. % 21.03/21.26 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 21.03/21.26 cut (((op2 (e22) (e21)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_Hef zenon_Hed). % 21.03/21.26 apply zenon_He5. apply refl_equal. % 21.03/21.26 apply zenon_He5. apply refl_equal. % 21.03/21.26 apply (zenon_L61_); trivial. % 21.03/21.26 (* end of lemma zenon_L62_ *) % 21.03/21.26 assert (zenon_L63_ : ((e22) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e22)) -> (~((op2 (e23) (e23)) = (op2 (e21) (e20)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H34 zenon_Hf0 zenon_Hf1. % 21.03/21.26 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf3 ]. % 21.03/21.26 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((op2 (e23) (e23)) = (op2 (e21) (e20)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hf1. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hf2. % 21.03/21.26 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 21.03/21.26 cut (((op2 (e21) (e20)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hf4]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((e22) = (op2 (e23) (e23))) = ((op2 (e21) (e20)) = (op2 (e23) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hf4. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H34. % 21.03/21.26 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 21.03/21.26 cut (((e22) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hf6]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf3 ]. % 21.03/21.26 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((e22) = (op2 (e21) (e20)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hf6. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hf2. % 21.03/21.26 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 21.03/21.26 cut (((op2 (e21) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_Hf7 zenon_Hf0). % 21.03/21.26 apply zenon_Hf3. apply refl_equal. % 21.03/21.26 apply zenon_Hf3. apply refl_equal. % 21.03/21.26 apply zenon_Hf5. apply refl_equal. % 21.03/21.26 apply zenon_Hf3. apply refl_equal. % 21.03/21.26 apply zenon_Hf3. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L63_ *) % 21.03/21.26 assert (zenon_L64_ : (~((op2 (e23) (e23)) = (op2 (e22) (e21)))) -> ((op2 (e21) (e20)) = (e22)) -> ((e22) = (op2 (e23) (e23))) -> ((op2 (e22) (e21)) = (e22)) -> False). % 21.03/21.26 do 0 intro. intros zenon_Hf8 zenon_Hf0 zenon_H34 zenon_Hf9. % 21.03/21.26 cut (((op2 (e21) (e20)) = (e22)) = ((op2 (e23) (e23)) = (op2 (e22) (e21)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hf8. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hf0. % 21.03/21.26 cut (((e22) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 21.03/21.26 cut (((op2 (e21) (e20)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hf4]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hf5 ]. % 21.03/21.26 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e21) (e20)) = (op2 (e23) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hf4. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hfb. % 21.03/21.26 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 21.03/21.26 cut (((op2 (e23) (e23)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hf1]. % 21.03/21.26 congruence. % 21.03/21.26 apply (zenon_L63_); trivial. % 21.03/21.26 apply zenon_Hf5. apply refl_equal. % 21.03/21.26 apply zenon_Hf5. apply refl_equal. % 21.03/21.26 apply zenon_Hfa. apply sym_equal. exact zenon_Hf9. % 21.03/21.26 (* end of lemma zenon_L64_ *) % 21.03/21.26 assert (zenon_L65_ : (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e20) (e21)) = (e22)) -> ((op2 (e22) (e21)) = (e22)) -> ((op2 (e21) (e20)) = (e22)) -> ((e22) = (op2 (e23) (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_Hfc zenon_Hfd zenon_Hf9 zenon_Hf0 zenon_H34. % 21.03/21.26 cut (((e22) = (op2 (e23) (e23))) = ((op2 (e20) (e21)) = (op2 (e22) (e21)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hfc. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H34. % 21.03/21.26 cut (((op2 (e23) (e23)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 21.03/21.26 cut (((e22) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e20) (e21)) = (op2 (e20) (e21)))); [ zenon_intro zenon_Hff | zenon_intro zenon_H100 ]. % 21.03/21.26 cut (((op2 (e20) (e21)) = (op2 (e20) (e21))) = ((e22) = (op2 (e20) (e21)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hfe. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hff. % 21.03/21.26 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 21.03/21.26 cut (((op2 (e20) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H101]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H101 zenon_Hfd). % 21.03/21.26 apply zenon_H100. apply refl_equal. % 21.03/21.26 apply zenon_H100. apply refl_equal. % 21.03/21.26 apply (zenon_L64_); trivial. % 21.03/21.26 (* end of lemma zenon_L65_ *) % 21.03/21.26 assert (zenon_L66_ : ((op2 (e22) (e22)) = (e23)) -> ((op2 (e22) (e21)) = (e23)) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H92 zenon_H102 zenon_H103. % 21.03/21.26 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 21.03/21.26 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e22) (e21)) = (op2 (e22) (e22)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H103. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H3a. % 21.03/21.26 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 21.03/21.26 cut (((op2 (e22) (e22)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op2 (e22) (e22)) = (e23)) = ((op2 (e22) (e22)) = (op2 (e22) (e21)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H104. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H92. % 21.03/21.26 cut (((e23) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 21.03/21.26 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 21.03/21.26 congruence. % 21.03/21.26 apply zenon_H3b. apply refl_equal. % 21.03/21.26 apply zenon_H105. apply sym_equal. exact zenon_H102. % 21.03/21.26 apply zenon_H3b. apply refl_equal. % 21.03/21.26 apply zenon_H3b. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L66_ *) % 21.03/21.26 assert (zenon_L67_ : (((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e22) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e21) (e21)) = (e20)) -> ((op2 (e23) (e22)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e21)) -> ((op2 (e22) (e23)) = (e21)) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e22)) -> ((op2 (e20) (e21)) = (e22)) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H106 zenon_He3 zenon_H5f zenon_Hdd zenon_H14 zenon_Hea zenon_Hcd zenon_H37 zenon_Hec zenon_H34 zenon_Hf0 zenon_Hfd zenon_Hfc zenon_H92 zenon_H103. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_He2 | zenon_intro zenon_H107 ]. % 21.03/21.26 apply (zenon_L60_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hed | zenon_intro zenon_H108 ]. % 21.03/21.26 apply (zenon_L62_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf9 | zenon_intro zenon_H102 ]. % 21.03/21.26 apply (zenon_L65_); trivial. % 21.03/21.26 apply (zenon_L66_); trivial. % 21.03/21.26 (* end of lemma zenon_L67_ *) % 21.03/21.26 assert (zenon_L68_ : (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e20) (e21)) = (e22)) -> ((op2 (e21) (e20)) = (e22)) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e23) (e21)) = (e21)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e22)) = (e20)) -> ((op2 (e21) (e21)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e22) (e21)) = (e23))))) -> ((e22) = (op2 (e23) (e23))) -> (~((e21) = (e22))) -> False). % 21.03/21.26 do 0 intro. intros zenon_Hd9 zenon_Hc1 zenon_Hc7 zenon_H103 zenon_H92 zenon_Hfc zenon_Hfd zenon_Hf0 zenon_Hec zenon_H37 zenon_Hea zenon_H14 zenon_Hdd zenon_H5f zenon_He3 zenon_H106 zenon_H34 zenon_H41. % 21.03/21.26 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc2 | zenon_intro zenon_Hda ]. % 21.03/21.26 apply (zenon_L54_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hdb ]. % 21.03/21.26 apply (zenon_L55_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Hcd | zenon_intro zenon_H40 ]. % 21.03/21.26 apply (zenon_L67_); trivial. % 21.03/21.26 apply (zenon_L16_); trivial. % 21.03/21.26 (* end of lemma zenon_L68_ *) % 21.03/21.26 assert (zenon_L69_ : (~((op2 (op2 (e23) (e23)) (e23)) = (op2 (e21) (e22)))) -> ((op2 (e22) (e23)) = (e21)) -> ((e22) = (op2 (e23) (e23))) -> ((op2 (e21) (e22)) = (e21)) -> False). % 21.03/21.26 do 0 intro. intros zenon_H109 zenon_Hcd zenon_H34 zenon_H10a. % 21.03/21.26 cut (((op2 (e22) (e23)) = (e21)) = ((op2 (op2 (e23) (e23)) (e23)) = (op2 (e21) (e22)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H109. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hcd. % 21.03/21.26 cut (((e21) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H10b]. % 21.03/21.26 cut (((op2 (e22) (e23)) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (op2 (e23) (e23)) (e23)) = (op2 (op2 (e23) (e23)) (e23)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e22) (e23)) = (op2 (op2 (e23) (e23)) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hcf. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hd0. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 21.03/21.26 congruence. % 21.03/21.26 apply (zenon_L12_); trivial. % 21.03/21.26 apply zenon_Hd1. apply refl_equal. % 21.03/21.26 apply zenon_Hd1. apply refl_equal. % 21.03/21.26 apply zenon_H10b. apply sym_equal. exact zenon_H10a. % 21.03/21.26 (* end of lemma zenon_L69_ *) % 21.03/21.26 assert (zenon_L70_ : ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e23) (e22)) = (e21)) -> ((op2 (e22) (e23)) = (e21)) -> ((op2 (e21) (e22)) = (e21)) -> ((e22) = (op2 (e23) (e23))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H37 zenon_H10c zenon_Hcd zenon_H10a zenon_H34 zenon_Hbb. % 21.03/21.26 elim (classic ((op2 (e23) (e22)) = (op2 (e23) (e22)))); [ zenon_intro zenon_H10d | zenon_intro zenon_H10e ]. % 21.03/21.26 cut (((op2 (e23) (e22)) = (op2 (e23) (e22))) = ((op2 (e21) (e22)) = (op2 (e23) (e22)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hbb. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H10d. % 21.03/21.26 cut (((op2 (e23) (e22)) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H10e]. % 21.03/21.26 cut (((op2 (e23) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((e21) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e23) (e22)) = (op2 (e21) (e22)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H10f. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H37. % 21.03/21.26 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H109]. % 21.03/21.26 cut (((e21) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e23) (e22)) = (op2 (e23) (e22)))); [ zenon_intro zenon_H10d | zenon_intro zenon_H10e ]. % 21.03/21.26 cut (((op2 (e23) (e22)) = (op2 (e23) (e22))) = ((e21) = (op2 (e23) (e22)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H110. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H10d. % 21.03/21.26 cut (((op2 (e23) (e22)) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H10e]. % 21.03/21.26 cut (((op2 (e23) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H111 zenon_H10c). % 21.03/21.26 apply zenon_H10e. apply refl_equal. % 21.03/21.26 apply zenon_H10e. apply refl_equal. % 21.03/21.26 apply (zenon_L69_); trivial. % 21.03/21.26 apply zenon_H10e. apply refl_equal. % 21.03/21.26 apply zenon_H10e. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L70_ *) % 21.03/21.26 assert (zenon_L71_ : (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e22)) = (e21)) -> ((op2 (e23) (e22)) = (e21)) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (e23) (e23))) -> (~((e21) = (e22))) -> False). % 21.03/21.26 do 0 intro. intros zenon_Hd9 zenon_Hc1 zenon_Hc7 zenon_Hbb zenon_H10a zenon_H10c zenon_H37 zenon_H34 zenon_H41. % 21.03/21.26 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc2 | zenon_intro zenon_Hda ]. % 21.03/21.26 apply (zenon_L54_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hdb ]. % 21.03/21.26 apply (zenon_L55_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Hcd | zenon_intro zenon_H40 ]. % 21.03/21.26 apply (zenon_L70_); trivial. % 21.03/21.26 apply (zenon_L16_); trivial. % 21.03/21.26 (* end of lemma zenon_L71_ *) % 21.03/21.26 assert (zenon_L72_ : (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e21) (e20)) = (e21))) -> (~((e20) = (e21))) -> (~((e21) = (e22))) -> (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e20) (e21)) = (e22)) -> ((op2 (e21) (e20)) = (e22)) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e21) (e21)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e22) (e21)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e20) (e20)) = (e21)) -> (((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e22)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (e23) (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H112 zenon_H113 zenon_H4b zenon_H41 zenon_Hd9 zenon_Hc1 zenon_Hbb zenon_H103 zenon_H92 zenon_Hfc zenon_Hfd zenon_Hf0 zenon_Hec zenon_H14 zenon_H5f zenon_He3 zenon_H106 zenon_Hd3 zenon_H4c zenon_H114 zenon_Hab zenon_H4e zenon_H115 zenon_Hc7 zenon_H37 zenon_H34. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_H117 | zenon_intro zenon_H116 ]. % 21.03/21.26 exact (zenon_H113 zenon_H117). % 21.03/21.26 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H31 | zenon_intro zenon_H118 ]. % 21.03/21.26 apply (zenon_L52_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10a | zenon_intro zenon_Hc8 ]. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4f | zenon_intro zenon_H119 ]. % 21.03/21.26 apply (zenon_L22_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_Hbc | zenon_intro zenon_H11a ]. % 21.03/21.26 apply (zenon_L53_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_Hac | zenon_intro zenon_Hdd ]. % 21.03/21.26 apply (zenon_L47_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H11b ]. % 21.03/21.26 apply (zenon_L58_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hea | zenon_intro zenon_H11c ]. % 21.03/21.26 apply (zenon_L68_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H10c | zenon_intro zenon_H40 ]. % 21.03/21.26 apply (zenon_L71_); trivial. % 21.03/21.26 apply (zenon_L16_); trivial. % 21.03/21.26 apply (zenon_L55_); trivial. % 21.03/21.26 (* end of lemma zenon_L72_ *) % 21.03/21.26 assert (zenon_L73_ : ((op2 (e22) (e20)) = (e20)) -> ((op2 (e22) (e20)) = (e22)) -> (~((e20) = (e22))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H11d zenon_H11e zenon_Hb2. % 21.03/21.26 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H42 | zenon_intro zenon_H3f ]. % 21.03/21.26 cut (((e22) = (e22)) = ((e20) = (e22))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hb2. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H42. % 21.03/21.26 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 21.03/21.26 cut (((e22) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op2 (e22) (e20)) = (e20)) = ((e22) = (e20))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hb3. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H11d. % 21.03/21.26 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 21.03/21.26 cut (((op2 (e22) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_Hb0 zenon_H11e). % 21.03/21.26 apply zenon_H5d. apply refl_equal. % 21.03/21.26 apply zenon_H3f. apply refl_equal. % 21.03/21.26 apply zenon_H3f. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L73_ *) % 21.03/21.26 assert (zenon_L74_ : (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e21)) = (e20)) -> ((op2 (e21) (e21)) = (e20)) -> ((e22) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H115 zenon_H4e zenon_Hbb zenon_Hab zenon_H14 zenon_He2 zenon_H5f zenon_H34 zenon_He3. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4f | zenon_intro zenon_H119 ]. % 21.03/21.26 apply (zenon_L22_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_Hbc | zenon_intro zenon_H11a ]. % 21.03/21.26 apply (zenon_L53_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_Hac | zenon_intro zenon_Hdd ]. % 21.03/21.26 apply (zenon_L47_); trivial. % 21.03/21.26 apply (zenon_L60_); trivial. % 21.03/21.26 (* end of lemma zenon_L74_ *) % 21.03/21.26 assert (zenon_L75_ : (~((op2 (e23) (op2 (e23) (e23))) = (op2 (e20) (e23)))) -> ((op2 (e23) (e22)) = (e20)) -> ((e22) = (op2 (e23) (e23))) -> ((op2 (e20) (e23)) = (e20)) -> False). % 21.03/21.26 do 0 intro. intros zenon_H11f zenon_Hdd zenon_H34 zenon_H5c. % 21.03/21.26 cut (((op2 (e23) (e22)) = (e20)) = ((op2 (e23) (op2 (e23) (e23))) = (op2 (e20) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H11f. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hdd. % 21.03/21.26 cut (((e20) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 21.03/21.26 cut (((op2 (e23) (e22)) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (op2 (e23) (e23))))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ]. % 21.03/21.26 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e23) (e22)) = (op2 (e23) (op2 (e23) (e23))))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hdf. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_He0. % 21.03/21.26 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 21.03/21.26 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 21.03/21.26 congruence. % 21.03/21.26 apply (zenon_L21_); trivial. % 21.03/21.26 apply zenon_He1. apply refl_equal. % 21.03/21.26 apply zenon_He1. apply refl_equal. % 21.03/21.26 apply zenon_H120. apply sym_equal. exact zenon_H5c. % 21.03/21.26 (* end of lemma zenon_L75_ *) % 21.03/21.26 assert (zenon_L76_ : (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((op2 (e20) (e23)) = (e20)) -> ((e22) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H115 zenon_H4e zenon_Hbb zenon_Hab zenon_H14 zenon_H121 zenon_H5c zenon_H34 zenon_Hc1. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4f | zenon_intro zenon_H119 ]. % 21.03/21.26 apply (zenon_L22_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_Hbc | zenon_intro zenon_H11a ]. % 21.03/21.26 apply (zenon_L53_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_Hac | zenon_intro zenon_Hdd ]. % 21.03/21.26 apply (zenon_L47_); trivial. % 21.03/21.26 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H122 | zenon_intro zenon_H123 ]. % 21.03/21.26 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((op2 (e20) (e23)) = (op2 (e22) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Hc1. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H122. % 21.03/21.26 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 21.03/21.26 cut (((op2 (e22) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e22) (e23)) = (op2 (e20) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H124. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H14. % 21.03/21.26 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H11f]. % 21.03/21.26 cut (((e20) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H125]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H122 | zenon_intro zenon_H123 ]. % 21.03/21.26 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e20) = (op2 (e22) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H125. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H122. % 21.03/21.26 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 21.03/21.26 cut (((op2 (e22) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H126]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H126 zenon_H121). % 21.03/21.26 apply zenon_H123. apply refl_equal. % 21.03/21.26 apply zenon_H123. apply refl_equal. % 21.03/21.26 apply (zenon_L75_); trivial. % 21.03/21.26 apply zenon_H123. apply refl_equal. % 21.03/21.26 apply zenon_H123. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L76_ *) % 21.03/21.26 assert (zenon_L77_ : (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e22) (e23)) = (e20))))) -> (~((e20) = (e22))) -> ((op2 (e22) (e20)) = (e22)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e21) (e21)) = (e20)) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e20)) -> ((e22) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H127 zenon_Hb2 zenon_H11e zenon_He3 zenon_H5f zenon_H115 zenon_H4e zenon_Hbb zenon_Hab zenon_H14 zenon_H5c zenon_H34 zenon_Hc1. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H11d | zenon_intro zenon_H128 ]. % 21.03/21.26 apply (zenon_L73_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_He2 | zenon_intro zenon_H129 ]. % 21.03/21.26 apply (zenon_L74_); trivial. % 21.03/21.26 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hac | zenon_intro zenon_H121 ]. % 21.03/21.26 apply (zenon_L47_); trivial. % 21.03/21.26 apply (zenon_L76_); trivial. % 21.03/21.26 (* end of lemma zenon_L77_ *) % 21.03/21.26 assert (zenon_L78_ : (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (e23))) -> ((op2 (e23) (e20)) = (e22)) -> False). % 21.03/21.26 do 0 intro. intros zenon_H12a zenon_H34 zenon_H12b. % 21.03/21.26 cut (((e22) = (op2 (e23) (e23))) = ((op2 (e23) (e20)) = (op2 (e23) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H12a. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H34. % 21.03/21.26 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 21.03/21.26 cut (((e22) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd5 ]. % 21.03/21.26 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((e22) = (op2 (e23) (e20)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H12c. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_Hd4. % 21.03/21.26 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 21.03/21.26 cut (((op2 (e23) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H12d zenon_H12b). % 21.03/21.26 apply zenon_Hd5. apply refl_equal. % 21.03/21.26 apply zenon_Hd5. apply refl_equal. % 21.03/21.26 apply zenon_Hf5. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L78_ *) % 21.03/21.26 assert (zenon_L79_ : ((op1 (e10) (e10)) = (e11)) -> ((op1 (e10) (e10)) = (e12)) -> (~((e11) = (e12))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H6a zenon_H12e zenon_H29. % 21.03/21.26 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H2a | zenon_intro zenon_H27 ]. % 21.03/21.26 cut (((e12) = (e12)) = ((e11) = (e12))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H29. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H2a. % 21.03/21.26 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 21.03/21.26 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op1 (e10) (e10)) = (e11)) = ((e12) = (e11))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H2b. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H6a. % 21.03/21.26 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 21.03/21.26 cut (((op1 (e10) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H12f zenon_H12e). % 21.03/21.26 apply zenon_H69. apply refl_equal. % 21.03/21.26 apply zenon_H27. apply refl_equal. % 21.03/21.26 apply zenon_H27. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L79_ *) % 21.03/21.26 assert (zenon_L80_ : ((op1 (e11) (e11)) = (e10)) -> ((op1 (e11) (e11)) = (e11)) -> (~((e10) = (e11))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H74 zenon_H19 zenon_H7d. % 21.03/21.26 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H130 | zenon_intro zenon_H69 ]. % 21.03/21.26 cut (((e11) = (e11)) = ((e10) = (e11))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H7d. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H130. % 21.03/21.26 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 21.03/21.26 cut (((e11) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op1 (e11) (e11)) = (e10)) = ((e11) = (e10))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H131. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H74. % 21.03/21.26 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 21.03/21.26 cut (((op1 (e11) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H18 zenon_H19). % 21.03/21.26 apply zenon_H72. apply refl_equal. % 21.03/21.26 apply zenon_H69. apply refl_equal. % 21.03/21.26 apply zenon_H69. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L80_ *) % 21.03/21.26 assert (zenon_L81_ : (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H132 zenon_H80 zenon_H133 zenon_H1c. % 21.03/21.26 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e11) (e12)) = (op1 (e13) (e12)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H132. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H80. % 21.03/21.26 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 21.03/21.26 cut (((e10) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_H135 | zenon_intro zenon_H136 ]. % 21.03/21.26 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((e10) = (op1 (e11) (e12)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H134. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H135. % 21.03/21.26 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 21.03/21.26 cut (((op1 (e11) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H137 zenon_H133). % 21.03/21.26 apply zenon_H136. apply refl_equal. % 21.03/21.26 apply zenon_H136. apply refl_equal. % 21.03/21.26 apply (zenon_L34_); trivial. % 21.03/21.26 (* end of lemma zenon_L81_ *) % 21.03/21.26 assert (zenon_L82_ : ((op1 (e12) (e10)) = (e10)) -> ((op1 (e12) (e10)) = (e12)) -> (~((e10) = (e12))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H138 zenon_H139 zenon_Ha3. % 21.03/21.26 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H2a | zenon_intro zenon_H27 ]. % 21.03/21.26 cut (((e12) = (e12)) = ((e10) = (e12))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Ha3. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H2a. % 21.03/21.26 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 21.03/21.26 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op1 (e12) (e10)) = (e10)) = ((e12) = (e10))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_Ha4. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H138. % 21.03/21.26 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 21.03/21.26 cut (((op1 (e12) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_Ha1 zenon_H139). % 21.03/21.26 apply zenon_H72. apply refl_equal. % 21.03/21.26 apply zenon_H27. apply refl_equal. % 21.03/21.26 apply zenon_H27. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L82_ *) % 21.03/21.26 assert (zenon_L83_ : (~((h4 (e12)) = (e22))) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H13a zenon_H13b zenon_H34. % 21.03/21.26 cut (((h4 (e12)) = (op2 (e23) (e23))) = ((h4 (e12)) = (e22))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H13a. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H13b. % 21.03/21.26 cut (((op2 (e23) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 21.03/21.26 cut (((h4 (e12)) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H13c]. % 21.03/21.26 congruence. % 21.03/21.26 apply zenon_H13c. apply refl_equal. % 21.03/21.26 apply zenon_H35. apply sym_equal. exact zenon_H34. % 21.03/21.26 (* end of lemma zenon_L83_ *) % 21.03/21.26 assert (zenon_L84_ : (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> ((op1 (e10) (e12)) = (e12)) -> ((op2 (e20) (e22)) = (e22)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (e23))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H13d zenon_H13e zenon_H13f zenon_H13 zenon_H14 zenon_H13b zenon_H34. % 21.03/21.26 cut (((h4 (e12)) = (op2 (e23) (e23))) = ((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H13d. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H13b. % 21.03/21.26 cut (((op2 (e23) (e23)) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 21.03/21.26 cut (((h4 (e12)) = (h4 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12))))); [ zenon_intro zenon_H142 | zenon_intro zenon_H143 ]. % 21.03/21.26 cut (((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12)))) = ((h4 (e12)) = (h4 (op1 (e10) (e12))))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H141. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H142. % 21.03/21.26 cut (((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H143]. % 21.03/21.26 cut (((h4 (op1 (e10) (e12))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H144]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op1 (e10) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H145]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H145 zenon_H13e). % 21.03/21.26 apply zenon_H143. apply refl_equal. % 21.03/21.26 apply zenon_H143. apply refl_equal. % 21.03/21.26 elim (classic ((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [ zenon_intro zenon_H146 | zenon_intro zenon_H147 ]. % 21.03/21.26 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12)))) = ((op2 (e23) (e23)) = (op2 (h4 (e10)) (h4 (e12))))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H140. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H146. % 21.03/21.26 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H147]. % 21.03/21.26 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H148]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((op2 (e20) (e22)) = (e22)) = ((op2 (h4 (e10)) (h4 (e12))) = (op2 (e23) (e23)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H148. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H13f. % 21.03/21.26 cut (((e22) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H149]. % 21.03/21.26 cut (((op2 (e20) (e22)) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [ zenon_intro zenon_H146 | zenon_intro zenon_H147 ]. % 21.03/21.26 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12)))) = ((op2 (e20) (e22)) = (op2 (h4 (e10)) (h4 (e12))))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H14a. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H146. % 21.03/21.26 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H147]. % 21.03/21.26 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H14b]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 21.03/21.26 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 21.03/21.26 congruence. % 21.03/21.26 apply (zenon_L1_); trivial. % 21.03/21.26 apply (zenon_L83_); trivial. % 21.03/21.26 apply zenon_H147. apply refl_equal. % 21.03/21.26 apply zenon_H147. apply refl_equal. % 21.03/21.26 exact (zenon_H149 zenon_H34). % 21.03/21.26 apply zenon_H147. apply refl_equal. % 21.03/21.26 apply zenon_H147. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L84_ *) % 21.03/21.26 assert (zenon_L85_ : ((e12) = (op1 (e13) (e13))) -> ((op1 (e11) (e10)) = (e12)) -> (~((op1 (e13) (e13)) = (op1 (e11) (e10)))) -> False). % 21.03/21.26 do 0 intro. intros zenon_H1c zenon_H14c zenon_H14d. % 21.03/21.26 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_H14e | zenon_intro zenon_H14f ]. % 21.03/21.26 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((op1 (e13) (e13)) = (op1 (e11) (e10)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H14d. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H14e. % 21.03/21.26 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 21.03/21.26 cut (((op1 (e11) (e10)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 21.03/21.26 congruence. % 21.03/21.26 cut (((e12) = (op1 (e13) (e13))) = ((op1 (e11) (e10)) = (op1 (e13) (e13)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H150. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H1c. % 21.03/21.26 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 21.03/21.26 cut (((e12) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H152]. % 21.03/21.26 congruence. % 21.03/21.26 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_H14e | zenon_intro zenon_H14f ]. % 21.03/21.26 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((e12) = (op1 (e11) (e10)))). % 21.03/21.26 intro zenon_D_pnotp. % 21.03/21.26 apply zenon_H152. % 21.03/21.26 rewrite <- zenon_D_pnotp. % 21.03/21.26 exact zenon_H14e. % 21.03/21.26 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 21.03/21.26 cut (((op1 (e11) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 21.03/21.26 congruence. % 21.03/21.26 exact (zenon_H153 zenon_H14c). % 21.03/21.26 apply zenon_H14f. apply refl_equal. % 21.03/21.26 apply zenon_H14f. apply refl_equal. % 21.03/21.26 apply zenon_H151. apply refl_equal. % 21.03/21.26 apply zenon_H14f. apply refl_equal. % 21.03/21.26 apply zenon_H14f. apply refl_equal. % 21.03/21.26 (* end of lemma zenon_L85_ *) % 21.03/21.26 assert (zenon_L86_ : (~((op1 (e13) (e13)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e10)) = (e12)) -> ((e12) = (op1 (e13) (e13))) -> ((op1 (e12) (e11)) = (e12)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H154 zenon_H14c zenon_H1c zenon_H155. % 21.03/21.27 cut (((op1 (e11) (e10)) = (e12)) = ((op1 (e13) (e13)) = (op1 (e12) (e11)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H154. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H14c. % 21.03/21.27 cut (((e12) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H156]. % 21.03/21.27 cut (((op1 (e11) (e10)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H157 | zenon_intro zenon_H151 ]. % 21.03/21.27 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e11) (e10)) = (op1 (e13) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H150. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H157. % 21.03/21.27 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 21.03/21.27 cut (((op1 (e13) (e13)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 21.03/21.27 congruence. % 21.03/21.27 apply (zenon_L85_); trivial. % 21.03/21.27 apply zenon_H151. apply refl_equal. % 21.03/21.27 apply zenon_H151. apply refl_equal. % 21.03/21.27 apply zenon_H156. apply sym_equal. exact zenon_H155. % 21.03/21.27 (* end of lemma zenon_L86_ *) % 21.03/21.27 assert (zenon_L87_ : ((op1 (e12) (e12)) = (e12)) -> ((op1 (e12) (e11)) = (e12)) -> ((op1 (e11) (e10)) = (e12)) -> ((e12) = (op1 (e13) (e13))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H158 zenon_H155 zenon_H14c zenon_H1c zenon_H159. % 21.03/21.27 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H22 | zenon_intro zenon_H23 ]. % 21.03/21.27 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e12) (e11)) = (op1 (e12) (e12)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H159. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H22. % 21.03/21.27 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 21.03/21.27 cut (((op1 (e12) (e12)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H15a]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((e12) = (op1 (e13) (e13))) = ((op1 (e12) (e12)) = (op1 (e12) (e11)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H15a. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1c. % 21.03/21.27 cut (((op1 (e13) (e13)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 21.03/21.27 cut (((e12) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H22 | zenon_intro zenon_H23 ]. % 21.03/21.27 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((e12) = (op1 (e12) (e12)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H15b. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H22. % 21.03/21.27 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 21.03/21.27 cut (((op1 (e12) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H15c zenon_H158). % 21.03/21.27 apply zenon_H23. apply refl_equal. % 21.03/21.27 apply zenon_H23. apply refl_equal. % 21.03/21.27 apply (zenon_L86_); trivial. % 21.03/21.27 apply zenon_H23. apply refl_equal. % 21.03/21.27 apply zenon_H23. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L87_ *) % 21.03/21.27 assert (zenon_L88_ : (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (e13))) -> ((op1 (e13) (e12)) = (e12)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H15d zenon_H1c zenon_H15e. % 21.03/21.27 cut (((e12) = (op1 (e13) (e13))) = ((op1 (e13) (e12)) = (op1 (e13) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H15d. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1c. % 21.03/21.27 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 21.03/21.27 cut (((e12) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H15f]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_H160 | zenon_intro zenon_H161 ]. % 21.03/21.27 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((e12) = (op1 (e13) (e12)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H15f. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H160. % 21.03/21.27 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 21.03/21.27 cut (((op1 (e13) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H162 zenon_H15e). % 21.03/21.27 apply zenon_H161. apply refl_equal. % 21.03/21.27 apply zenon_H161. apply refl_equal. % 21.03/21.27 apply zenon_H151. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L88_ *) % 21.03/21.27 assert (zenon_L89_ : (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> ((e22) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e20) (e22)) = (e22)) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e10)) = (e12)) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H163 zenon_H34 zenon_H13b zenon_H14 zenon_H13 zenon_H13f zenon_H13d zenon_H164 zenon_H159 zenon_H14c zenon_H155 zenon_H15d zenon_H1c. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H13e | zenon_intro zenon_H165 ]. % 21.03/21.27 apply (zenon_L84_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H167 | zenon_intro zenon_H166 ]. % 21.03/21.27 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_H135 | zenon_intro zenon_H136 ]. % 21.03/21.27 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((op1 (e11) (e10)) = (op1 (e11) (e12)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H164. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H135. % 21.03/21.27 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 21.03/21.27 cut (((op1 (e11) (e12)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((e12) = (op1 (e13) (e13))) = ((op1 (e11) (e12)) = (op1 (e11) (e10)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H168. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1c. % 21.03/21.27 cut (((op1 (e13) (e13)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 21.03/21.27 cut (((e12) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H169]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_H135 | zenon_intro zenon_H136 ]. % 21.03/21.27 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((e12) = (op1 (e11) (e12)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H169. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H135. % 21.03/21.27 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 21.03/21.27 cut (((op1 (e11) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H16a zenon_H167). % 21.03/21.27 apply zenon_H136. apply refl_equal. % 21.03/21.27 apply zenon_H136. apply refl_equal. % 21.03/21.27 apply (zenon_L85_); trivial. % 21.03/21.27 apply zenon_H136. apply refl_equal. % 21.03/21.27 apply zenon_H136. apply refl_equal. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H158 | zenon_intro zenon_H15e ]. % 21.03/21.27 apply (zenon_L87_); trivial. % 21.03/21.27 apply (zenon_L88_); trivial. % 21.03/21.27 (* end of lemma zenon_L89_ *) % 21.03/21.27 assert (zenon_L90_ : (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e10) (e13)) = (e11)) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H16b zenon_H1f zenon_H16c zenon_H1c. % 21.03/21.27 cut (((e11) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e10) (e13)) = (op1 (e12) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H16b. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1f. % 21.03/21.27 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 21.03/21.27 cut (((e11) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_H16e | zenon_intro zenon_H16f ]. % 21.03/21.27 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((e11) = (op1 (e10) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H16d. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H16e. % 21.03/21.27 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H16f]. % 21.03/21.27 cut (((op1 (e10) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H170]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H170 zenon_H16c). % 21.03/21.27 apply zenon_H16f. apply refl_equal. % 21.03/21.27 apply zenon_H16f. apply refl_equal. % 21.03/21.27 apply (zenon_L4_); trivial. % 21.03/21.27 (* end of lemma zenon_L90_ *) % 21.03/21.27 assert (zenon_L91_ : (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e11) (e13)) = (e11)) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H171 zenon_H1f zenon_H172 zenon_H1c. % 21.03/21.27 cut (((e11) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e11) (e13)) = (op1 (e12) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H171. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1f. % 21.03/21.27 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 21.03/21.27 cut (((e11) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H173]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H174 | zenon_intro zenon_H175 ]. % 21.03/21.27 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e11) = (op1 (e11) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H173. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H174. % 21.03/21.27 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H175]. % 21.03/21.27 cut (((op1 (e11) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H76 zenon_H172). % 21.03/21.27 apply zenon_H175. apply refl_equal. % 21.03/21.27 apply zenon_H175. apply refl_equal. % 21.03/21.27 apply (zenon_L4_); trivial. % 21.03/21.27 (* end of lemma zenon_L91_ *) % 21.03/21.27 assert (zenon_L92_ : (~((op1 (op1 (e13) (e13)) (e13)) = (op1 (e10) (e10)))) -> ((op1 (e12) (e13)) = (e11)) -> ((e12) = (op1 (e13) (e13))) -> ((op1 (e10) (e10)) = (e11)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H176 zenon_H177 zenon_H1c zenon_H6a. % 21.03/21.27 cut (((op1 (e12) (e13)) = (e11)) = ((op1 (op1 (e13) (e13)) (e13)) = (op1 (e10) (e10)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H176. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H177. % 21.03/21.27 cut (((e11) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 21.03/21.27 cut (((op1 (e12) (e13)) = (op1 (op1 (e13) (e13)) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (op1 (e13) (e13)) (e13)) = (op1 (op1 (e13) (e13)) (e13)))); [ zenon_intro zenon_H17a | zenon_intro zenon_H17b ]. % 21.03/21.27 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e12) (e13)) = (op1 (op1 (e13) (e13)) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H179. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H17a. % 21.03/21.27 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (op1 (e13) (e13)) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 21.03/21.27 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 21.03/21.27 congruence. % 21.03/21.27 apply (zenon_L4_); trivial. % 21.03/21.27 apply zenon_H17b. apply refl_equal. % 21.03/21.27 apply zenon_H17b. apply refl_equal. % 21.03/21.27 apply zenon_H178. apply sym_equal. exact zenon_H6a. % 21.03/21.27 (* end of lemma zenon_L92_ *) % 21.03/21.27 assert (zenon_L93_ : ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e13) (e10)) = (e11)) -> ((op1 (e12) (e13)) = (e11)) -> ((op1 (e10) (e10)) = (e11)) -> ((e12) = (op1 (e13) (e13))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1f zenon_H17c zenon_H177 zenon_H6a zenon_H1c zenon_H17d. % 21.03/21.27 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H17e | zenon_intro zenon_H17f ]. % 21.03/21.27 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((op1 (e10) (e10)) = (op1 (e13) (e10)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H17d. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H17e. % 21.03/21.27 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 21.03/21.27 cut (((op1 (e13) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H180]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((e11) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e13) (e10)) = (op1 (e10) (e10)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H180. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1f. % 21.03/21.27 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 21.03/21.27 cut (((e11) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H17e | zenon_intro zenon_H17f ]. % 21.03/21.27 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e11) = (op1 (e13) (e10)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H181. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H17e. % 21.03/21.27 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 21.03/21.27 cut (((op1 (e13) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H182]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H182 zenon_H17c). % 21.03/21.27 apply zenon_H17f. apply refl_equal. % 21.03/21.27 apply zenon_H17f. apply refl_equal. % 21.03/21.27 apply (zenon_L92_); trivial. % 21.03/21.27 apply zenon_H17f. apply refl_equal. % 21.03/21.27 apply zenon_H17f. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L93_ *) % 21.03/21.27 assert (zenon_L94_ : (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e10)) = (e11)) -> ((op1 (e13) (e10)) = (e11)) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((e12) = (op1 (e13) (e13))) -> (~((e11) = (e12))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H183 zenon_H16b zenon_H171 zenon_H17d zenon_H6a zenon_H17c zenon_H1f zenon_H1c zenon_H29. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H16c | zenon_intro zenon_H184 ]. % 21.03/21.27 apply (zenon_L90_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H172 | zenon_intro zenon_H185 ]. % 21.03/21.27 apply (zenon_L91_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H177 | zenon_intro zenon_H28 ]. % 21.03/21.27 apply (zenon_L93_); trivial. % 21.03/21.27 apply (zenon_L8_); trivial. % 21.03/21.27 (* end of lemma zenon_L94_ *) % 21.03/21.27 assert (zenon_L95_ : (~((op1 (e13) (op1 (e13) (e13))) = (op1 (e11) (e11)))) -> ((op1 (e13) (e12)) = (e10)) -> ((e12) = (op1 (e13) (e13))) -> ((op1 (e11) (e11)) = (e10)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H186 zenon_H187 zenon_H1c zenon_H74. % 21.03/21.27 cut (((op1 (e13) (e12)) = (e10)) = ((op1 (e13) (op1 (e13) (e13))) = (op1 (e11) (e11)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H186. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H187. % 21.03/21.27 cut (((e10) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 21.03/21.27 cut (((op1 (e13) (e12)) = (op1 (e13) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (op1 (e13) (e13))))); [ zenon_intro zenon_H18a | zenon_intro zenon_H18b ]. % 21.03/21.27 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e13) (e12)) = (op1 (e13) (op1 (e13) (e13))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H189. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H18a. % 21.03/21.27 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H18b]. % 21.03/21.27 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 21.03/21.27 congruence. % 21.03/21.27 apply (zenon_L34_); trivial. % 21.03/21.27 apply zenon_H18b. apply refl_equal. % 21.03/21.27 apply zenon_H18b. apply refl_equal. % 21.03/21.27 apply zenon_H188. apply sym_equal. exact zenon_H74. % 21.03/21.27 (* end of lemma zenon_L95_ *) % 21.03/21.27 assert (zenon_L96_ : ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e11)) = (e10)) -> ((op1 (e13) (e12)) = (e10)) -> ((op1 (e11) (e11)) = (e10)) -> ((e12) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H80 zenon_H18c zenon_H187 zenon_H74 zenon_H1c zenon_H18d. % 21.03/21.27 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H18e | zenon_intro zenon_H18f ]. % 21.03/21.27 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((op1 (e11) (e11)) = (op1 (e12) (e11)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H18d. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H18e. % 21.03/21.27 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 21.03/21.27 cut (((op1 (e12) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e12) (e11)) = (op1 (e11) (e11)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H190. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H80. % 21.03/21.27 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H186]. % 21.03/21.27 cut (((e10) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H18e | zenon_intro zenon_H18f ]. % 21.03/21.27 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((e10) = (op1 (e12) (e11)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H191. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H18e. % 21.03/21.27 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 21.03/21.27 cut (((op1 (e12) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H192 zenon_H18c). % 21.03/21.27 apply zenon_H18f. apply refl_equal. % 21.03/21.27 apply zenon_H18f. apply refl_equal. % 21.03/21.27 apply (zenon_L95_); trivial. % 21.03/21.27 apply zenon_H18f. apply refl_equal. % 21.03/21.27 apply zenon_H18f. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L96_ *) % 21.03/21.27 assert (zenon_L97_ : (~((op1 (op1 (e13) (e13)) (e13)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e13)) = (e11)) -> ((e12) = (op1 (e13) (e13))) -> ((op1 (e13) (e11)) = (e11)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H193 zenon_H177 zenon_H1c zenon_H194. % 21.03/21.27 cut (((op1 (e12) (e13)) = (e11)) = ((op1 (op1 (e13) (e13)) (e13)) = (op1 (e13) (e11)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H193. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H177. % 21.03/21.27 cut (((e11) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 21.03/21.27 cut (((op1 (e12) (e13)) = (op1 (op1 (e13) (e13)) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (op1 (e13) (e13)) (e13)) = (op1 (op1 (e13) (e13)) (e13)))); [ zenon_intro zenon_H17a | zenon_intro zenon_H17b ]. % 21.03/21.27 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e12) (e13)) = (op1 (op1 (e13) (e13)) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H179. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H17a. % 21.03/21.27 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (op1 (e13) (e13)) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 21.03/21.27 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 21.03/21.27 congruence. % 21.03/21.27 apply (zenon_L4_); trivial. % 21.03/21.27 apply zenon_H17b. apply refl_equal. % 21.03/21.27 apply zenon_H17b. apply refl_equal. % 21.03/21.27 apply zenon_H195. apply sym_equal. exact zenon_H194. % 21.03/21.27 (* end of lemma zenon_L97_ *) % 21.03/21.27 assert (zenon_L98_ : (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e12) (e13)) = (e11)) -> ((op1 (e13) (e11)) = (e11)) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H196 zenon_H1f zenon_H197 zenon_H177 zenon_H194 zenon_H1c. % 21.03/21.27 cut (((e11) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e12) (e11)) = (op1 (e13) (e11)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H196. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1f. % 21.03/21.27 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 21.03/21.27 cut (((e11) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H18e | zenon_intro zenon_H18f ]. % 21.03/21.27 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((e11) = (op1 (e12) (e11)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H198. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H18e. % 21.03/21.27 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 21.03/21.27 cut (((op1 (e12) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H199 zenon_H197). % 21.03/21.27 apply zenon_H18f. apply refl_equal. % 21.03/21.27 apply zenon_H18f. apply refl_equal. % 21.03/21.27 apply (zenon_L97_); trivial. % 21.03/21.27 (* end of lemma zenon_L98_ *) % 21.03/21.27 assert (zenon_L99_ : ((op1 (e12) (e12)) = (e13)) -> ((op1 (e12) (e11)) = (e13)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H8a zenon_H19a zenon_H159. % 21.03/21.27 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H22 | zenon_intro zenon_H23 ]. % 21.03/21.27 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e12) (e11)) = (op1 (e12) (e12)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H159. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H22. % 21.03/21.27 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 21.03/21.27 cut (((op1 (e12) (e12)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H15a]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op1 (e12) (e12)) = (e13)) = ((op1 (e12) (e12)) = (op1 (e12) (e11)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H15a. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H8a. % 21.03/21.27 cut (((e13) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H19b]. % 21.03/21.27 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 21.03/21.27 congruence. % 21.03/21.27 apply zenon_H23. apply refl_equal. % 21.03/21.27 apply zenon_H19b. apply sym_equal. exact zenon_H19a. % 21.03/21.27 apply zenon_H23. apply refl_equal. % 21.03/21.27 apply zenon_H23. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L99_ *) % 21.03/21.27 assert (zenon_L100_ : (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e10)) -> ((op1 (e13) (e12)) = (e10)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e11)) -> ((op1 (e12) (e13)) = (e11)) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e13) (e13))) -> ((op1 (e11) (e10)) = (e12)) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H19c zenon_H18d zenon_H74 zenon_H187 zenon_H80 zenon_H194 zenon_H177 zenon_H1f zenon_H196 zenon_H1c zenon_H14c zenon_H158 zenon_H8a zenon_H159. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18c | zenon_intro zenon_H19d ]. % 21.03/21.27 apply (zenon_L96_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H19e ]. % 21.03/21.27 apply (zenon_L98_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H155 | zenon_intro zenon_H19a ]. % 21.03/21.27 apply (zenon_L87_); trivial. % 21.03/21.27 apply (zenon_L99_); trivial. % 21.03/21.27 (* end of lemma zenon_L100_ *) % 21.03/21.27 assert (zenon_L101_ : (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e13)) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e11) (e10)) = (e12)) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e13) (e11)) = (e11)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e10)) -> ((op1 (e11) (e11)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> ((e12) = (op1 (e13) (e13))) -> (~((e11) = (e12))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H183 zenon_H16b zenon_H171 zenon_H159 zenon_H8a zenon_H158 zenon_H14c zenon_H196 zenon_H1f zenon_H194 zenon_H80 zenon_H187 zenon_H74 zenon_H18d zenon_H19c zenon_H1c zenon_H29. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H16c | zenon_intro zenon_H184 ]. % 21.03/21.27 apply (zenon_L90_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H172 | zenon_intro zenon_H185 ]. % 21.03/21.27 apply (zenon_L91_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H177 | zenon_intro zenon_H28 ]. % 21.03/21.27 apply (zenon_L100_); trivial. % 21.03/21.27 apply (zenon_L8_); trivial. % 21.03/21.27 (* end of lemma zenon_L101_ *) % 21.03/21.27 assert (zenon_L102_ : (~((op1 (op1 (e13) (e13)) (e13)) = (op1 (e11) (e12)))) -> ((op1 (e12) (e13)) = (e11)) -> ((e12) = (op1 (e13) (e13))) -> ((op1 (e11) (e12)) = (e11)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H19f zenon_H177 zenon_H1c zenon_H1a0. % 21.03/21.27 cut (((op1 (e12) (e13)) = (e11)) = ((op1 (op1 (e13) (e13)) (e13)) = (op1 (e11) (e12)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H19f. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H177. % 21.03/21.27 cut (((e11) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 21.03/21.27 cut (((op1 (e12) (e13)) = (op1 (op1 (e13) (e13)) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (op1 (e13) (e13)) (e13)) = (op1 (op1 (e13) (e13)) (e13)))); [ zenon_intro zenon_H17a | zenon_intro zenon_H17b ]. % 21.03/21.27 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e12) (e13)) = (op1 (op1 (e13) (e13)) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H179. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H17a. % 21.03/21.27 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (op1 (e13) (e13)) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 21.03/21.27 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 21.03/21.27 congruence. % 21.03/21.27 apply (zenon_L4_); trivial. % 21.03/21.27 apply zenon_H17b. apply refl_equal. % 21.03/21.27 apply zenon_H17b. apply refl_equal. % 21.03/21.27 apply zenon_H1a1. apply sym_equal. exact zenon_H1a0. % 21.03/21.27 (* end of lemma zenon_L102_ *) % 21.03/21.27 assert (zenon_L103_ : (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e11)) -> ((op1 (e13) (e12)) = (e11)) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((e12) = (op1 (e13) (e13))) -> (~((e11) = (e12))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H183 zenon_H16b zenon_H171 zenon_H132 zenon_H1a0 zenon_H1a2 zenon_H1f zenon_H1c zenon_H29. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H16c | zenon_intro zenon_H184 ]. % 21.03/21.27 apply (zenon_L90_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H172 | zenon_intro zenon_H185 ]. % 21.03/21.27 apply (zenon_L91_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H177 | zenon_intro zenon_H28 ]. % 21.03/21.27 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_H160 | zenon_intro zenon_H161 ]. % 21.03/21.27 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((op1 (e11) (e12)) = (op1 (e13) (e12)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H132. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H160. % 21.03/21.27 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 21.03/21.27 cut (((op1 (e13) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1a3]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((e11) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e13) (e12)) = (op1 (e11) (e12)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1a3. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1f. % 21.03/21.27 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 21.03/21.27 cut (((e11) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1a4]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_H160 | zenon_intro zenon_H161 ]. % 21.03/21.27 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((e11) = (op1 (e13) (e12)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1a4. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H160. % 21.03/21.27 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 21.03/21.27 cut (((op1 (e13) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H1a5 zenon_H1a2). % 21.03/21.27 apply zenon_H161. apply refl_equal. % 21.03/21.27 apply zenon_H161. apply refl_equal. % 21.03/21.27 apply (zenon_L102_); trivial. % 21.03/21.27 apply zenon_H161. apply refl_equal. % 21.03/21.27 apply zenon_H161. apply refl_equal. % 21.03/21.27 apply (zenon_L8_); trivial. % 21.03/21.27 (* end of lemma zenon_L103_ *) % 21.03/21.27 assert (zenon_L104_ : (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e11) (e10)) = (e11))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e13)) = (e12))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e10)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e10)) = (e12)) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> ((e22) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e20) (e22)) = (e22)) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e10)) -> (~((e10) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1a6 zenon_H1a7 zenon_H7d zenon_H1a8 zenon_H1a9 zenon_H6a zenon_H17d zenon_H19c zenon_H18d zenon_H74 zenon_H80 zenon_H196 zenon_H14c zenon_H8a zenon_H159 zenon_H132 zenon_H16b zenon_H183 zenon_H29 zenon_H163 zenon_H34 zenon_H13b zenon_H14 zenon_H13 zenon_H13f zenon_H13d zenon_H164 zenon_H15d zenon_H138 zenon_Ha3 zenon_H1aa zenon_H9c zenon_H7f zenon_H1ab zenon_H171 zenon_H1f zenon_H1c. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_H1ad | zenon_intro zenon_H1ac ]. % 21.03/21.27 exact (zenon_H1a7 zenon_H1ad). % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H19 | zenon_intro zenon_H1ae ]. % 21.03/21.27 apply (zenon_L80_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1ae); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H172 ]. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_H81 | zenon_intro zenon_H1af ]. % 21.03/21.27 apply (zenon_L35_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H133 | zenon_intro zenon_H1b0 ]. % 21.03/21.27 apply (zenon_L81_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H9d | zenon_intro zenon_H187 ]. % 21.03/21.27 apply (zenon_L42_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H139 | zenon_intro zenon_H1b1 ]. % 21.03/21.27 apply (zenon_L82_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H155 | zenon_intro zenon_H1b2 ]. % 21.03/21.27 apply (zenon_L89_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H158 | zenon_intro zenon_H1b3 ]. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_H17c | zenon_intro zenon_H1b4 ]. % 21.03/21.27 apply (zenon_L94_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H194 | zenon_intro zenon_H1b5 ]. % 21.03/21.27 apply (zenon_L101_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H28 ]. % 21.03/21.27 apply (zenon_L103_); trivial. % 21.03/21.27 apply (zenon_L8_); trivial. % 21.03/21.27 exact (zenon_H1a8 zenon_H1b3). % 21.03/21.27 apply (zenon_L91_); trivial. % 21.03/21.27 (* end of lemma zenon_L104_ *) % 21.03/21.27 assert (zenon_L105_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e11)) = (e10)) -> ((op1 (e11) (e11)) = (e10)) -> ((e12) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1ab zenon_H7f zenon_H132 zenon_H9c zenon_H80 zenon_H18c zenon_H74 zenon_H1c zenon_H18d. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_H81 | zenon_intro zenon_H1af ]. % 21.03/21.27 apply (zenon_L35_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H133 | zenon_intro zenon_H1b0 ]. % 21.03/21.27 apply (zenon_L81_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H9d | zenon_intro zenon_H187 ]. % 21.03/21.27 apply (zenon_L42_); trivial. % 21.03/21.27 apply (zenon_L96_); trivial. % 21.03/21.27 (* end of lemma zenon_L105_ *) % 21.03/21.27 assert (zenon_L106_ : (~((op1 (e13) (op1 (e13) (e13))) = (op1 (e10) (e13)))) -> ((op1 (e13) (e12)) = (e10)) -> ((e12) = (op1 (e13) (e13))) -> ((op1 (e10) (e13)) = (e10)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1b6 zenon_H187 zenon_H1c zenon_H8f. % 21.03/21.27 cut (((op1 (e13) (e12)) = (e10)) = ((op1 (e13) (op1 (e13) (e13))) = (op1 (e10) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1b6. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H187. % 21.03/21.27 cut (((e10) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 21.03/21.27 cut (((op1 (e13) (e12)) = (op1 (e13) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (op1 (e13) (e13))))); [ zenon_intro zenon_H18a | zenon_intro zenon_H18b ]. % 21.03/21.27 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e13) (e12)) = (op1 (e13) (op1 (e13) (e13))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H189. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H18a. % 21.03/21.27 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H18b]. % 21.03/21.27 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 21.03/21.27 congruence. % 21.03/21.27 apply (zenon_L34_); trivial. % 21.03/21.27 apply zenon_H18b. apply refl_equal. % 21.03/21.27 apply zenon_H18b. apply refl_equal. % 21.03/21.27 apply zenon_H1b7. apply sym_equal. exact zenon_H8f. % 21.03/21.27 (* end of lemma zenon_L106_ *) % 21.03/21.27 assert (zenon_L107_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e10) (e13)) = (e10)) -> ((e12) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1ab zenon_H7f zenon_H132 zenon_H9c zenon_H80 zenon_H1b8 zenon_H8f zenon_H1c zenon_H16b. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_H81 | zenon_intro zenon_H1af ]. % 21.03/21.27 apply (zenon_L35_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H133 | zenon_intro zenon_H1b0 ]. % 21.03/21.27 apply (zenon_L81_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H9d | zenon_intro zenon_H187 ]. % 21.03/21.27 apply (zenon_L42_); trivial. % 21.03/21.27 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ]. % 21.03/21.27 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((op1 (e10) (e13)) = (op1 (e12) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H16b. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1b9. % 21.03/21.27 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 21.03/21.27 cut (((op1 (e12) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e12) (e13)) = (op1 (e10) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1bb. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H80. % 21.03/21.27 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 21.03/21.27 cut (((e10) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ]. % 21.03/21.27 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e10) = (op1 (e12) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1bc. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1b9. % 21.03/21.27 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 21.03/21.27 cut (((op1 (e12) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H1bd]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H1bd zenon_H1b8). % 21.03/21.27 apply zenon_H1ba. apply refl_equal. % 21.03/21.27 apply zenon_H1ba. apply refl_equal. % 21.03/21.27 apply (zenon_L106_); trivial. % 21.03/21.27 apply zenon_H1ba. apply refl_equal. % 21.03/21.27 apply zenon_H1ba. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L107_ *) % 21.03/21.27 assert (zenon_L108_ : (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((e10) = (e12))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e10)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e10)) -> ((e12) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1be zenon_Ha3 zenon_H139 zenon_H18d zenon_H74 zenon_H1ab zenon_H7f zenon_H132 zenon_H9c zenon_H80 zenon_H8f zenon_H1c zenon_H16b. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1be); [ zenon_intro zenon_H138 | zenon_intro zenon_H1bf ]. % 21.03/21.27 apply (zenon_L82_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H18c | zenon_intro zenon_H1c0 ]. % 21.03/21.27 apply (zenon_L105_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H9d | zenon_intro zenon_H1b8 ]. % 21.03/21.27 apply (zenon_L42_); trivial. % 21.03/21.27 apply (zenon_L107_); trivial. % 21.03/21.27 (* end of lemma zenon_L108_ *) % 21.03/21.27 assert (zenon_L109_ : (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (e13))) -> ((op1 (e13) (e10)) = (e12)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1c1 zenon_H1c zenon_H1c2. % 21.03/21.27 cut (((e12) = (op1 (e13) (e13))) = ((op1 (e13) (e10)) = (op1 (e13) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1c1. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1c. % 21.03/21.27 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 21.03/21.27 cut (((e12) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1c3]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H17e | zenon_intro zenon_H17f ]. % 21.03/21.27 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e12) = (op1 (e13) (e10)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1c3. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H17e. % 21.03/21.27 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 21.03/21.27 cut (((op1 (e13) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H1c4]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H1c4 zenon_H1c2). % 21.03/21.27 apply zenon_H17f. apply refl_equal. % 21.03/21.27 apply zenon_H17f. apply refl_equal. % 21.03/21.27 apply zenon_H151. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L109_ *) % 21.03/21.27 assert (zenon_L110_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e11) (e10)) = (e11))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e13)) = (e12))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> ((e22) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e20) (e22)) = (e22)) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e11) (e11)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1c5 zenon_H1c6 zenon_H1c7 zenon_H1a6 zenon_H1a7 zenon_H7d zenon_H1a8 zenon_H1a9 zenon_H6a zenon_H17d zenon_H19c zenon_H196 zenon_H8a zenon_H159 zenon_H183 zenon_H29 zenon_H163 zenon_H34 zenon_H13b zenon_H14 zenon_H13 zenon_H13f zenon_H13d zenon_H164 zenon_H15d zenon_H1aa zenon_H171 zenon_H1f zenon_H16b zenon_H80 zenon_H9c zenon_H132 zenon_H7f zenon_H1ab zenon_H74 zenon_H18d zenon_Ha3 zenon_H1be zenon_H1c1 zenon_H1c. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c8 ]. % 21.03/21.27 apply (zenon_L33_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1c9 ]. % 21.03/21.27 exact (zenon_H1c6 zenon_H1ca). % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H81 | zenon_intro zenon_H8f ]. % 21.03/21.27 apply (zenon_L35_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H12e | zenon_intro zenon_H1cb ]. % 21.03/21.27 apply (zenon_L79_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H14c | zenon_intro zenon_H1cc ]. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1be); [ zenon_intro zenon_H138 | zenon_intro zenon_H1bf ]. % 21.03/21.27 apply (zenon_L104_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H18c | zenon_intro zenon_H1c0 ]. % 21.03/21.27 apply (zenon_L105_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H9d | zenon_intro zenon_H1b8 ]. % 21.03/21.27 apply (zenon_L42_); trivial. % 21.03/21.27 apply (zenon_L107_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H139 | zenon_intro zenon_H1c2 ]. % 21.03/21.27 apply (zenon_L108_); trivial. % 21.03/21.27 apply (zenon_L109_); trivial. % 21.03/21.27 (* end of lemma zenon_L110_ *) % 21.03/21.27 assert (zenon_L111_ : (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (e23))) -> ((op2 (e20) (e23)) = (e22)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1cd zenon_H34 zenon_H1ce. % 21.03/21.27 cut (((e22) = (op2 (e23) (e23))) = ((op2 (e20) (e23)) = (op2 (e23) (e23)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1cd. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H34. % 21.03/21.27 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 21.03/21.27 cut (((e22) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1cf]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 21.03/21.27 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((e22) = (op2 (e20) (e23)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1cf. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_Hc4. % 21.03/21.27 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 21.03/21.27 cut (((op2 (e20) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1d0]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H1d0 zenon_H1ce). % 21.03/21.27 apply zenon_Hc5. apply refl_equal. % 21.03/21.27 apply zenon_Hc5. apply refl_equal. % 21.03/21.27 apply zenon_Hf5. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L111_ *) % 21.03/21.27 assert (zenon_L112_ : ((op2 (e21) (e20)) = (e22)) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (e23))) -> (~((op2 (e23) (e23)) = (op2 (h4 (e11)) (h4 (e10))))) -> False). % 21.03/21.27 do 0 intro. intros zenon_Hf0 zenon_H87 zenon_H37 zenon_H13 zenon_H14 zenon_H34 zenon_H1d1. % 21.03/21.27 elim (classic ((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H1d3 ]. % 21.03/21.27 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10)))) = ((op2 (e23) (e23)) = (op2 (h4 (e11)) (h4 (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1d1. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1d2. % 21.03/21.27 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H1d3]. % 21.03/21.27 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1d4]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op2 (e21) (e20)) = (e22)) = ((op2 (h4 (e11)) (h4 (e10))) = (op2 (e23) (e23)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1d4. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_Hf0. % 21.03/21.27 cut (((e22) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H149]. % 21.03/21.27 cut (((op2 (e21) (e20)) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H1d5]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H1d3 ]. % 21.03/21.27 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10)))) = ((op2 (e21) (e20)) = (op2 (h4 (e11)) (h4 (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1d5. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1d2. % 21.03/21.27 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H1d3]. % 21.03/21.27 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 21.03/21.27 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 21.03/21.27 congruence. % 21.03/21.27 apply (zenon_L36_); trivial. % 21.03/21.27 apply (zenon_L1_); trivial. % 21.03/21.27 apply zenon_H1d3. apply refl_equal. % 21.03/21.27 apply zenon_H1d3. apply refl_equal. % 21.03/21.27 exact (zenon_H149 zenon_H34). % 21.03/21.27 apply zenon_H1d3. apply refl_equal. % 21.03/21.27 apply zenon_H1d3. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L112_ *) % 21.03/21.27 assert (zenon_L113_ : (~((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((op1 (e11) (e10)) = (e12)) -> ((op2 (e21) (e20)) = (e22)) -> ((e22) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1d7 zenon_H13b zenon_H14c zenon_Hf0 zenon_H34 zenon_H87 zenon_H37 zenon_H13 zenon_H14. % 21.03/21.27 cut (((h4 (e12)) = (op2 (e23) (e23))) = ((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1d7. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H13b. % 21.03/21.27 cut (((op2 (e23) (e23)) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H1d1]. % 21.03/21.27 cut (((h4 (e12)) = (h4 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H1d8]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10))))); [ zenon_intro zenon_H1d9 | zenon_intro zenon_H1da ]. % 21.03/21.27 cut (((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10)))) = ((h4 (e12)) = (h4 (op1 (e11) (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1d8. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1d9. % 21.03/21.27 cut (((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 21.03/21.27 cut (((h4 (op1 (e11) (e10))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op1 (e11) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H153 zenon_H14c). % 21.03/21.27 apply zenon_H1da. apply refl_equal. % 21.03/21.27 apply zenon_H1da. apply refl_equal. % 21.03/21.27 apply (zenon_L112_); trivial. % 21.03/21.27 (* end of lemma zenon_L113_ *) % 21.03/21.27 assert (zenon_L114_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((e11) = (e12))) -> ((op1 (e10) (e10)) = (e11)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e22)) -> ((h4 (e12)) = (op2 (e23) (e23))) -> (~((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e11) (e11)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1c5 zenon_H7d zenon_H1c6 zenon_H1c7 zenon_H29 zenon_H6a zenon_H14 zenon_H13 zenon_H37 zenon_H87 zenon_H34 zenon_Hf0 zenon_H13b zenon_H1d7 zenon_H16b zenon_H80 zenon_H9c zenon_H132 zenon_H7f zenon_H1ab zenon_H74 zenon_H18d zenon_Ha3 zenon_H1be zenon_H1c1 zenon_H1c. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c8 ]. % 21.03/21.27 apply (zenon_L33_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1c9 ]. % 21.03/21.27 exact (zenon_H1c6 zenon_H1ca). % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H81 | zenon_intro zenon_H8f ]. % 21.03/21.27 apply (zenon_L35_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H12e | zenon_intro zenon_H1cb ]. % 21.03/21.27 apply (zenon_L79_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H14c | zenon_intro zenon_H1cc ]. % 21.03/21.27 apply (zenon_L113_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H139 | zenon_intro zenon_H1c2 ]. % 21.03/21.27 apply (zenon_L108_); trivial. % 21.03/21.27 apply (zenon_L109_); trivial. % 21.03/21.27 (* end of lemma zenon_L114_ *) % 21.03/21.27 assert (zenon_L115_ : ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e20)) -> ((op2 (e23) (e22)) = (e20)) -> ((op2 (e20) (e23)) = (e20)) -> ((e22) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H14 zenon_H1dc zenon_Hdd zenon_H5c zenon_H34 zenon_H1dd. % 21.03/21.27 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcb ]. % 21.03/21.27 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((op2 (e20) (e23)) = (op2 (e21) (e23)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1dd. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_Hca. % 21.03/21.27 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 21.03/21.27 cut (((op2 (e21) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e21) (e23)) = (op2 (e20) (e23)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1de. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H14. % 21.03/21.27 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H11f]. % 21.03/21.27 cut (((e20) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1df]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcb ]. % 21.03/21.27 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e20) = (op2 (e21) (e23)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1df. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_Hca. % 21.03/21.27 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 21.03/21.27 cut (((op2 (e21) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1e0]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H1e0 zenon_H1dc). % 21.03/21.27 apply zenon_Hcb. apply refl_equal. % 21.03/21.27 apply zenon_Hcb. apply refl_equal. % 21.03/21.27 apply (zenon_L75_); trivial. % 21.03/21.27 apply zenon_Hcb. apply refl_equal. % 21.03/21.27 apply zenon_Hcb. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L115_ *) % 21.03/21.27 assert (zenon_L116_ : (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (e23))) -> ((op2 (e21) (e23)) = (e22)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1e1 zenon_H34 zenon_H1e2. % 21.03/21.27 cut (((e22) = (op2 (e23) (e23))) = ((op2 (e21) (e23)) = (op2 (e23) (e23)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1e1. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H34. % 21.03/21.27 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 21.03/21.27 cut (((e22) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1e3]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcb ]. % 21.03/21.27 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e22) = (op2 (e21) (e23)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1e3. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_Hca. % 21.03/21.27 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 21.03/21.27 cut (((op2 (e21) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1e4]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H1e4 zenon_H1e2). % 21.03/21.27 apply zenon_Hcb. apply refl_equal. % 21.03/21.27 apply zenon_Hcb. apply refl_equal. % 21.03/21.27 apply zenon_Hf5. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L116_ *) % 21.03/21.27 assert (zenon_L117_ : (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (e13))) -> ((op1 (e11) (e13)) = (e12)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1e5 zenon_H1c zenon_H1e6. % 21.03/21.27 cut (((e12) = (op1 (e13) (e13))) = ((op1 (e11) (e13)) = (op1 (e13) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1e5. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1c. % 21.03/21.27 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 21.03/21.27 cut (((e12) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1e7]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H174 | zenon_intro zenon_H175 ]. % 21.03/21.27 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e12) = (op1 (e11) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1e7. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H174. % 21.03/21.27 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H175]. % 21.03/21.27 cut (((op1 (e11) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H1e8 zenon_H1e6). % 21.03/21.27 apply zenon_H175. apply refl_equal. % 21.03/21.27 apply zenon_H175. apply refl_equal. % 21.03/21.27 apply zenon_H151. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L117_ *) % 21.03/21.27 assert (zenon_L118_ : (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((op1 (e11) (e13)) = (e13)) -> ((op2 (e21) (e23)) = (e23)) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1e9 zenon_H1ea zenon_H1eb zenon_H87 zenon_H37 zenon_H1ec. % 21.03/21.27 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1e9. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1ec. % 21.03/21.27 cut (((e23) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1ed]. % 21.03/21.27 cut (((h4 (e13)) = (h4 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13))))); [ zenon_intro zenon_H1ef | zenon_intro zenon_H1f0 ]. % 21.03/21.27 cut (((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13)))) = ((h4 (e13)) = (h4 (op1 (e11) (e13))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1ee. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1ef. % 21.03/21.27 cut (((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1f0]. % 21.03/21.27 cut (((h4 (op1 (e11) (e13))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op1 (e11) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H1f2 zenon_H1ea). % 21.03/21.27 apply zenon_H1f0. apply refl_equal. % 21.03/21.27 apply zenon_H1f0. apply refl_equal. % 21.03/21.27 elim (classic ((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H1f4 ]. % 21.03/21.27 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13)))) = ((e23) = (op2 (h4 (e11)) (h4 (e13))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1ed. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1f3. % 21.03/21.27 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 21.03/21.27 cut (((op2 (h4 (e11)) (h4 (e13))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op2 (e21) (e23)) = (e23)) = ((op2 (h4 (e11)) (h4 (e13))) = (e23))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1f5. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1eb. % 21.03/21.27 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 21.03/21.27 cut (((op2 (e21) (e23)) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H1f4 ]. % 21.03/21.27 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13)))) = ((op2 (e21) (e23)) = (op2 (h4 (e11)) (h4 (e13))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1f6. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1f3. % 21.03/21.27 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 21.03/21.27 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1f7]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 21.03/21.27 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 21.03/21.27 congruence. % 21.03/21.27 apply (zenon_L36_); trivial. % 21.03/21.27 exact (zenon_H1f8 zenon_H1ec). % 21.03/21.27 apply zenon_H1f4. apply refl_equal. % 21.03/21.27 apply zenon_H1f4. apply refl_equal. % 21.03/21.27 apply zenon_H32. apply refl_equal. % 21.03/21.27 apply zenon_H1f4. apply refl_equal. % 21.03/21.27 apply zenon_H1f4. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L118_ *) % 21.03/21.27 assert (zenon_L119_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((e10) = (e11))) -> (~((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((op2 (e21) (e23)) = (e23)) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1c5 zenon_H6a zenon_H7d zenon_H1c6 zenon_H1ab zenon_H7f zenon_H132 zenon_H9c zenon_H1f9 zenon_H1fa zenon_H80 zenon_H1f zenon_H171 zenon_H1c zenon_H1e5 zenon_H1e9 zenon_H1eb zenon_H87 zenon_H37 zenon_H1ec. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c8 ]. % 21.03/21.27 apply (zenon_L33_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1c9 ]. % 21.03/21.27 exact (zenon_H1c6 zenon_H1ca). % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H81 | zenon_intro zenon_H8f ]. % 21.03/21.27 apply (zenon_L35_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_H81 | zenon_intro zenon_H1af ]. % 21.03/21.27 apply (zenon_L35_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H133 | zenon_intro zenon_H1b0 ]. % 21.03/21.27 apply (zenon_L81_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H9d | zenon_intro zenon_H187 ]. % 21.03/21.27 apply (zenon_L42_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H1fc | zenon_intro zenon_H1fb ]. % 21.03/21.27 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H174 | zenon_intro zenon_H175 ]. % 21.03/21.27 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((op1 (e10) (e13)) = (op1 (e11) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1fa. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H174. % 21.03/21.27 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H175]. % 21.03/21.27 cut (((op1 (e11) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e11) (e13)) = (op1 (e10) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1fd. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H80. % 21.03/21.27 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 21.03/21.27 cut (((e10) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1fe]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H174 | zenon_intro zenon_H175 ]. % 21.03/21.27 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e10) = (op1 (e11) (e13)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H1fe. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H174. % 21.03/21.27 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H175]. % 21.03/21.27 cut (((op1 (e11) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H1ff]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H1ff zenon_H1fc). % 21.03/21.27 apply zenon_H175. apply refl_equal. % 21.03/21.27 apply zenon_H175. apply refl_equal. % 21.03/21.27 apply (zenon_L106_); trivial. % 21.03/21.27 apply zenon_H175. apply refl_equal. % 21.03/21.27 apply zenon_H175. apply refl_equal. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H172 | zenon_intro zenon_H200 ]. % 21.03/21.27 apply (zenon_L91_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H1ea ]. % 21.03/21.27 apply (zenon_L117_); trivial. % 21.03/21.27 apply (zenon_L118_); trivial. % 21.03/21.27 (* end of lemma zenon_L119_ *) % 21.03/21.27 assert (zenon_L120_ : (((op2 (e22) (e22)) = (e22))/\(~((op2 (e22) (e22)) = (e22)))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H201. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H201). zenon_intro zenon_H203. zenon_intro zenon_H202. % 21.03/21.27 exact (zenon_H202 zenon_H203). % 21.03/21.27 (* end of lemma zenon_L120_ *) % 21.03/21.27 assert (zenon_L121_ : (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (e23))) -> ((op2 (e23) (e22)) = (e22)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H204 zenon_H34 zenon_H205. % 21.03/21.27 cut (((e22) = (op2 (e23) (e23))) = ((op2 (e23) (e22)) = (op2 (e23) (e23)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H204. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H34. % 21.03/21.27 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 21.03/21.27 cut (((e22) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op2 (e23) (e22)) = (op2 (e23) (e22)))); [ zenon_intro zenon_H10d | zenon_intro zenon_H10e ]. % 21.03/21.27 cut (((op2 (e23) (e22)) = (op2 (e23) (e22))) = ((e22) = (op2 (e23) (e22)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H206. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H10d. % 21.03/21.27 cut (((op2 (e23) (e22)) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H10e]. % 21.03/21.27 cut (((op2 (e23) (e22)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H207 zenon_H205). % 21.03/21.27 apply zenon_H10e. apply refl_equal. % 21.03/21.27 apply zenon_H10e. apply refl_equal. % 21.03/21.27 apply zenon_Hf5. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L121_ *) % 21.03/21.27 assert (zenon_L122_ : (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e20) (e23)) = (e20)) -> ((op2 (e21) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e22)) = (e21)) -> ((op2 (e22) (e23)) = (e21)) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (e23) (e23))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e22)) = (e23))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H208 zenon_H1dd zenon_H5c zenon_H1dc zenon_H14 zenon_Hbb zenon_H10a zenon_Hcd zenon_H37 zenon_H34 zenon_H204 zenon_H209. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_Hdd | zenon_intro zenon_H20a ]. % 21.03/21.27 apply (zenon_L115_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H10c | zenon_intro zenon_H20b ]. % 21.03/21.27 apply (zenon_L70_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H205 | zenon_intro zenon_H20c ]. % 21.03/21.27 apply (zenon_L121_); trivial. % 21.03/21.27 exact (zenon_H209 zenon_H20c). % 21.03/21.27 (* end of lemma zenon_L122_ *) % 21.03/21.27 assert (zenon_L123_ : (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e22)) = (e23))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e21)) -> ((op2 (e21) (e22)) = (e21)) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e20)) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (e23) (e23))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((e10) = (e11))) -> (~((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H20d zenon_H209 zenon_H204 zenon_Hcd zenon_H10a zenon_Hbb zenon_H14 zenon_H5c zenon_H1dd zenon_H208 zenon_Hc7 zenon_H34 zenon_H1e1 zenon_H1c5 zenon_H6a zenon_H7d zenon_H1c6 zenon_H1ab zenon_H7f zenon_H132 zenon_H9c zenon_H1f9 zenon_H1fa zenon_H80 zenon_H1f zenon_H171 zenon_H1c zenon_H1e5 zenon_H1e9 zenon_H87 zenon_H37 zenon_H1ec. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H1dc | zenon_intro zenon_H20e ]. % 21.03/21.27 apply (zenon_L122_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H20f ]. % 21.03/21.27 apply (zenon_L55_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1eb ]. % 21.03/21.27 apply (zenon_L116_); trivial. % 21.03/21.27 apply (zenon_L119_); trivial. % 21.03/21.27 (* end of lemma zenon_L123_ *) % 21.03/21.27 assert (zenon_L124_ : ((op2 (e22) (e20)) = (e20)) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e12)) (h4 (e10))))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H11d zenon_H13b zenon_H34 zenon_H13 zenon_H14 zenon_H210. % 21.03/21.27 elim (classic ((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10)))) = ((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e12)) (h4 (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H210. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H211. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H213]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op2 (e22) (e20)) = (e20)) = ((op2 (h4 (e12)) (h4 (e10))) = (op2 (e23) (op2 (e23) (e23))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H213. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H11d. % 21.03/21.27 cut (((e20) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 21.03/21.27 cut (((op2 (e22) (e20)) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10)))) = ((op2 (e22) (e20)) = (op2 (h4 (e12)) (h4 (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H215. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H211. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H216]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 21.03/21.27 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 21.03/21.27 congruence. % 21.03/21.27 apply (zenon_L83_); trivial. % 21.03/21.27 apply (zenon_L1_); trivial. % 21.03/21.27 apply zenon_H212. apply refl_equal. % 21.03/21.27 apply zenon_H212. apply refl_equal. % 21.03/21.27 exact (zenon_H214 zenon_H14). % 21.03/21.27 apply zenon_H212. apply refl_equal. % 21.03/21.27 apply zenon_H212. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L124_ *) % 21.03/21.27 assert (zenon_L125_ : (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> ((op1 (e12) (e10)) = (e10)) -> ((op2 (e22) (e20)) = (e20)) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H217 zenon_H138 zenon_H11d zenon_H13b zenon_H34 zenon_H13 zenon_H14. % 21.03/21.27 cut (((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) = ((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H217. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H13. % 21.03/21.27 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 21.03/21.27 cut (((h4 (e10)) = (h4 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10))))); [ zenon_intro zenon_H219 | zenon_intro zenon_H21a ]. % 21.03/21.27 cut (((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10)))) = ((h4 (e10)) = (h4 (op1 (e12) (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H218. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H219. % 21.03/21.27 cut (((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 21.03/21.27 cut (((h4 (op1 (e12) (e10))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op1 (e12) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H21c]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H21c zenon_H138). % 21.03/21.27 apply zenon_H21a. apply refl_equal. % 21.03/21.27 apply zenon_H21a. apply refl_equal. % 21.03/21.27 apply (zenon_L124_); trivial. % 21.03/21.27 (* end of lemma zenon_L125_ *) % 21.03/21.27 assert (zenon_L126_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((e10) = (e11))) -> (~((op1 (e10) (e11)) = (e10))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((op2 (e22) (e20)) = (e20)) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e10)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1c5 zenon_H6a zenon_H7d zenon_H1c6 zenon_H1be zenon_H14 zenon_H13 zenon_H34 zenon_H13b zenon_H11d zenon_H217 zenon_H18d zenon_H74 zenon_H1ab zenon_H7f zenon_H132 zenon_H9c zenon_H80 zenon_H1c zenon_H16b. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c8 ]. % 21.03/21.27 apply (zenon_L33_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1c9 ]. % 21.03/21.27 exact (zenon_H1c6 zenon_H1ca). % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H81 | zenon_intro zenon_H8f ]. % 21.03/21.27 apply (zenon_L35_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1be); [ zenon_intro zenon_H138 | zenon_intro zenon_H1bf ]. % 21.03/21.27 apply (zenon_L125_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H18c | zenon_intro zenon_H1c0 ]. % 21.03/21.27 apply (zenon_L105_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H9d | zenon_intro zenon_H1b8 ]. % 21.03/21.27 apply (zenon_L42_); trivial. % 21.03/21.27 apply (zenon_L107_); trivial. % 21.03/21.27 (* end of lemma zenon_L126_ *) % 21.03/21.27 assert (zenon_L127_ : ((op2 (e22) (e21)) = (e22)) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (e23) (e23))) -> (~((op2 (e23) (e23)) = (op2 (h4 (e12)) (h4 (e11))))) -> False). % 21.03/21.27 do 0 intro. intros zenon_Hf9 zenon_H13b zenon_H87 zenon_H37 zenon_H34 zenon_H21d. % 21.03/21.27 elim (classic ((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [ zenon_intro zenon_H21e | zenon_intro zenon_H21f ]. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11)))) = ((op2 (e23) (e23)) = (op2 (h4 (e12)) (h4 (e11))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H21d. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H21e. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H220]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op2 (e22) (e21)) = (e22)) = ((op2 (h4 (e12)) (h4 (e11))) = (op2 (e23) (e23)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H220. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_Hf9. % 21.03/21.27 cut (((e22) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H149]. % 21.03/21.27 cut (((op2 (e22) (e21)) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [ zenon_intro zenon_H21e | zenon_intro zenon_H21f ]. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11)))) = ((op2 (e22) (e21)) = (op2 (h4 (e12)) (h4 (e11))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H221. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H21e. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H222]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 21.03/21.27 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 21.03/21.27 congruence. % 21.03/21.27 apply (zenon_L83_); trivial. % 21.03/21.27 apply (zenon_L36_); trivial. % 21.03/21.27 apply zenon_H21f. apply refl_equal. % 21.03/21.27 apply zenon_H21f. apply refl_equal. % 21.03/21.27 exact (zenon_H149 zenon_H34). % 21.03/21.27 apply zenon_H21f. apply refl_equal. % 21.03/21.27 apply zenon_H21f. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L127_ *) % 21.03/21.27 assert (zenon_L128_ : (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((op1 (e12) (e11)) = (e12)) -> ((op2 (e22) (e21)) = (e22)) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H223 zenon_H155 zenon_Hf9 zenon_H13b zenon_H34 zenon_H87 zenon_H37. % 21.03/21.27 cut (((h4 (e12)) = (op2 (e23) (e23))) = ((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H223. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H13b. % 21.03/21.27 cut (((op2 (e23) (e23)) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 21.03/21.27 cut (((h4 (e12)) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H224]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [ zenon_intro zenon_H225 | zenon_intro zenon_H226 ]. % 21.03/21.27 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11)))) = ((h4 (e12)) = (h4 (op1 (e12) (e11))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H224. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H225. % 21.03/21.27 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H226]. % 21.03/21.27 cut (((h4 (op1 (e12) (e11))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H227]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op1 (e12) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H26 zenon_H155). % 21.03/21.27 apply zenon_H226. apply refl_equal. % 21.03/21.27 apply zenon_H226. apply refl_equal. % 21.03/21.27 apply (zenon_L127_); trivial. % 21.03/21.27 (* end of lemma zenon_L128_ *) % 21.03/21.27 assert (zenon_L129_ : (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e10)) -> ((op1 (e13) (e12)) = (e10)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (e13))) -> ((op1 (e13) (e11)) = (e11)) -> ((op1 (e12) (e13)) = (e11)) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((op2 (e22) (e21)) = (e22)) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H19c zenon_H18d zenon_H74 zenon_H187 zenon_H80 zenon_H1c zenon_H194 zenon_H177 zenon_H1f zenon_H196 zenon_H37 zenon_H87 zenon_H34 zenon_H13b zenon_Hf9 zenon_H223 zenon_H8a zenon_H159. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H18c | zenon_intro zenon_H19d ]. % 21.03/21.27 apply (zenon_L96_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H197 | zenon_intro zenon_H19e ]. % 21.03/21.27 apply (zenon_L98_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H155 | zenon_intro zenon_H19a ]. % 21.03/21.27 apply (zenon_L128_); trivial. % 21.03/21.27 apply (zenon_L99_); trivial. % 21.03/21.27 (* end of lemma zenon_L129_ *) % 21.03/21.27 assert (zenon_L130_ : (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e13)) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((op2 (e22) (e21)) = (e22)) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e13) (e11)) = (e11)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e10)) -> ((op1 (e11) (e11)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> ((e12) = (op1 (e13) (e13))) -> (~((e11) = (e12))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H183 zenon_H16b zenon_H171 zenon_H159 zenon_H8a zenon_H223 zenon_Hf9 zenon_H13b zenon_H34 zenon_H87 zenon_H37 zenon_H196 zenon_H1f zenon_H194 zenon_H80 zenon_H187 zenon_H74 zenon_H18d zenon_H19c zenon_H1c zenon_H29. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H16c | zenon_intro zenon_H184 ]. % 21.03/21.27 apply (zenon_L90_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H172 | zenon_intro zenon_H185 ]. % 21.03/21.27 apply (zenon_L91_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H177 | zenon_intro zenon_H28 ]. % 21.03/21.27 apply (zenon_L129_); trivial. % 21.03/21.27 apply (zenon_L8_); trivial. % 21.03/21.27 (* end of lemma zenon_L130_ *) % 21.03/21.27 assert (zenon_L131_ : (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e11) (e10)) = (e11))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e13)) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((op2 (e22) (e21)) = (e22)) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e11) (e11)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1a6 zenon_H1a7 zenon_H7d zenon_H29 zenon_H183 zenon_H16b zenon_H132 zenon_H159 zenon_H8a zenon_H223 zenon_Hf9 zenon_H13b zenon_H34 zenon_H87 zenon_H37 zenon_H196 zenon_H80 zenon_H74 zenon_H18d zenon_H19c zenon_H17d zenon_H6a zenon_H1a9 zenon_H9c zenon_H7f zenon_H1ab zenon_H171 zenon_H1f zenon_H1c. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_H1ad | zenon_intro zenon_H1ac ]. % 21.03/21.27 exact (zenon_H1a7 zenon_H1ad). % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H19 | zenon_intro zenon_H1ae ]. % 21.03/21.27 apply (zenon_L80_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1ae); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H172 ]. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_H81 | zenon_intro zenon_H1af ]. % 21.03/21.27 apply (zenon_L35_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H133 | zenon_intro zenon_H1b0 ]. % 21.03/21.27 apply (zenon_L81_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H9d | zenon_intro zenon_H187 ]. % 21.03/21.27 apply (zenon_L42_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_H17c | zenon_intro zenon_H1b4 ]. % 21.03/21.27 apply (zenon_L94_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H194 | zenon_intro zenon_H1b5 ]. % 21.03/21.27 apply (zenon_L130_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H28 ]. % 21.03/21.27 apply (zenon_L103_); trivial. % 21.03/21.27 apply (zenon_L8_); trivial. % 21.03/21.27 apply (zenon_L91_); trivial. % 21.03/21.27 (* end of lemma zenon_L131_ *) % 21.03/21.27 assert (zenon_L132_ : (((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e22) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e21) (e21)) = (e20)) -> ((op2 (e23) (e22)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e21)) -> ((op2 (e22) (e23)) = (e21)) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e12) = (op1 (e13) (e13))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e10)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (e23) (e23))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e10)) = (e11))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H106 zenon_He3 zenon_H5f zenon_Hdd zenon_H14 zenon_Hea zenon_Hcd zenon_Hec zenon_H1c zenon_H1f zenon_H171 zenon_H1ab zenon_H7f zenon_H9c zenon_H1a9 zenon_H6a zenon_H17d zenon_H19c zenon_H18d zenon_H74 zenon_H80 zenon_H196 zenon_H37 zenon_H87 zenon_H34 zenon_H13b zenon_H223 zenon_H8a zenon_H159 zenon_H132 zenon_H16b zenon_H183 zenon_H29 zenon_H7d zenon_H1a7 zenon_H1a6 zenon_H92 zenon_H103. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_He2 | zenon_intro zenon_H107 ]. % 21.03/21.27 apply (zenon_L60_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hed | zenon_intro zenon_H108 ]. % 21.03/21.27 apply (zenon_L62_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf9 | zenon_intro zenon_H102 ]. % 21.03/21.27 apply (zenon_L131_); trivial. % 21.03/21.27 apply (zenon_L66_); trivial. % 21.03/21.27 (* end of lemma zenon_L132_ *) % 21.03/21.27 assert (zenon_L133_ : (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e23)) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e11) (e10)) = (e11))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e13)) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e11) (e11)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((e12) = (op1 (e13) (e13))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e21)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e22)) = (e20)) -> ((op2 (e21) (e21)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e22) (e21)) = (e23))))) -> ((e22) = (op2 (e23) (e23))) -> (~((e21) = (e22))) -> False). % 21.03/21.27 do 0 intro. intros zenon_Hd9 zenon_Hc1 zenon_Hc7 zenon_H103 zenon_H92 zenon_H1a6 zenon_H1a7 zenon_H7d zenon_H29 zenon_H183 zenon_H16b zenon_H132 zenon_H159 zenon_H8a zenon_H223 zenon_H13b zenon_H87 zenon_H37 zenon_H196 zenon_H80 zenon_H74 zenon_H18d zenon_H19c zenon_H17d zenon_H6a zenon_H1a9 zenon_H9c zenon_H7f zenon_H1ab zenon_H171 zenon_H1f zenon_H1c zenon_Hec zenon_Hea zenon_H14 zenon_Hdd zenon_H5f zenon_He3 zenon_H106 zenon_H34 zenon_H41. % 21.03/21.27 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc2 | zenon_intro zenon_Hda ]. % 21.03/21.27 apply (zenon_L54_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hdb ]. % 21.03/21.27 apply (zenon_L55_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Hcd | zenon_intro zenon_H40 ]. % 21.03/21.27 apply (zenon_L132_); trivial. % 21.03/21.27 apply (zenon_L16_); trivial. % 21.03/21.27 (* end of lemma zenon_L133_ *) % 21.03/21.27 assert (zenon_L134_ : ((h4 (e13)) = (e23)) -> ((op1 (e12) (e12)) = (e13)) -> (~((e23) = (h4 (op1 (e12) (e12))))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1ec zenon_H8a zenon_H228. % 21.03/21.27 elim (classic ((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12))))); [ zenon_intro zenon_H229 | zenon_intro zenon_H22a ]. % 21.03/21.27 cut (((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12)))) = ((e23) = (h4 (op1 (e12) (e12))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H228. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H229. % 21.03/21.27 cut (((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H22a]. % 21.03/21.27 cut (((h4 (op1 (e12) (e12))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H22b]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e12) (e12))) = (e23))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H22b. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1ec. % 21.03/21.27 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 21.03/21.27 cut (((h4 (e13)) = (h4 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H22c]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12))))); [ zenon_intro zenon_H229 | zenon_intro zenon_H22a ]. % 21.03/21.27 cut (((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12)))) = ((h4 (e13)) = (h4 (op1 (e12) (e12))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H22c. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H229. % 21.03/21.27 cut (((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H22a]. % 21.03/21.27 cut (((h4 (op1 (e12) (e12))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H22d]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op1 (e12) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H22e]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H22e zenon_H8a). % 21.03/21.27 apply zenon_H22a. apply refl_equal. % 21.03/21.27 apply zenon_H22a. apply refl_equal. % 21.03/21.27 apply zenon_H32. apply refl_equal. % 21.03/21.27 apply zenon_H22a. apply refl_equal. % 21.03/21.27 apply zenon_H22a. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L134_ *) % 21.03/21.27 assert (zenon_L135_ : ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> ((op1 (e12) (e12)) = (e13)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H92 zenon_H13b zenon_H34 zenon_H1ec zenon_H8a zenon_H22f. % 21.03/21.27 elim (classic ((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [ zenon_intro zenon_H230 | zenon_intro zenon_H231 ]. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12)))) = ((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H22f. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H230. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H231]. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e12))) = (h4 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H232]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op2 (e22) (e22)) = (e23)) = ((op2 (h4 (e12)) (h4 (e12))) = (h4 (op1 (e12) (e12))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H232. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H92. % 21.03/21.27 cut (((e23) = (h4 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H228]. % 21.03/21.27 cut (((op2 (e22) (e22)) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H233]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [ zenon_intro zenon_H230 | zenon_intro zenon_H231 ]. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12)))) = ((op2 (e22) (e22)) = (op2 (h4 (e12)) (h4 (e12))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H233. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H230. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H231]. % 21.03/21.27 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H234]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 21.03/21.27 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 21.03/21.27 congruence. % 21.03/21.27 apply (zenon_L83_); trivial. % 21.03/21.27 apply (zenon_L83_); trivial. % 21.03/21.27 apply zenon_H231. apply refl_equal. % 21.03/21.27 apply zenon_H231. apply refl_equal. % 21.03/21.27 apply (zenon_L134_); trivial. % 21.03/21.27 apply zenon_H231. apply refl_equal. % 21.03/21.27 apply zenon_H231. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L135_ *) % 21.03/21.27 assert (zenon_L136_ : (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((op1 (e12) (e13)) = (e11)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (e23) (e23))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H235 zenon_H87 zenon_H177 zenon_H1ec zenon_H13b. % 21.03/21.27 cut (((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) = ((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H235. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H87. % 21.03/21.27 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H236]. % 21.03/21.27 cut (((h4 (e11)) = (h4 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H237]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13))))); [ zenon_intro zenon_H238 | zenon_intro zenon_H239 ]. % 21.03/21.27 cut (((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13)))) = ((h4 (e11)) = (h4 (op1 (e12) (e13))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H237. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H238. % 21.03/21.27 cut (((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H239]. % 21.03/21.27 cut (((h4 (op1 (e12) (e13))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H23a]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op1 (e12) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H23b]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H23b zenon_H177). % 21.03/21.27 apply zenon_H239. apply refl_equal. % 21.03/21.27 apply zenon_H239. apply refl_equal. % 21.03/21.27 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H23c]. % 21.03/21.27 cut (((op2 (e23) (e23)) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 21.03/21.27 congruence. % 21.03/21.27 apply zenon_H23d. apply sym_equal. exact zenon_H13b. % 21.03/21.27 apply zenon_H23c. apply sym_equal. exact zenon_H1ec. % 21.03/21.27 (* end of lemma zenon_L136_ *) % 21.03/21.27 assert (zenon_L137_ : (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e20)) -> ((e22) = (op2 (e23) (e23))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H23e zenon_H14 zenon_H23f zenon_H34. % 21.03/21.27 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e23) (e20)) = (op2 (e23) (e22)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H23e. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H14. % 21.03/21.27 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 21.03/21.27 cut (((e20) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H240]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd5 ]. % 21.03/21.27 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((e20) = (op2 (e23) (e20)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H240. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_Hd4. % 21.03/21.27 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 21.03/21.27 cut (((op2 (e23) (e20)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H241 zenon_H23f). % 21.03/21.27 apply zenon_Hd5. apply refl_equal. % 21.03/21.27 apply zenon_Hd5. apply refl_equal. % 21.03/21.27 apply (zenon_L21_); trivial. % 21.03/21.27 (* end of lemma zenon_L137_ *) % 21.03/21.27 assert (zenon_L138_ : (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e10)) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H242 zenon_H80 zenon_H243 zenon_H1c. % 21.03/21.27 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e13) (e10)) = (op1 (e13) (e12)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H242. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H80. % 21.03/21.27 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 21.03/21.27 cut (((e10) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H244]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H17e | zenon_intro zenon_H17f ]. % 21.03/21.27 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e10) = (op1 (e13) (e10)))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H244. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H17e. % 21.03/21.27 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 21.03/21.27 cut (((op1 (e13) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H245 zenon_H243). % 21.03/21.27 apply zenon_H17f. apply refl_equal. % 21.03/21.27 apply zenon_H17f. apply refl_equal. % 21.03/21.27 apply (zenon_L34_); trivial. % 21.03/21.27 (* end of lemma zenon_L138_ *) % 21.03/21.27 assert (zenon_L139_ : ((h4 (e13)) = (e23)) -> ((op1 (e13) (e10)) = (e13)) -> (~((e23) = (h4 (op1 (e13) (e10))))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1ec zenon_H246 zenon_H247. % 21.03/21.27 elim (classic ((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [ zenon_intro zenon_H248 | zenon_intro zenon_H249 ]. % 21.03/21.27 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10)))) = ((e23) = (h4 (op1 (e13) (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H247. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H248. % 21.03/21.27 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H249]. % 21.03/21.27 cut (((h4 (op1 (e13) (e10))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H24a]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e13) (e10))) = (e23))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H24a. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H1ec. % 21.03/21.27 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 21.03/21.27 cut (((h4 (e13)) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H24b]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [ zenon_intro zenon_H248 | zenon_intro zenon_H249 ]. % 21.03/21.27 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10)))) = ((h4 (e13)) = (h4 (op1 (e13) (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H24b. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H248. % 21.03/21.27 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H249]. % 21.03/21.27 cut (((h4 (op1 (e13) (e10))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H24c]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op1 (e13) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_Ha7 zenon_H246). % 21.03/21.27 apply zenon_H249. apply refl_equal. % 21.03/21.27 apply zenon_H249. apply refl_equal. % 21.03/21.27 apply zenon_H32. apply refl_equal. % 21.03/21.27 apply zenon_H249. apply refl_equal. % 21.03/21.27 apply zenon_H249. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L139_ *) % 21.03/21.27 assert (zenon_L140_ : ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((op1 (e13) (e10)) = (e13)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H24d zenon_H13 zenon_H14 zenon_H1ec zenon_H246 zenon_H24e. % 21.03/21.27 elim (classic ((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [ zenon_intro zenon_H24f | zenon_intro zenon_H250 ]. % 21.03/21.27 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10)))) = ((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H24e. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H24f. % 21.03/21.27 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H250]. % 21.03/21.27 cut (((op2 (h4 (e13)) (h4 (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H251]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op2 (e23) (e20)) = (e23)) = ((op2 (h4 (e13)) (h4 (e10))) = (h4 (op1 (e13) (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H251. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H24d. % 21.03/21.27 cut (((e23) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H247]. % 21.03/21.27 cut (((op2 (e23) (e20)) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H252]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [ zenon_intro zenon_H24f | zenon_intro zenon_H250 ]. % 21.03/21.27 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10)))) = ((op2 (e23) (e20)) = (op2 (h4 (e13)) (h4 (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H252. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H24f. % 21.03/21.27 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H250]. % 21.03/21.27 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H253]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 21.03/21.27 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H1f8 zenon_H1ec). % 21.03/21.27 apply (zenon_L1_); trivial. % 21.03/21.27 apply zenon_H250. apply refl_equal. % 21.03/21.27 apply zenon_H250. apply refl_equal. % 21.03/21.27 apply (zenon_L139_); trivial. % 21.03/21.27 apply zenon_H250. apply refl_equal. % 21.03/21.27 apply zenon_H250. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L140_ *) % 21.03/21.27 assert (zenon_L141_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e10)) = (e11)) -> ((op1 (e12) (e13)) = (e11)) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((e12) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H254 zenon_H80 zenon_H242 zenon_H17d zenon_H6a zenon_H177 zenon_H1f zenon_H1c zenon_H1c1 zenon_H24d zenon_H13 zenon_H14 zenon_H1ec zenon_H24e. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H243 | zenon_intro zenon_H255 ]. % 21.03/21.27 apply (zenon_L138_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H17c | zenon_intro zenon_H256 ]. % 21.03/21.27 apply (zenon_L93_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H246 ]. % 21.03/21.27 apply (zenon_L109_); trivial. % 21.03/21.27 apply (zenon_L140_); trivial. % 21.03/21.27 (* end of lemma zenon_L141_ *) % 21.03/21.27 assert (zenon_L142_ : (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((e12) = (op1 (e13) (e13))) -> (~((e11) = (e12))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H183 zenon_H16b zenon_H171 zenon_H24e zenon_H1ec zenon_H14 zenon_H13 zenon_H24d zenon_H1c1 zenon_H1f zenon_H6a zenon_H17d zenon_H242 zenon_H80 zenon_H254 zenon_H1c zenon_H29. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H16c | zenon_intro zenon_H184 ]. % 21.03/21.27 apply (zenon_L90_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H172 | zenon_intro zenon_H185 ]. % 21.03/21.27 apply (zenon_L91_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H177 | zenon_intro zenon_H28 ]. % 21.03/21.27 apply (zenon_L141_); trivial. % 21.03/21.27 apply (zenon_L8_); trivial. % 21.03/21.27 (* end of lemma zenon_L142_ *) % 21.03/21.27 assert (zenon_L143_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e20) (e20)) = (e21)) -> ((op2 (e22) (e23)) = (e21)) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (e23) (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((e12) = (op1 (e13) (e13))) -> (~((e11) = (e12))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H257 zenon_H23e zenon_Hd3 zenon_H4c zenon_Hcd zenon_H37 zenon_H34 zenon_H12a zenon_H183 zenon_H16b zenon_H171 zenon_H24e zenon_H1ec zenon_H14 zenon_H13 zenon_H1c1 zenon_H1f zenon_H6a zenon_H17d zenon_H242 zenon_H80 zenon_H254 zenon_H1c zenon_H29. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H23f | zenon_intro zenon_H258 ]. % 21.03/21.27 apply (zenon_L137_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H259 ]. % 21.03/21.27 apply (zenon_L57_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H12b | zenon_intro zenon_H24d ]. % 21.03/21.27 apply (zenon_L78_); trivial. % 21.03/21.27 apply (zenon_L142_); trivial. % 21.03/21.27 (* end of lemma zenon_L143_ *) % 21.03/21.27 assert (zenon_L144_ : ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((op1 (e13) (e11)) = (e11)) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> (~((e21) = (h4 (op1 (e13) (e11))))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H87 zenon_H194 zenon_H37 zenon_H25a. % 21.03/21.27 elim (classic ((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [ zenon_intro zenon_H25b | zenon_intro zenon_H25c ]. % 21.03/21.27 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11)))) = ((e21) = (h4 (op1 (e13) (e11))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H25a. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H25b. % 21.03/21.27 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H25c]. % 21.03/21.27 cut (((h4 (op1 (e13) (e11))) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H25d]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) = ((h4 (op1 (e13) (e11))) = (e21))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H25d. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H87. % 21.03/21.27 cut (((op2 (op2 (e23) (e23)) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 21.03/21.27 cut (((h4 (e11)) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [ zenon_intro zenon_H25b | zenon_intro zenon_H25c ]. % 21.03/21.27 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11)))) = ((h4 (e11)) = (h4 (op1 (e13) (e11))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H25e. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H25b. % 21.03/21.27 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H25c]. % 21.03/21.27 cut (((h4 (op1 (e13) (e11))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H25f]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op1 (e13) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H260]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H260 zenon_H194). % 21.03/21.27 apply zenon_H25c. apply refl_equal. % 21.03/21.27 apply zenon_H25c. apply refl_equal. % 21.03/21.27 apply zenon_H88. apply sym_equal. exact zenon_H37. % 21.03/21.27 apply zenon_H25c. apply refl_equal. % 21.03/21.27 apply zenon_H25c. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L144_ *) % 21.03/21.27 assert (zenon_L145_ : ((op2 (e23) (e21)) = (e21)) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> ((op1 (e13) (e11)) = (e11)) -> (~((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))) -> False). % 21.03/21.27 do 0 intro. intros zenon_Hea zenon_H1ec zenon_H87 zenon_H37 zenon_H194 zenon_H261. % 21.03/21.27 elim (classic ((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [ zenon_intro zenon_H262 | zenon_intro zenon_H263 ]. % 21.03/21.27 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11)))) = ((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H261. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H262. % 21.03/21.27 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H263]. % 21.03/21.27 cut (((op2 (h4 (e13)) (h4 (e11))) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op2 (e23) (e21)) = (e21)) = ((op2 (h4 (e13)) (h4 (e11))) = (h4 (op1 (e13) (e11))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H264. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_Hea. % 21.03/21.27 cut (((e21) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H25a]. % 21.03/21.27 cut (((op2 (e23) (e21)) = (op2 (h4 (e13)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H265]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [ zenon_intro zenon_H262 | zenon_intro zenon_H263 ]. % 21.03/21.27 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11)))) = ((op2 (e23) (e21)) = (op2 (h4 (e13)) (h4 (e11))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H265. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H262. % 21.03/21.27 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H263]. % 21.03/21.27 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H266]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 21.03/21.27 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H1f8 zenon_H1ec). % 21.03/21.27 apply (zenon_L36_); trivial. % 21.03/21.27 apply zenon_H263. apply refl_equal. % 21.03/21.27 apply zenon_H263. apply refl_equal. % 21.03/21.27 apply (zenon_L144_); trivial. % 21.03/21.27 apply zenon_H263. apply refl_equal. % 21.03/21.27 apply zenon_H263. apply refl_equal. % 21.03/21.27 (* end of lemma zenon_L145_ *) % 21.03/21.27 assert (zenon_L146_ : (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e11) (e10)) = (e11))) -> (~((e10) = (e11))) -> ((op1 (e11) (e11)) = (e10)) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op2 (e23) (e21)) = (e21)) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (e23))) -> (~((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (e13))) -> ((e12) = (op1 (e13) (e13))) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1a6 zenon_H1a7 zenon_H7d zenon_H74 zenon_H29 zenon_H183 zenon_H16b zenon_H132 zenon_Hea zenon_H1ec zenon_H87 zenon_H37 zenon_H261 zenon_H17d zenon_H6a zenon_H1a9 zenon_H171 zenon_H1f zenon_H1c. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_H1ad | zenon_intro zenon_H1ac ]. % 21.03/21.27 exact (zenon_H1a7 zenon_H1ad). % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H19 | zenon_intro zenon_H1ae ]. % 21.03/21.27 apply (zenon_L80_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1ae); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H172 ]. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_H17c | zenon_intro zenon_H1b4 ]. % 21.03/21.27 apply (zenon_L94_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H194 | zenon_intro zenon_H1b5 ]. % 21.03/21.27 apply (zenon_L145_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H28 ]. % 21.03/21.27 apply (zenon_L103_); trivial. % 21.03/21.27 apply (zenon_L8_); trivial. % 21.03/21.27 apply (zenon_L91_); trivial. % 21.03/21.27 (* end of lemma zenon_L146_ *) % 21.03/21.27 assert (zenon_L147_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H1ab zenon_H7f zenon_H132 zenon_H1c zenon_H80 zenon_H9c zenon_H267 zenon_H13 zenon_H13b zenon_H1ec. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_H81 | zenon_intro zenon_H1af ]. % 21.03/21.27 apply (zenon_L35_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H133 | zenon_intro zenon_H1b0 ]. % 21.03/21.27 apply (zenon_L81_); trivial. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H9d | zenon_intro zenon_H187 ]. % 21.03/21.27 apply (zenon_L42_); trivial. % 21.03/21.27 cut (((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) = ((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H267. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H13. % 21.03/21.27 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H268]. % 21.03/21.27 cut (((h4 (e10)) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H269]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [ zenon_intro zenon_H26a | zenon_intro zenon_H26b ]. % 21.03/21.27 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12)))) = ((h4 (e10)) = (h4 (op1 (e13) (e12))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H269. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H26a. % 21.03/21.27 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H26b]. % 21.03/21.27 cut (((h4 (op1 (e13) (e12))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H26c]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op1 (e13) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H26d]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H26d zenon_H187). % 21.03/21.27 apply zenon_H26b. apply refl_equal. % 21.03/21.27 apply zenon_H26b. apply refl_equal. % 21.03/21.27 cut (((op2 (e23) (e23)) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 21.03/21.27 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H23c]. % 21.03/21.27 congruence. % 21.03/21.27 apply zenon_H23c. apply sym_equal. exact zenon_H1ec. % 21.03/21.27 apply zenon_H23d. apply sym_equal. exact zenon_H13b. % 21.03/21.27 (* end of lemma zenon_L147_ *) % 21.03/21.27 assert (zenon_L148_ : (~((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))) -> ((h4 (e12)) = (op2 (e23) (e23))) -> ((e12) = (op1 (e13) (e13))) -> ((h4 (e13)) = (e23)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H26e zenon_H13b zenon_H1c zenon_H1ec. % 21.03/21.27 cut (((h4 (e12)) = (op2 (e23) (e23))) = ((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H26e. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H13b. % 21.03/21.27 cut (((op2 (e23) (e23)) = (op2 (h4 (e13)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 21.03/21.27 cut (((h4 (e12)) = (h4 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H270]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13))))); [ zenon_intro zenon_H271 | zenon_intro zenon_H272 ]. % 21.03/21.27 cut (((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13)))) = ((h4 (e12)) = (h4 (op1 (e13) (e13))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H270. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H271. % 21.03/21.27 cut (((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H272]. % 21.03/21.27 cut (((h4 (op1 (e13) (e13))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H273]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op1 (e13) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 21.03/21.27 congruence. % 21.03/21.27 apply zenon_H1d. apply sym_equal. exact zenon_H1c. % 21.03/21.27 apply zenon_H272. apply refl_equal. % 21.03/21.27 apply zenon_H272. apply refl_equal. % 21.03/21.27 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H23c]. % 21.03/21.27 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H23c]. % 21.03/21.27 congruence. % 21.03/21.27 apply zenon_H23c. apply sym_equal. exact zenon_H1ec. % 21.03/21.27 apply zenon_H23c. apply sym_equal. exact zenon_H1ec. % 21.03/21.27 (* end of lemma zenon_L148_ *) % 21.03/21.27 assert (zenon_L149_ : (~(((h4 (e10)) = (e23))\/(((h4 (e11)) = (e23))\/(((h4 (e12)) = (e23))\/((h4 (e13)) = (e23)))))) -> ((h4 (e13)) = (e23)) -> False). % 21.03/21.27 do 0 intro. intros zenon_H274 zenon_H1ec. % 21.03/21.27 apply (zenon_notor_s _ _ zenon_H274). zenon_intro zenon_H276. zenon_intro zenon_H275. % 21.03/21.27 apply (zenon_notor_s _ _ zenon_H275). zenon_intro zenon_H278. zenon_intro zenon_H277. % 21.03/21.27 apply (zenon_notor_s _ _ zenon_H277). zenon_intro zenon_H279. zenon_intro zenon_H1f8. % 21.03/21.27 exact (zenon_H1f8 zenon_H1ec). % 21.03/21.27 (* end of lemma zenon_L149_ *) % 21.03/21.27 apply NNPP. intro zenon_G. % 21.03/21.27 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H27b. zenon_intro zenon_H27a. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H27a). zenon_intro zenon_H27d. zenon_intro zenon_H27c. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H27c). zenon_intro zenon_H27f. zenon_intro zenon_H27e. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H27e). zenon_intro zenon_H281. zenon_intro zenon_H280. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H280). zenon_intro zenon_H283. zenon_intro zenon_H282. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H282). zenon_intro zenon_H285. zenon_intro zenon_H284. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H284). zenon_intro zenon_H287. zenon_intro zenon_H286. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H286). zenon_intro zenon_H1f9. zenon_intro zenon_H288. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H288). zenon_intro zenon_H28a. zenon_intro zenon_H289. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H289). zenon_intro zenon_H19c. zenon_intro zenon_H28b. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H28b). zenon_intro zenon_H28d. zenon_intro zenon_H28c. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H28c). zenon_intro zenon_H28f. zenon_intro zenon_H28e. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H28e). zenon_intro zenon_H254. zenon_intro zenon_H290. % 21.03/21.27 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H1c5. zenon_intro zenon_H291. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H291). zenon_intro zenon_H293. zenon_intro zenon_H292. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H292). zenon_intro zenon_H295. zenon_intro zenon_H294. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H294). zenon_intro zenon_H297. zenon_intro zenon_H296. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H296). zenon_intro zenon_H299. zenon_intro zenon_H298. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H298). zenon_intro zenon_H1c7. zenon_intro zenon_H29a. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29c. zenon_intro zenon_H29b. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H29b). zenon_intro zenon_H29e. zenon_intro zenon_H29d. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H29d). zenon_intro zenon_H2a0. zenon_intro zenon_H29f. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H29f). zenon_intro zenon_H2a2. zenon_intro zenon_H2a1. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2a1). zenon_intro zenon_H1a6. zenon_intro zenon_H2a3. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2a3). zenon_intro zenon_H2a5. zenon_intro zenon_H2a4. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2a4). zenon_intro zenon_H2a7. zenon_intro zenon_H2a6. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2a6). zenon_intro zenon_H2a9. zenon_intro zenon_H2a8. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2ab. zenon_intro zenon_H2aa. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2aa). zenon_intro zenon_H2ad. zenon_intro zenon_H2ac. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2ac). zenon_intro zenon_H1be. zenon_intro zenon_H2ae. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H1ab. zenon_intro zenon_H2af. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H2b1. zenon_intro zenon_H2b0. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H2b3. zenon_intro zenon_H2b2. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2b2). zenon_intro zenon_H1aa. zenon_intro zenon_H2b4. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2b4). zenon_intro zenon_H163. zenon_intro zenon_H2b5. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2b5). zenon_intro zenon_H2b7. zenon_intro zenon_H2b6. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2b6). zenon_intro zenon_H2b9. zenon_intro zenon_H2b8. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2b8). zenon_intro zenon_H2bb. zenon_intro zenon_H2ba. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2ba). zenon_intro zenon_H2bd. zenon_intro zenon_H2bc. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2bc). zenon_intro zenon_H1a9. zenon_intro zenon_H2be. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2be). zenon_intro zenon_H183. zenon_intro zenon_H2bf. % 21.03/21.27 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H2c1. zenon_intro zenon_H2c0. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2c0). zenon_intro zenon_H2c3. zenon_intro zenon_H2c2. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2c2). zenon_intro zenon_H2c5. zenon_intro zenon_H2c4. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2c4). zenon_intro zenon_H2c7. zenon_intro zenon_H2c6. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2c6). zenon_intro zenon_H2c9. zenon_intro zenon_H2c8. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2c8). zenon_intro zenon_H2cb. zenon_intro zenon_H2ca. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2ca). zenon_intro zenon_H2cd. zenon_intro zenon_H2cc. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2cc). zenon_intro zenon_H20d. zenon_intro zenon_H2ce. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2ce). zenon_intro zenon_H2d0. zenon_intro zenon_H2cf. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2cf). zenon_intro zenon_H106. zenon_intro zenon_H2d1. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2d1). zenon_intro zenon_H2d3. zenon_intro zenon_H2d2. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2d2). zenon_intro zenon_H2d5. zenon_intro zenon_H2d4. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2d4). zenon_intro zenon_H257. zenon_intro zenon_H2d6. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2d6). zenon_intro zenon_H2d8. zenon_intro zenon_H2d7. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2d7). zenon_intro zenon_H208. zenon_intro zenon_H2d9. % 21.03/21.27 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H56. zenon_intro zenon_H2da. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2da). zenon_intro zenon_H2dc. zenon_intro zenon_H2db. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2db). zenon_intro zenon_H2de. zenon_intro zenon_H2dd. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2dd). zenon_intro zenon_H2e0. zenon_intro zenon_H2df. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2df). zenon_intro zenon_H2e2. zenon_intro zenon_H2e1. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2e1). zenon_intro zenon_H2e4. zenon_intro zenon_H2e3. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2e3). zenon_intro zenon_H2e6. zenon_intro zenon_H2e5. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2e5). zenon_intro zenon_H2e8. zenon_intro zenon_H2e7. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2e7). zenon_intro zenon_H2ea. zenon_intro zenon_H2e9. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2e9). zenon_intro zenon_H2ec. zenon_intro zenon_H2eb. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2eb). zenon_intro zenon_H112. zenon_intro zenon_H2ed. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2ed). zenon_intro zenon_H2ef. zenon_intro zenon_H2ee. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H2f1. zenon_intro zenon_H2f0. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2f6). zenon_intro zenon_H127. zenon_intro zenon_H2f8. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2f8). zenon_intro zenon_H115. zenon_intro zenon_H2f9. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2f9). zenon_intro zenon_H2fb. zenon_intro zenon_H2fa. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2fa). zenon_intro zenon_H2fd. zenon_intro zenon_H2fc. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2fc). zenon_intro zenon_H2ff. zenon_intro zenon_H2fe. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H2fe). zenon_intro zenon_H301. zenon_intro zenon_H300. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H300). zenon_intro zenon_H303. zenon_intro zenon_H302. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H302). zenon_intro zenon_H305. zenon_intro zenon_H304. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H304). zenon_intro zenon_H307. zenon_intro zenon_H306. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H306). zenon_intro zenon_H309. zenon_intro zenon_H308. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H308). zenon_intro zenon_H114. zenon_intro zenon_H30a. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H30a). zenon_intro zenon_Hd9. zenon_intro zenon_H30b. % 21.03/21.27 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H30d. zenon_intro zenon_H30c. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H30c). zenon_intro zenon_H30f. zenon_intro zenon_H30e. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H30e). zenon_intro zenon_H17d. zenon_intro zenon_H310. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H310). zenon_intro zenon_H312. zenon_intro zenon_H311. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H311). zenon_intro zenon_H314. zenon_intro zenon_H313. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H313). zenon_intro zenon_H316. zenon_intro zenon_H315. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H315). zenon_intro zenon_H318. zenon_intro zenon_H317. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H317). zenon_intro zenon_H31a. zenon_intro zenon_H319. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H319). zenon_intro zenon_H31c. zenon_intro zenon_H31b. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H31b). zenon_intro zenon_H18d. zenon_intro zenon_H31d. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H31d). zenon_intro zenon_H31f. zenon_intro zenon_H31e. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H31e). zenon_intro zenon_H196. zenon_intro zenon_H320. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H320). zenon_intro zenon_H322. zenon_intro zenon_H321. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H321). zenon_intro zenon_H8c. zenon_intro zenon_H323. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H323). zenon_intro zenon_H7f. zenon_intro zenon_H324. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H324). zenon_intro zenon_H326. zenon_intro zenon_H325. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H325). zenon_intro zenon_H132. zenon_intro zenon_H327. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H327). zenon_intro zenon_H9c. zenon_intro zenon_H328. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H328). zenon_intro zenon_H1fa. zenon_intro zenon_H329. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H329). zenon_intro zenon_H16b. zenon_intro zenon_H32a. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H32a). zenon_intro zenon_H32c. zenon_intro zenon_H32b. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H32b). zenon_intro zenon_H171. zenon_intro zenon_H32d. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H32d). zenon_intro zenon_H1e5. zenon_intro zenon_H32e. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H32e). zenon_intro zenon_H330. zenon_intro zenon_H32f. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H32f). zenon_intro zenon_H332. zenon_intro zenon_H331. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H331). zenon_intro zenon_H334. zenon_intro zenon_H333. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H333). zenon_intro zenon_H336. zenon_intro zenon_H335. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H335). zenon_intro zenon_H338. zenon_intro zenon_H337. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H337). zenon_intro zenon_H33a. zenon_intro zenon_H339. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H339). zenon_intro zenon_H33c. zenon_intro zenon_H33b. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H33b). zenon_intro zenon_H33e. zenon_intro zenon_H33d. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H33d). zenon_intro zenon_H164. zenon_intro zenon_H33f. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H33f). zenon_intro zenon_H341. zenon_intro zenon_H340. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H340). zenon_intro zenon_H343. zenon_intro zenon_H342. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H342). zenon_intro zenon_H345. zenon_intro zenon_H344. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H344). zenon_intro zenon_H347. zenon_intro zenon_H346. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H346). zenon_intro zenon_H349. zenon_intro zenon_H348. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H348). zenon_intro zenon_H34b. zenon_intro zenon_H34a. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H34a). zenon_intro zenon_H34d. zenon_intro zenon_H34c. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H34c). zenon_intro zenon_H159. zenon_intro zenon_H34e. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H34e). zenon_intro zenon_H350. zenon_intro zenon_H34f. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H34f). zenon_intro zenon_H1e. zenon_intro zenon_H351. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H351). zenon_intro zenon_H353. zenon_intro zenon_H352. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H352). zenon_intro zenon_H242. zenon_intro zenon_H354. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H354). zenon_intro zenon_H1c1. zenon_intro zenon_H355. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H355). zenon_intro zenon_H357. zenon_intro zenon_H356. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H356). zenon_intro zenon_H358. zenon_intro zenon_H15d. % 21.03/21.27 apply (zenon_and_s _ _ ax6). zenon_intro zenon_H35a. zenon_intro zenon_H359. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H359). zenon_intro zenon_H35c. zenon_intro zenon_H35b. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H35b). zenon_intro zenon_Hd3. zenon_intro zenon_H35d. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H35d). zenon_intro zenon_H35f. zenon_intro zenon_H35e. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H35e). zenon_intro zenon_H361. zenon_intro zenon_H360. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H360). zenon_intro zenon_H363. zenon_intro zenon_H362. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H362). zenon_intro zenon_H365. zenon_intro zenon_H364. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H364). zenon_intro zenon_Hfc. zenon_intro zenon_H366. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H366). zenon_intro zenon_H368. zenon_intro zenon_H367. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H367). zenon_intro zenon_He3. zenon_intro zenon_H369. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H369). zenon_intro zenon_H36b. zenon_intro zenon_H36a. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H36a). zenon_intro zenon_Hec. zenon_intro zenon_H36c. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H36c). zenon_intro zenon_H36e. zenon_intro zenon_H36d. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H36d). zenon_intro zenon_H94. zenon_intro zenon_H36f. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H36f). zenon_intro zenon_H4e. zenon_intro zenon_H370. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H370). zenon_intro zenon_H372. zenon_intro zenon_H371. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H371). zenon_intro zenon_Hbb. zenon_intro zenon_H373. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H373). zenon_intro zenon_Hab. zenon_intro zenon_H374. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H374). zenon_intro zenon_H1dd. zenon_intro zenon_H375. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H375). zenon_intro zenon_Hc1. zenon_intro zenon_H376. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H376). zenon_intro zenon_H1cd. zenon_intro zenon_H377. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H377). zenon_intro zenon_Hc7. zenon_intro zenon_H378. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H378). zenon_intro zenon_H1e1. zenon_intro zenon_H379. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H379). zenon_intro zenon_H37b. zenon_intro zenon_H37a. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H37a). zenon_intro zenon_H37d. zenon_intro zenon_H37c. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H37c). zenon_intro zenon_H37f. zenon_intro zenon_H37e. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H37e). zenon_intro zenon_H381. zenon_intro zenon_H380. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H380). zenon_intro zenon_H383. zenon_intro zenon_H382. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H382). zenon_intro zenon_H385. zenon_intro zenon_H384. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H384). zenon_intro zenon_H387. zenon_intro zenon_H386. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H386). zenon_intro zenon_H389. zenon_intro zenon_H388. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H388). zenon_intro zenon_H38b. zenon_intro zenon_H38a. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H38a). zenon_intro zenon_H38d. zenon_intro zenon_H38c. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H38c). zenon_intro zenon_H38f. zenon_intro zenon_H38e. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H38e). zenon_intro zenon_H391. zenon_intro zenon_H390. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H390). zenon_intro zenon_H393. zenon_intro zenon_H392. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H392). zenon_intro zenon_H395. zenon_intro zenon_H394. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H394). zenon_intro zenon_H397. zenon_intro zenon_H396. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H396). zenon_intro zenon_H399. zenon_intro zenon_H398. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H398). zenon_intro zenon_H103. zenon_intro zenon_H39a. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H39a). zenon_intro zenon_H39c. zenon_intro zenon_H39b. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H39b). zenon_intro zenon_H36. zenon_intro zenon_H39d. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H39d). zenon_intro zenon_H39f. zenon_intro zenon_H39e. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H39e). zenon_intro zenon_H23e. zenon_intro zenon_H3a0. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3a0). zenon_intro zenon_H12a. zenon_intro zenon_H3a1. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3a1). zenon_intro zenon_H3a3. zenon_intro zenon_H3a2. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3a2). zenon_intro zenon_H3a4. zenon_intro zenon_H204. % 21.03/21.27 apply (zenon_and_s _ _ ax7). zenon_intro zenon_H7d. zenon_intro zenon_H3a5. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3a5). zenon_intro zenon_Ha3. zenon_intro zenon_H3a6. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3a6). zenon_intro zenon_H75. zenon_intro zenon_H3a7. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3a7). zenon_intro zenon_H29. zenon_intro zenon_H3a8. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3a8). zenon_intro zenon_H6c. zenon_intro zenon_H3a9. % 21.03/21.27 apply (zenon_and_s _ _ ax8). zenon_intro zenon_H4b. zenon_intro zenon_H3aa. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3aa). zenon_intro zenon_Hb2. zenon_intro zenon_H3ab. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3ab). zenon_intro zenon_H60. zenon_intro zenon_H3ac. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3ac). zenon_intro zenon_H41. zenon_intro zenon_H3ad. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3ad). zenon_intro zenon_H7a. zenon_intro zenon_H3ae. % 21.03/21.27 apply (zenon_and_s _ _ ax10). zenon_intro zenon_H3b0. zenon_intro zenon_H3af. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3af). zenon_intro zenon_H3b2. zenon_intro zenon_H3b1. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3b1). zenon_intro zenon_H3b4. zenon_intro zenon_H3b3. % 21.03/21.27 apply (zenon_and_s _ _ ax11). zenon_intro zenon_H3b6. zenon_intro zenon_H3b5. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3b5). zenon_intro zenon_H3b8. zenon_intro zenon_H3b7. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3b7). zenon_intro zenon_H3ba. zenon_intro zenon_H3b9. % 21.03/21.27 apply (zenon_and_s _ _ ax12). zenon_intro zenon_H80. zenon_intro zenon_H3bb. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3bb). zenon_intro zenon_H1f. zenon_intro zenon_H1c. % 21.03/21.27 apply (zenon_and_s _ _ ax13). zenon_intro zenon_H14. zenon_intro zenon_H3bc. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3bc). zenon_intro zenon_H37. zenon_intro zenon_H34. % 21.03/21.27 apply (zenon_and_s _ _ ax17). zenon_intro zenon_H1ec. zenon_intro zenon_H3bd. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3bd). zenon_intro zenon_H13. zenon_intro zenon_H3be. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3be). zenon_intro zenon_H87. zenon_intro zenon_H13b. % 21.03/21.27 apply (zenon_notor_s _ _ zenon_G). zenon_intro zenon_H3c0. zenon_intro zenon_H3bf. % 21.03/21.27 apply (zenon_notor_s _ _ zenon_H3bf). zenon_intro zenon_H3c2. zenon_intro zenon_H3c1. % 21.03/21.27 apply (zenon_notor_s _ _ zenon_H3c1). zenon_intro zenon_H3c4. zenon_intro zenon_H3c3. % 21.03/21.27 apply (zenon_notand_s _ _ zenon_H3c3); [ zenon_intro zenon_H3c6 | zenon_intro zenon_H3c5 ]. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H3b8); [ zenon_intro zenon_H3c8 | zenon_intro zenon_H3c7 ]. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H4c. zenon_intro zenon_H55. % 21.03/21.27 apply (zenon_or_s _ _ zenon_H3b2); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3c9 ]. % 21.03/21.27 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H6a. zenon_intro zenon_H1c6. % 21.03/21.27 cut (((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) = ((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H3c6. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H87. % 21.03/21.27 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3cb]. % 21.03/21.27 cut (((h4 (e11)) = (h4 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3cc]. % 21.03/21.27 congruence. % 21.03/21.27 elim (classic ((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10))))); [ zenon_intro zenon_H3cd | zenon_intro zenon_H3ce ]. % 21.03/21.27 cut (((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10)))) = ((h4 (e11)) = (h4 (op1 (e10) (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H3cc. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H3cd. % 21.03/21.27 cut (((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3ce]. % 21.03/21.27 cut (((h4 (op1 (e10) (e10))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H3cf]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op1 (e10) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3d0]. % 21.03/21.27 congruence. % 21.03/21.27 exact (zenon_H3d0 zenon_H6a). % 21.03/21.27 apply zenon_H3ce. apply refl_equal. % 21.03/21.27 apply zenon_H3ce. apply refl_equal. % 21.03/21.27 elim (classic ((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [ zenon_intro zenon_H3d1 | zenon_intro zenon_H3d2 ]. % 21.03/21.27 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10)))) = ((op2 (op2 (e23) (e23)) (e23)) = (op2 (h4 (e10)) (h4 (e10))))). % 21.03/21.27 intro zenon_D_pnotp. % 21.03/21.27 apply zenon_H3cb. % 21.03/21.27 rewrite <- zenon_D_pnotp. % 21.03/21.27 exact zenon_H3d1. % 21.03/21.27 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3d2]. % 21.03/21.27 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3d3]. % 21.03/21.27 congruence. % 21.03/21.27 cut (((op2 (e20) (e20)) = (e21)) = ((op2 (h4 (e10)) (h4 (e10))) = (op2 (op2 (e23) (e23)) (e23)))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H3d3. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H4c. % 21.03/21.28 cut (((e21) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3d4]. % 21.03/21.28 cut (((op2 (e20) (e20)) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3d5]. % 21.03/21.28 congruence. % 21.03/21.28 elim (classic ((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [ zenon_intro zenon_H3d1 | zenon_intro zenon_H3d2 ]. % 21.03/21.28 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10)))) = ((op2 (e20) (e20)) = (op2 (h4 (e10)) (h4 (e10))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H3d5. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H3d1. % 21.03/21.28 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3d2]. % 21.03/21.28 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H3d6]. % 21.03/21.28 congruence. % 21.03/21.28 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 21.03/21.28 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 21.03/21.28 congruence. % 21.03/21.28 apply (zenon_L1_); trivial. % 21.03/21.28 apply (zenon_L1_); trivial. % 21.03/21.28 apply zenon_H3d2. apply refl_equal. % 21.03/21.28 apply zenon_H3d2. apply refl_equal. % 21.03/21.28 exact (zenon_H3d4 zenon_H37). % 21.03/21.28 apply zenon_H3d2. apply refl_equal. % 21.03/21.28 apply zenon_H3d2. apply refl_equal. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c9); [ zenon_intro zenon_H17 | zenon_intro zenon_H3d7 ]. % 21.03/21.28 apply (zenon_L2_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d7); [ zenon_intro zenon_H25 | zenon_intro zenon_H2d ]. % 21.03/21.28 apply (zenon_L6_); trivial. % 21.03/21.28 apply (zenon_L9_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c7); [ zenon_intro zenon_H2f | zenon_intro zenon_H3d8 ]. % 21.03/21.28 apply (zenon_L10_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H3d | zenon_intro zenon_H45 ]. % 21.03/21.28 apply (zenon_L14_); trivial. % 21.03/21.28 apply (zenon_L17_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H3c5); [ zenon_intro zenon_H3da | zenon_intro zenon_H3d9 ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b6); [ zenon_intro zenon_H47 | zenon_intro zenon_H3db ]. % 21.03/21.28 apply (zenon_L18_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3dd | zenon_intro zenon_H3dc ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H5f. zenon_intro zenon_H113. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b8); [ zenon_intro zenon_H3c8 | zenon_intro zenon_H3c7 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H4c. zenon_intro zenon_H55. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b9); [ zenon_intro zenon_H54 | zenon_intro zenon_H3de ]. % 21.03/21.28 apply (zenon_L23_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3de); [ zenon_intro zenon_H5e | zenon_intro zenon_H3df ]. % 21.03/21.28 apply (zenon_L25_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3df); [ zenon_intro zenon_H3e0 | zenon_intro zenon_Ha8 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e0). zenon_intro zenon_H92. zenon_intro zenon_H3e1. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b0); [ zenon_intro zenon_H66 | zenon_intro zenon_H3e2 ]. % 21.03/21.28 apply (zenon_L26_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e2); [ zenon_intro zenon_H3e4 | zenon_intro zenon_H3e3 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e4). zenon_intro zenon_H74. zenon_intro zenon_H1a7. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b2); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3c9 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H6a. zenon_intro zenon_H1c6. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b3); [ zenon_intro zenon_H70 | zenon_intro zenon_H3e5 ]. % 21.03/21.28 apply (zenon_L29_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e5); [ zenon_intro zenon_H73 | zenon_intro zenon_H3e6 ]. % 21.03/21.28 apply (zenon_L31_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e6); [ zenon_intro zenon_H3e7 | zenon_intro zenon_H99 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e7). zenon_intro zenon_H8a. zenon_intro zenon_H1a8. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H49 | zenon_intro zenon_H59 ]. % 21.03/21.28 apply (zenon_L20_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 21.03/21.28 exact (zenon_H55 zenon_H5b). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4f | zenon_intro zenon_H5c ]. % 21.03/21.28 apply (zenon_L22_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H2e6); [ zenon_intro zenon_H58 | zenon_intro zenon_H3e8 ]. % 21.03/21.28 apply (zenon_L32_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e8); [ zenon_intro zenon_H3ea | zenon_intro zenon_H3e9 ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c8 ]. % 21.03/21.28 apply (zenon_L33_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1c9 ]. % 21.03/21.28 exact (zenon_H1c6 zenon_H1ca). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H81 | zenon_intro zenon_H8f ]. % 21.03/21.28 apply (zenon_L35_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H29c); [ zenon_intro zenon_H6b | zenon_intro zenon_H3eb ]. % 21.03/21.28 apply (zenon_L28_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3eb); [ zenon_intro zenon_H3ed | zenon_intro zenon_H3ec ]. % 21.03/21.28 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H3da. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H1ec. % 21.03/21.28 cut (((e23) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3ee]. % 21.03/21.28 cut (((h4 (e13)) = (h4 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3ef]. % 21.03/21.28 congruence. % 21.03/21.28 elim (classic ((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11))))); [ zenon_intro zenon_H3f0 | zenon_intro zenon_H3f1 ]. % 21.03/21.28 cut (((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11)))) = ((h4 (e13)) = (h4 (op1 (e10) (e11))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H3ef. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H3f0. % 21.03/21.28 cut (((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3f1]. % 21.03/21.28 cut (((h4 (op1 (e10) (e11))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H3f2]. % 21.03/21.28 congruence. % 21.03/21.28 cut (((op1 (e10) (e11)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H3f3]. % 21.03/21.28 congruence. % 21.03/21.28 exact (zenon_H3f3 zenon_H3ed). % 21.03/21.28 apply zenon_H3f1. apply refl_equal. % 21.03/21.28 apply zenon_H3f1. apply refl_equal. % 21.03/21.28 elim (classic ((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [ zenon_intro zenon_H3f4 | zenon_intro zenon_H3f5 ]. % 21.03/21.28 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11)))) = ((e23) = (op2 (h4 (e10)) (h4 (e11))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H3ee. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H3f4. % 21.03/21.28 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3f5]. % 21.03/21.28 cut (((op2 (h4 (e10)) (h4 (e11))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H3f6]. % 21.03/21.28 congruence. % 21.03/21.28 cut (((op2 (e20) (e21)) = (e23)) = ((op2 (h4 (e10)) (h4 (e11))) = (e23))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H3f6. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H3ea. % 21.03/21.28 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 21.03/21.28 cut (((op2 (e20) (e21)) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3f7]. % 21.03/21.28 congruence. % 21.03/21.28 elim (classic ((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [ zenon_intro zenon_H3f4 | zenon_intro zenon_H3f5 ]. % 21.03/21.28 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11)))) = ((op2 (e20) (e21)) = (op2 (h4 (e10)) (h4 (e11))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H3f7. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H3f4. % 21.03/21.28 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3f5]. % 21.03/21.28 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H3f8]. % 21.03/21.28 congruence. % 21.03/21.28 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 21.03/21.28 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 21.03/21.28 congruence. % 21.03/21.28 apply (zenon_L1_); trivial. % 21.03/21.28 apply (zenon_L36_); trivial. % 21.03/21.28 apply zenon_H3f5. apply refl_equal. % 21.03/21.28 apply zenon_H3f5. apply refl_equal. % 21.03/21.28 apply zenon_H32. apply refl_equal. % 21.03/21.28 apply zenon_H3f5. apply refl_equal. % 21.03/21.28 apply zenon_H3f5. apply refl_equal. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3ec); [ zenon_intro zenon_H8b | zenon_intro zenon_H90 ]. % 21.03/21.28 apply (zenon_L37_); trivial. % 21.03/21.28 apply (zenon_L38_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e9); [ zenon_intro zenon_H93 | zenon_intro zenon_H97 ]. % 21.03/21.28 apply (zenon_L39_); trivial. % 21.03/21.28 apply (zenon_L40_); trivial. % 21.03/21.28 apply (zenon_L41_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c9); [ zenon_intro zenon_H17 | zenon_intro zenon_H3d7 ]. % 21.03/21.28 apply (zenon_L2_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d7); [ zenon_intro zenon_H25 | zenon_intro zenon_H2d ]. % 21.03/21.28 apply (zenon_L6_); trivial. % 21.03/21.28 apply (zenon_L9_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha6 ]. % 21.03/21.28 apply (zenon_L43_); trivial. % 21.03/21.28 apply (zenon_L45_); trivial. % 21.03/21.28 apply (zenon_L46_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c7); [ zenon_intro zenon_H2f | zenon_intro zenon_H3d8 ]. % 21.03/21.28 apply (zenon_L10_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H3d | zenon_intro zenon_H45 ]. % 21.03/21.28 apply (zenon_L14_); trivial. % 21.03/21.28 apply (zenon_L17_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3dc); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 21.03/21.28 apply (zenon_L48_); trivial. % 21.03/21.28 apply (zenon_L50_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H3d9); [ zenon_intro zenon_H13d | zenon_intro zenon_H3f9 ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b6); [ zenon_intro zenon_H47 | zenon_intro zenon_H3db ]. % 21.03/21.28 apply (zenon_L18_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3dd | zenon_intro zenon_H3dc ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H5f. zenon_intro zenon_H113. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b8); [ zenon_intro zenon_H3c8 | zenon_intro zenon_H3c7 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H4c. zenon_intro zenon_H55. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b9); [ zenon_intro zenon_H54 | zenon_intro zenon_H3de ]. % 21.03/21.28 apply (zenon_L23_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3de); [ zenon_intro zenon_H5e | zenon_intro zenon_H3df ]. % 21.03/21.28 apply (zenon_L25_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3df); [ zenon_intro zenon_H3e0 | zenon_intro zenon_Ha8 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e0). zenon_intro zenon_H92. zenon_intro zenon_H3e1. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b0); [ zenon_intro zenon_H66 | zenon_intro zenon_H3e2 ]. % 21.03/21.28 apply (zenon_L26_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e2); [ zenon_intro zenon_H3e4 | zenon_intro zenon_H3e3 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e4). zenon_intro zenon_H74. zenon_intro zenon_H1a7. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b2); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3c9 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H6a. zenon_intro zenon_H1c6. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b3); [ zenon_intro zenon_H70 | zenon_intro zenon_H3e5 ]. % 21.03/21.28 apply (zenon_L29_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e5); [ zenon_intro zenon_H73 | zenon_intro zenon_H3e6 ]. % 21.03/21.28 apply (zenon_L31_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e6); [ zenon_intro zenon_H3e7 | zenon_intro zenon_H99 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e7). zenon_intro zenon_H8a. zenon_intro zenon_H1a8. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H49 | zenon_intro zenon_H59 ]. % 21.03/21.28 apply (zenon_L20_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 21.03/21.28 exact (zenon_H55 zenon_H5b). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4f | zenon_intro zenon_H5c ]. % 21.03/21.28 apply (zenon_L22_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H3fa ]. % 21.03/21.28 apply (zenon_L51_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3fa); [ zenon_intro zenon_Hfd | zenon_intro zenon_H3fb ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H3fc ]. % 21.03/21.28 apply (zenon_L51_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3fc); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H3fd ]. % 21.03/21.28 apply (zenon_L72_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3fd); [ zenon_intro zenon_H11e | zenon_intro zenon_H12b ]. % 21.03/21.28 apply (zenon_L77_); trivial. % 21.03/21.28 apply (zenon_L78_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3fb); [ zenon_intro zenon_H13f | zenon_intro zenon_H1ce ]. % 21.03/21.28 apply (zenon_L110_); trivial. % 21.03/21.28 apply (zenon_L111_); trivial. % 21.03/21.28 apply (zenon_L41_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c9); [ zenon_intro zenon_H17 | zenon_intro zenon_H3d7 ]. % 21.03/21.28 apply (zenon_L2_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d7); [ zenon_intro zenon_H25 | zenon_intro zenon_H2d ]. % 21.03/21.28 apply (zenon_L6_); trivial. % 21.03/21.28 apply (zenon_L9_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha6 ]. % 21.03/21.28 apply (zenon_L43_); trivial. % 21.03/21.28 apply (zenon_L45_); trivial. % 21.03/21.28 apply (zenon_L46_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c7); [ zenon_intro zenon_H2f | zenon_intro zenon_H3d8 ]. % 21.03/21.28 apply (zenon_L10_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H3d | zenon_intro zenon_H45 ]. % 21.03/21.28 apply (zenon_L14_); trivial. % 21.03/21.28 apply (zenon_L17_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3dc); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 21.03/21.28 apply (zenon_L48_); trivial. % 21.03/21.28 apply (zenon_L50_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H3f9); [ zenon_intro zenon_H3ff | zenon_intro zenon_H3fe ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b8); [ zenon_intro zenon_H3c8 | zenon_intro zenon_H3c7 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H4c. zenon_intro zenon_H55. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b2); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3c9 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H6a. zenon_intro zenon_H1c6. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H49 | zenon_intro zenon_H59 ]. % 21.03/21.28 apply (zenon_L20_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 21.03/21.28 exact (zenon_H55 zenon_H5b). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4f | zenon_intro zenon_H5c ]. % 21.03/21.28 apply (zenon_L22_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c8 ]. % 21.03/21.28 apply (zenon_L33_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1c9 ]. % 21.03/21.28 exact (zenon_H1c6 zenon_H1ca). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H81 | zenon_intro zenon_H8f ]. % 21.03/21.28 apply (zenon_L35_); trivial. % 21.03/21.28 cut (((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) = ((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H3ff. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H13. % 21.03/21.28 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H400]. % 21.03/21.28 cut (((h4 (e10)) = (h4 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H401]. % 21.03/21.28 congruence. % 21.03/21.28 elim (classic ((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13))))); [ zenon_intro zenon_H402 | zenon_intro zenon_H403 ]. % 21.03/21.28 cut (((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13)))) = ((h4 (e10)) = (h4 (op1 (e10) (e13))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H401. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H402. % 21.03/21.28 cut (((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H403]. % 21.03/21.28 cut (((h4 (op1 (e10) (e13))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H404]. % 21.03/21.28 congruence. % 21.03/21.28 cut (((op1 (e10) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 21.03/21.28 congruence. % 21.03/21.28 exact (zenon_H71 zenon_H8f). % 21.03/21.28 apply zenon_H403. apply refl_equal. % 21.03/21.28 apply zenon_H403. apply refl_equal. % 21.03/21.28 elim (classic ((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [ zenon_intro zenon_H405 | zenon_intro zenon_H406 ]. % 21.03/21.28 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13)))) = ((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e10)) (h4 (e13))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H400. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H405. % 21.03/21.28 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H406]. % 21.03/21.28 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H407]. % 21.03/21.28 congruence. % 21.03/21.28 cut (((op2 (e20) (e23)) = (e20)) = ((op2 (h4 (e10)) (h4 (e13))) = (op2 (e23) (op2 (e23) (e23))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H407. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H5c. % 21.03/21.28 cut (((e20) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 21.03/21.28 cut (((op2 (e20) (e23)) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H408]. % 21.03/21.28 congruence. % 21.03/21.28 elim (classic ((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [ zenon_intro zenon_H405 | zenon_intro zenon_H406 ]. % 21.03/21.28 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13)))) = ((op2 (e20) (e23)) = (op2 (h4 (e10)) (h4 (e13))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H408. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H405. % 21.03/21.28 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H406]. % 21.03/21.28 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H409]. % 21.03/21.28 congruence. % 21.03/21.28 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 21.03/21.28 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 21.03/21.28 congruence. % 21.03/21.28 apply (zenon_L1_); trivial. % 21.03/21.28 exact (zenon_H1f8 zenon_H1ec). % 21.03/21.28 apply zenon_H406. apply refl_equal. % 21.03/21.28 apply zenon_H406. apply refl_equal. % 21.03/21.28 exact (zenon_H214 zenon_H14). % 21.03/21.28 apply zenon_H406. apply refl_equal. % 21.03/21.28 apply zenon_H406. apply refl_equal. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c9); [ zenon_intro zenon_H17 | zenon_intro zenon_H3d7 ]. % 21.03/21.28 apply (zenon_L2_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d7); [ zenon_intro zenon_H25 | zenon_intro zenon_H2d ]. % 21.03/21.28 apply (zenon_L6_); trivial. % 21.03/21.28 apply (zenon_L9_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c7); [ zenon_intro zenon_H2f | zenon_intro zenon_H3d8 ]. % 21.03/21.28 apply (zenon_L10_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H3d | zenon_intro zenon_H45 ]. % 21.03/21.28 apply (zenon_L14_); trivial. % 21.03/21.28 apply (zenon_L17_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H3fe); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H40a ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b6); [ zenon_intro zenon_H47 | zenon_intro zenon_H3db ]. % 21.03/21.28 apply (zenon_L18_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3dd | zenon_intro zenon_H3dc ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H5f. zenon_intro zenon_H113. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b8); [ zenon_intro zenon_H3c8 | zenon_intro zenon_H3c7 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H4c. zenon_intro zenon_H55. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b0); [ zenon_intro zenon_H66 | zenon_intro zenon_H3e2 ]. % 21.03/21.28 apply (zenon_L26_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e2); [ zenon_intro zenon_H3e4 | zenon_intro zenon_H3e3 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e4). zenon_intro zenon_H74. zenon_intro zenon_H1a7. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b2); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3c9 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H6a. zenon_intro zenon_H1c6. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H49 | zenon_intro zenon_H59 ]. % 21.03/21.28 apply (zenon_L20_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 21.03/21.28 exact (zenon_H55 zenon_H5b). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4f | zenon_intro zenon_H5c ]. % 21.03/21.28 apply (zenon_L22_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H3fc ]. % 21.03/21.28 apply (zenon_L51_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3fc); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H3fd ]. % 21.03/21.28 apply (zenon_L114_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3fd); [ zenon_intro zenon_H11e | zenon_intro zenon_H12b ]. % 21.03/21.28 apply (zenon_L77_); trivial. % 21.03/21.28 apply (zenon_L78_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c9); [ zenon_intro zenon_H17 | zenon_intro zenon_H3d7 ]. % 21.03/21.28 apply (zenon_L2_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d7); [ zenon_intro zenon_H25 | zenon_intro zenon_H2d ]. % 21.03/21.28 apply (zenon_L6_); trivial. % 21.03/21.28 apply (zenon_L9_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha6 ]. % 21.03/21.28 apply (zenon_L43_); trivial. % 21.03/21.28 apply (zenon_L45_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c7); [ zenon_intro zenon_H2f | zenon_intro zenon_H3d8 ]. % 21.03/21.28 apply (zenon_L10_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H3d | zenon_intro zenon_H45 ]. % 21.03/21.28 apply (zenon_L14_); trivial. % 21.03/21.28 apply (zenon_L17_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3dc); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 21.03/21.28 apply (zenon_L48_); trivial. % 21.03/21.28 apply (zenon_L50_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H40a); [ zenon_intro zenon_H40c | zenon_intro zenon_H40b ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b6); [ zenon_intro zenon_H47 | zenon_intro zenon_H3db ]. % 21.03/21.28 apply (zenon_L18_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3dd | zenon_intro zenon_H3dc ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H5f. zenon_intro zenon_H113. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b0); [ zenon_intro zenon_H66 | zenon_intro zenon_H3e2 ]. % 21.03/21.28 apply (zenon_L26_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e2); [ zenon_intro zenon_H3e4 | zenon_intro zenon_H3e3 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e4). zenon_intro zenon_H74. zenon_intro zenon_H1a7. % 21.03/21.28 cut (((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) = ((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H40c. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H13. % 21.03/21.28 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H40d]. % 21.03/21.28 cut (((h4 (e10)) = (h4 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H40e]. % 21.03/21.28 congruence. % 21.03/21.28 elim (classic ((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11))))); [ zenon_intro zenon_H40f | zenon_intro zenon_H410 ]. % 21.03/21.28 cut (((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11)))) = ((h4 (e10)) = (h4 (op1 (e11) (e11))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H40e. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H40f. % 21.03/21.28 cut (((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H410]. % 21.03/21.28 cut (((h4 (op1 (e11) (e11))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H411]. % 21.03/21.28 congruence. % 21.03/21.28 cut (((op1 (e11) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H412]. % 21.03/21.28 congruence. % 21.03/21.28 exact (zenon_H412 zenon_H74). % 21.03/21.28 apply zenon_H410. apply refl_equal. % 21.03/21.28 apply zenon_H410. apply refl_equal. % 21.03/21.28 elim (classic ((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [ zenon_intro zenon_H413 | zenon_intro zenon_H414 ]. % 21.03/21.28 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11)))) = ((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e11)) (h4 (e11))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H40d. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H413. % 21.03/21.28 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H414]. % 21.03/21.28 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H415]. % 21.03/21.28 congruence. % 21.03/21.28 cut (((op2 (e21) (e21)) = (e20)) = ((op2 (h4 (e11)) (h4 (e11))) = (op2 (e23) (op2 (e23) (e23))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H415. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H5f. % 21.03/21.28 cut (((e20) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 21.03/21.28 cut (((op2 (e21) (e21)) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H416]. % 21.03/21.28 congruence. % 21.03/21.28 elim (classic ((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [ zenon_intro zenon_H413 | zenon_intro zenon_H414 ]. % 21.03/21.28 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11)))) = ((op2 (e21) (e21)) = (op2 (h4 (e11)) (h4 (e11))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H416. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H413. % 21.03/21.28 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H414]. % 21.03/21.28 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H417]. % 21.03/21.28 congruence. % 21.03/21.28 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 21.03/21.28 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 21.03/21.28 congruence. % 21.03/21.28 apply (zenon_L36_); trivial. % 21.03/21.28 apply (zenon_L36_); trivial. % 21.03/21.28 apply zenon_H414. apply refl_equal. % 21.03/21.28 apply zenon_H414. apply refl_equal. % 21.03/21.28 exact (zenon_H214 zenon_H14). % 21.03/21.28 apply zenon_H414. apply refl_equal. % 21.03/21.28 apply zenon_H414. apply refl_equal. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha6 ]. % 21.03/21.28 apply (zenon_L43_); trivial. % 21.03/21.28 apply (zenon_L45_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3dc); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 21.03/21.28 apply (zenon_L48_); trivial. % 21.03/21.28 apply (zenon_L50_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H40b); [ zenon_intro zenon_H419 | zenon_intro zenon_H418 ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b6); [ zenon_intro zenon_H47 | zenon_intro zenon_H3db ]. % 21.03/21.28 apply (zenon_L18_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3dd | zenon_intro zenon_H3dc ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H5f. zenon_intro zenon_H113. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b0); [ zenon_intro zenon_H66 | zenon_intro zenon_H3e2 ]. % 21.03/21.28 apply (zenon_L26_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e2); [ zenon_intro zenon_H3e4 | zenon_intro zenon_H3e3 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e4). zenon_intro zenon_H74. zenon_intro zenon_H1a7. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_H117 | zenon_intro zenon_H116 ]. % 21.03/21.28 exact (zenon_H113 zenon_H117). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H31 | zenon_intro zenon_H118 ]. % 21.03/21.28 apply (zenon_L52_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10a | zenon_intro zenon_Hc8 ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_H1ad | zenon_intro zenon_H1ac ]. % 21.03/21.28 exact (zenon_H1a7 zenon_H1ad). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H19 | zenon_intro zenon_H1ae ]. % 21.03/21.28 apply (zenon_L80_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H1ae); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H172 ]. % 21.03/21.28 cut (((h4 (e11)) = (op2 (op2 (e23) (e23)) (e23))) = ((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H419. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H87. % 21.03/21.28 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H41a]. % 21.03/21.28 cut (((h4 (e11)) = (h4 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H41b]. % 21.03/21.28 congruence. % 21.03/21.28 elim (classic ((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12))))); [ zenon_intro zenon_H41c | zenon_intro zenon_H41d ]. % 21.03/21.28 cut (((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12)))) = ((h4 (e11)) = (h4 (op1 (e11) (e12))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H41b. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H41c. % 21.03/21.28 cut (((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H41d]. % 21.03/21.28 cut (((h4 (op1 (e11) (e12))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H41e]. % 21.03/21.28 congruence. % 21.03/21.28 cut (((op1 (e11) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H41f]. % 21.03/21.28 congruence. % 21.03/21.28 exact (zenon_H41f zenon_H1a0). % 21.03/21.28 apply zenon_H41d. apply refl_equal. % 21.03/21.28 apply zenon_H41d. apply refl_equal. % 21.03/21.28 elim (classic ((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [ zenon_intro zenon_H420 | zenon_intro zenon_H421 ]. % 21.03/21.28 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12)))) = ((op2 (op2 (e23) (e23)) (e23)) = (op2 (h4 (e11)) (h4 (e12))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H41a. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H420. % 21.03/21.28 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H421]. % 21.03/21.28 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H422]. % 21.03/21.28 congruence. % 21.03/21.28 cut (((op2 (e21) (e22)) = (e21)) = ((op2 (h4 (e11)) (h4 (e12))) = (op2 (op2 (e23) (e23)) (e23)))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H422. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H10a. % 21.03/21.28 cut (((e21) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3d4]. % 21.03/21.28 cut (((op2 (e21) (e22)) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H423]. % 21.03/21.28 congruence. % 21.03/21.28 elim (classic ((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [ zenon_intro zenon_H420 | zenon_intro zenon_H421 ]. % 21.03/21.28 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12)))) = ((op2 (e21) (e22)) = (op2 (h4 (e11)) (h4 (e12))))). % 21.03/21.28 intro zenon_D_pnotp. % 21.03/21.28 apply zenon_H423. % 21.03/21.28 rewrite <- zenon_D_pnotp. % 21.03/21.28 exact zenon_H420. % 21.03/21.28 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H421]. % 21.03/21.28 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H424]. % 21.03/21.28 congruence. % 21.03/21.28 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 21.03/21.28 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 21.03/21.28 congruence. % 21.03/21.28 apply (zenon_L36_); trivial. % 21.03/21.28 apply (zenon_L83_); trivial. % 21.03/21.28 apply zenon_H421. apply refl_equal. % 21.03/21.28 apply zenon_H421. apply refl_equal. % 21.03/21.28 exact (zenon_H3d4 zenon_H37). % 21.03/21.28 apply zenon_H421. apply refl_equal. % 21.03/21.28 apply zenon_H421. apply refl_equal. % 21.03/21.28 apply (zenon_L91_); trivial. % 21.03/21.28 apply (zenon_L55_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha6 ]. % 21.03/21.28 apply (zenon_L43_); trivial. % 21.03/21.28 apply (zenon_L45_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3dc); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 21.03/21.28 apply (zenon_L48_); trivial. % 21.03/21.28 apply (zenon_L50_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H418); [ zenon_intro zenon_H1e9 | zenon_intro zenon_H425 ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b6); [ zenon_intro zenon_H47 | zenon_intro zenon_H3db ]. % 21.03/21.28 apply (zenon_L18_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3dd | zenon_intro zenon_H3dc ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H5f. zenon_intro zenon_H113. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b8); [ zenon_intro zenon_H3c8 | zenon_intro zenon_H3c7 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H4c. zenon_intro zenon_H55. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3ba); [ zenon_intro zenon_H427 | zenon_intro zenon_H426 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H427). zenon_intro zenon_Hb7. zenon_intro zenon_H53. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b2); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3c9 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H6a. zenon_intro zenon_H1c6. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H49 | zenon_intro zenon_H59 ]. % 21.03/21.28 apply (zenon_L20_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 21.03/21.28 exact (zenon_H55 zenon_H5b). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4f | zenon_intro zenon_H5c ]. % 21.03/21.28 exact (zenon_H53 zenon_H4f). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4f | zenon_intro zenon_H119 ]. % 21.03/21.28 exact (zenon_H53 zenon_H4f). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_Hbc | zenon_intro zenon_H11a ]. % 21.03/21.28 apply (zenon_L53_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_Hac | zenon_intro zenon_Hdd ]. % 21.03/21.28 apply (zenon_L47_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H1dc | zenon_intro zenon_H20e ]. % 21.03/21.28 apply (zenon_L115_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H20f ]. % 21.03/21.28 apply (zenon_L55_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1eb ]. % 21.03/21.28 apply (zenon_L116_); trivial. % 21.03/21.28 apply (zenon_L119_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c9); [ zenon_intro zenon_H17 | zenon_intro zenon_H3d7 ]. % 21.03/21.28 apply (zenon_L2_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d7); [ zenon_intro zenon_H25 | zenon_intro zenon_H2d ]. % 21.03/21.28 apply (zenon_L6_); trivial. % 21.03/21.28 apply (zenon_L9_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H426); [ zenon_intro zenon_H429 | zenon_intro zenon_H428 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H429). zenon_intro zenon_H42b. zenon_intro zenon_H42a. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_H117 | zenon_intro zenon_H116 ]. % 21.03/21.28 exact (zenon_H113 zenon_H117). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H31 | zenon_intro zenon_H118 ]. % 21.03/21.28 apply (zenon_L52_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10a | zenon_intro zenon_Hc8 ]. % 21.03/21.28 exact (zenon_H42a zenon_H10a). % 21.03/21.28 apply (zenon_L55_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H428); [ zenon_intro zenon_H201 | zenon_intro zenon_H42c ]. % 21.03/21.28 apply (zenon_L120_); trivial. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H42c). zenon_intro zenon_H42d. zenon_intro zenon_H209. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b2); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3c9 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H6a. zenon_intro zenon_H1c6. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H49 | zenon_intro zenon_H59 ]. % 21.03/21.28 apply (zenon_L20_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 21.03/21.28 exact (zenon_H55 zenon_H5b). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4f | zenon_intro zenon_H5c ]. % 21.03/21.28 apply (zenon_L22_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_H117 | zenon_intro zenon_H116 ]. % 21.03/21.28 exact (zenon_H113 zenon_H117). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H31 | zenon_intro zenon_H118 ]. % 21.03/21.28 apply (zenon_L52_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10a | zenon_intro zenon_Hc8 ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc2 | zenon_intro zenon_Hda ]. % 21.03/21.28 apply (zenon_L54_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hdb ]. % 21.03/21.28 apply (zenon_L55_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Hcd | zenon_intro zenon_H40 ]. % 21.03/21.28 apply (zenon_L123_); trivial. % 21.03/21.28 apply (zenon_L16_); trivial. % 21.03/21.28 apply (zenon_L55_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c9); [ zenon_intro zenon_H17 | zenon_intro zenon_H3d7 ]. % 21.03/21.28 apply (zenon_L2_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d7); [ zenon_intro zenon_H25 | zenon_intro zenon_H2d ]. % 21.03/21.28 apply (zenon_L6_); trivial. % 21.03/21.28 apply (zenon_L9_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c7); [ zenon_intro zenon_H2f | zenon_intro zenon_H3d8 ]. % 21.03/21.28 apply (zenon_L10_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H3d | zenon_intro zenon_H45 ]. % 21.03/21.28 apply (zenon_L14_); trivial. % 21.03/21.28 apply (zenon_L17_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3dc); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 21.03/21.28 apply (zenon_L48_); trivial. % 21.03/21.28 apply (zenon_L50_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H425); [ zenon_intro zenon_H217 | zenon_intro zenon_H42e ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b6); [ zenon_intro zenon_H47 | zenon_intro zenon_H3db ]. % 21.03/21.28 apply (zenon_L18_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3dd | zenon_intro zenon_H3dc ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H5f. zenon_intro zenon_H113. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b8); [ zenon_intro zenon_H3c8 | zenon_intro zenon_H3c7 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H4c. zenon_intro zenon_H55. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b0); [ zenon_intro zenon_H66 | zenon_intro zenon_H3e2 ]. % 21.03/21.28 apply (zenon_L26_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e2); [ zenon_intro zenon_H3e4 | zenon_intro zenon_H3e3 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e4). zenon_intro zenon_H74. zenon_intro zenon_H1a7. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b2); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3c9 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H6a. zenon_intro zenon_H1c6. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H49 | zenon_intro zenon_H59 ]. % 21.03/21.28 apply (zenon_L20_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 21.03/21.28 exact (zenon_H55 zenon_H5b). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4f | zenon_intro zenon_H5c ]. % 21.03/21.28 apply (zenon_L22_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H11d | zenon_intro zenon_H128 ]. % 21.03/21.28 apply (zenon_L126_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_He2 | zenon_intro zenon_H129 ]. % 21.03/21.28 apply (zenon_L74_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hac | zenon_intro zenon_H121 ]. % 21.03/21.28 apply (zenon_L47_); trivial. % 21.03/21.28 apply (zenon_L76_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c9); [ zenon_intro zenon_H17 | zenon_intro zenon_H3d7 ]. % 21.03/21.28 apply (zenon_L2_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d7); [ zenon_intro zenon_H25 | zenon_intro zenon_H2d ]. % 21.03/21.28 apply (zenon_L6_); trivial. % 21.03/21.28 apply (zenon_L9_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha6 ]. % 21.03/21.28 apply (zenon_L43_); trivial. % 21.03/21.28 apply (zenon_L45_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c7); [ zenon_intro zenon_H2f | zenon_intro zenon_H3d8 ]. % 21.03/21.28 apply (zenon_L10_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H3d | zenon_intro zenon_H45 ]. % 21.03/21.28 apply (zenon_L14_); trivial. % 21.03/21.28 apply (zenon_L17_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3dc); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 21.03/21.28 apply (zenon_L48_); trivial. % 21.03/21.28 apply (zenon_L50_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H42e); [ zenon_intro zenon_H223 | zenon_intro zenon_H42f ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b6); [ zenon_intro zenon_H47 | zenon_intro zenon_H3db ]. % 21.03/21.28 apply (zenon_L18_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3dd | zenon_intro zenon_H3dc ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H5f. zenon_intro zenon_H113. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b8); [ zenon_intro zenon_H3c8 | zenon_intro zenon_H3c7 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H4c. zenon_intro zenon_H55. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b9); [ zenon_intro zenon_H54 | zenon_intro zenon_H3de ]. % 21.03/21.28 apply (zenon_L23_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3de); [ zenon_intro zenon_H5e | zenon_intro zenon_H3df ]. % 21.03/21.28 apply (zenon_L25_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3df); [ zenon_intro zenon_H3e0 | zenon_intro zenon_Ha8 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e0). zenon_intro zenon_H92. zenon_intro zenon_H3e1. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b0); [ zenon_intro zenon_H66 | zenon_intro zenon_H3e2 ]. % 21.03/21.28 apply (zenon_L26_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e2); [ zenon_intro zenon_H3e4 | zenon_intro zenon_H3e3 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e4). zenon_intro zenon_H74. zenon_intro zenon_H1a7. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b2); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3c9 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H6a. zenon_intro zenon_H1c6. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b3); [ zenon_intro zenon_H70 | zenon_intro zenon_H3e5 ]. % 21.03/21.28 apply (zenon_L29_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e5); [ zenon_intro zenon_H73 | zenon_intro zenon_H3e6 ]. % 21.03/21.28 apply (zenon_L31_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e6); [ zenon_intro zenon_H3e7 | zenon_intro zenon_H99 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e7). zenon_intro zenon_H8a. zenon_intro zenon_H1a8. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_H117 | zenon_intro zenon_H116 ]. % 21.03/21.28 exact (zenon_H113 zenon_H117). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H31 | zenon_intro zenon_H118 ]. % 21.03/21.28 apply (zenon_L52_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10a | zenon_intro zenon_Hc8 ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4f | zenon_intro zenon_H119 ]. % 21.03/21.28 apply (zenon_L22_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_Hbc | zenon_intro zenon_H11a ]. % 21.03/21.28 apply (zenon_L53_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_Hac | zenon_intro zenon_Hdd ]. % 21.03/21.28 apply (zenon_L47_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H11b ]. % 21.03/21.28 apply (zenon_L58_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hea | zenon_intro zenon_H11c ]. % 21.03/21.28 apply (zenon_L133_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H10c | zenon_intro zenon_H40 ]. % 21.03/21.28 apply (zenon_L71_); trivial. % 21.03/21.28 apply (zenon_L16_); trivial. % 21.03/21.28 apply (zenon_L55_); trivial. % 21.03/21.28 apply (zenon_L41_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c9); [ zenon_intro zenon_H17 | zenon_intro zenon_H3d7 ]. % 21.03/21.28 apply (zenon_L2_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d7); [ zenon_intro zenon_H25 | zenon_intro zenon_H2d ]. % 21.03/21.28 apply (zenon_L6_); trivial. % 21.03/21.28 apply (zenon_L9_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha6 ]. % 21.03/21.28 apply (zenon_L43_); trivial. % 21.03/21.28 apply (zenon_L45_); trivial. % 21.03/21.28 apply (zenon_L46_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c7); [ zenon_intro zenon_H2f | zenon_intro zenon_H3d8 ]. % 21.03/21.28 apply (zenon_L10_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H3d | zenon_intro zenon_H45 ]. % 21.03/21.28 apply (zenon_L14_); trivial. % 21.03/21.28 apply (zenon_L17_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3dc); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 21.03/21.28 apply (zenon_L48_); trivial. % 21.03/21.28 apply (zenon_L50_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H42f); [ zenon_intro zenon_H22f | zenon_intro zenon_H430 ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b6); [ zenon_intro zenon_H47 | zenon_intro zenon_H3db ]. % 21.03/21.28 apply (zenon_L18_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3dd | zenon_intro zenon_H3dc ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H5f. zenon_intro zenon_H113. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b8); [ zenon_intro zenon_H3c8 | zenon_intro zenon_H3c7 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H4c. zenon_intro zenon_H55. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b9); [ zenon_intro zenon_H54 | zenon_intro zenon_H3de ]. % 21.03/21.28 apply (zenon_L23_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3de); [ zenon_intro zenon_H5e | zenon_intro zenon_H3df ]. % 21.03/21.28 apply (zenon_L25_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3df); [ zenon_intro zenon_H3e0 | zenon_intro zenon_Ha8 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e0). zenon_intro zenon_H92. zenon_intro zenon_H3e1. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b0); [ zenon_intro zenon_H66 | zenon_intro zenon_H3e2 ]. % 21.03/21.28 apply (zenon_L26_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e2); [ zenon_intro zenon_H3e4 | zenon_intro zenon_H3e3 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e4). zenon_intro zenon_H74. zenon_intro zenon_H1a7. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b2); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3c9 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H6a. zenon_intro zenon_H1c6. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b3); [ zenon_intro zenon_H70 | zenon_intro zenon_H3e5 ]. % 21.03/21.28 apply (zenon_L29_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e5); [ zenon_intro zenon_H73 | zenon_intro zenon_H3e6 ]. % 21.03/21.28 apply (zenon_L31_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e6); [ zenon_intro zenon_H3e7 | zenon_intro zenon_H99 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e7). zenon_intro zenon_H8a. zenon_intro zenon_H1a8. % 21.03/21.28 apply (zenon_L135_); trivial. % 21.03/21.28 apply (zenon_L41_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c9); [ zenon_intro zenon_H17 | zenon_intro zenon_H3d7 ]. % 21.03/21.28 apply (zenon_L2_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d7); [ zenon_intro zenon_H25 | zenon_intro zenon_H2d ]. % 21.03/21.28 apply (zenon_L6_); trivial. % 21.03/21.28 apply (zenon_L9_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha6 ]. % 21.03/21.28 apply (zenon_L43_); trivial. % 21.03/21.28 apply (zenon_L45_); trivial. % 21.03/21.28 apply (zenon_L46_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c7); [ zenon_intro zenon_H2f | zenon_intro zenon_H3d8 ]. % 21.03/21.28 apply (zenon_L10_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H3d | zenon_intro zenon_H45 ]. % 21.03/21.28 apply (zenon_L14_); trivial. % 21.03/21.28 apply (zenon_L17_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3dc); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 21.03/21.28 apply (zenon_L48_); trivial. % 21.03/21.28 apply (zenon_L50_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H430); [ zenon_intro zenon_H235 | zenon_intro zenon_H431 ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H16c | zenon_intro zenon_H184 ]. % 21.03/21.28 apply (zenon_L90_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H172 | zenon_intro zenon_H185 ]. % 21.03/21.28 apply (zenon_L91_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H177 | zenon_intro zenon_H28 ]. % 21.03/21.28 apply (zenon_L136_); trivial. % 21.03/21.28 apply (zenon_L8_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H431); [ zenon_intro zenon_H24e | zenon_intro zenon_H432 ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b8); [ zenon_intro zenon_H3c8 | zenon_intro zenon_H3c7 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H4c. zenon_intro zenon_H55. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b2); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3c9 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H6a. zenon_intro zenon_H1c6. % 21.03/21.28 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc2 | zenon_intro zenon_Hda ]. % 21.03/21.28 apply (zenon_L54_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hdb ]. % 21.03/21.28 apply (zenon_L55_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Hcd | zenon_intro zenon_H40 ]. % 21.03/21.28 apply (zenon_L143_); trivial. % 21.03/21.28 apply (zenon_L16_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c9); [ zenon_intro zenon_H17 | zenon_intro zenon_H3d7 ]. % 21.03/21.28 apply (zenon_L2_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d7); [ zenon_intro zenon_H25 | zenon_intro zenon_H2d ]. % 21.03/21.28 apply (zenon_L6_); trivial. % 21.03/21.28 apply (zenon_L9_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c7); [ zenon_intro zenon_H2f | zenon_intro zenon_H3d8 ]. % 21.03/21.28 apply (zenon_L10_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H3d | zenon_intro zenon_H45 ]. % 21.03/21.28 apply (zenon_L14_); trivial. % 21.03/21.28 apply (zenon_L17_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H432); [ zenon_intro zenon_H261 | zenon_intro zenon_H433 ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b6); [ zenon_intro zenon_H47 | zenon_intro zenon_H3db ]. % 21.03/21.28 apply (zenon_L18_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3dd | zenon_intro zenon_H3dc ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H5f. zenon_intro zenon_H113. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b8); [ zenon_intro zenon_H3c8 | zenon_intro zenon_H3c7 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H4c. zenon_intro zenon_H55. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b0); [ zenon_intro zenon_H66 | zenon_intro zenon_H3e2 ]. % 21.03/21.28 apply (zenon_L26_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e2); [ zenon_intro zenon_H3e4 | zenon_intro zenon_H3e3 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3e4). zenon_intro zenon_H74. zenon_intro zenon_H1a7. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3b2); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3c9 ]. % 21.03/21.28 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H6a. zenon_intro zenon_H1c6. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_H117 | zenon_intro zenon_H116 ]. % 21.03/21.28 exact (zenon_H113 zenon_H117). % 21.03/21.28 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H31 | zenon_intro zenon_H118 ]. % 21.03/21.28 apply (zenon_L52_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10a | zenon_intro zenon_Hc8 ]. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H11b ]. % 21.03/21.28 apply (zenon_L58_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hea | zenon_intro zenon_H11c ]. % 21.03/21.28 apply (zenon_L146_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H10c | zenon_intro zenon_H40 ]. % 21.03/21.28 apply (zenon_L71_); trivial. % 21.03/21.28 apply (zenon_L16_); trivial. % 21.03/21.28 apply (zenon_L55_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c9); [ zenon_intro zenon_H17 | zenon_intro zenon_H3d7 ]. % 21.03/21.28 apply (zenon_L2_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d7); [ zenon_intro zenon_H25 | zenon_intro zenon_H2d ]. % 21.03/21.28 apply (zenon_L6_); trivial. % 21.03/21.28 apply (zenon_L9_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha6 ]. % 21.03/21.28 apply (zenon_L43_); trivial. % 21.03/21.28 apply (zenon_L45_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3c7); [ zenon_intro zenon_H2f | zenon_intro zenon_H3d8 ]. % 21.03/21.28 apply (zenon_L10_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H3d | zenon_intro zenon_H45 ]. % 21.03/21.28 apply (zenon_L14_); trivial. % 21.03/21.28 apply (zenon_L17_); trivial. % 21.03/21.28 apply (zenon_or_s _ _ zenon_H3dc); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 21.03/21.28 apply (zenon_L48_); trivial. % 21.03/21.28 apply (zenon_L50_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H433); [ zenon_intro zenon_H267 | zenon_intro zenon_H434 ]. % 21.03/21.28 apply (zenon_L147_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H434); [ zenon_intro zenon_H26e | zenon_intro zenon_H435 ]. % 21.03/21.28 apply (zenon_L148_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H435); [ zenon_intro zenon_H437 | zenon_intro zenon_H436 ]. % 21.03/21.28 apply (zenon_notor_s _ _ zenon_H437). zenon_intro zenon_H12. zenon_intro zenon_H438. % 21.03/21.28 apply (zenon_L1_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H436); [ zenon_intro zenon_H43a | zenon_intro zenon_H439 ]. % 21.03/21.28 apply (zenon_notor_s _ _ zenon_H43a). zenon_intro zenon_H43c. zenon_intro zenon_H43b. % 21.03/21.28 apply (zenon_notor_s _ _ zenon_H43b). zenon_intro zenon_H86. zenon_intro zenon_H43d. % 21.03/21.28 apply (zenon_L36_); trivial. % 21.03/21.28 apply (zenon_notand_s _ _ zenon_H439); [ zenon_intro zenon_H43e | zenon_intro zenon_H274 ]. % 21.03/21.28 apply (zenon_notor_s _ _ zenon_H43e). zenon_intro zenon_H440. zenon_intro zenon_H43f. % 21.03/21.28 apply (zenon_notor_s _ _ zenon_H43f). zenon_intro zenon_H442. zenon_intro zenon_H441. % 21.03/21.28 apply (zenon_notor_s _ _ zenon_H441). zenon_intro zenon_H13a. zenon_intro zenon_H443. % 21.03/21.28 apply (zenon_L83_); trivial. % 21.03/21.28 apply (zenon_L149_); trivial. % 21.03/21.28 Qed. % 21.03/21.28 % SZS output end Proof % 21.03/21.28 (* END-PROOF *) % 21.03/21.28 nodes searched: 1133627 % 21.03/21.28 max branch formulas: 1928 % 21.03/21.28 proof nodes created: 9948 % 21.03/21.28 formulas created: 551897 % 21.03/21.28 %------------------------------------------------------------------------------