%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG112+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n020.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 18:29:28 EDT 2022 % Result : Theorem 47.01s 47.20s % Output : Proof 47.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ALG112+1 : TPTP v8.1.0. Released v2.7.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n020.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Wed Jun 8 14:04:36 EDT 2022 % 0.13/0.34 % CPUTime : % 47.01/47.20 (* PROOF-FOUND *) % 47.01/47.20 % SZS status Theorem % 47.01/47.20 (* BEGIN-PROOF *) % 47.01/47.20 % SZS output start Proof % 47.01/47.20 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))))))))))))))))))))))))))). % 47.01/47.20 Proof. % 47.01/47.20 assert (zenon_L1_ : (~((h2 (e10)) = (e20))) -> ((h2 (e10)) = (op2 (op2 (e21) (e21)) (e21))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H12 zenon_H13 zenon_H14. % 47.01/47.20 cut (((h2 (e10)) = (op2 (op2 (e21) (e21)) (e21))) = ((h2 (e10)) = (e20))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H12. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H13. % 47.01/47.20 cut (((op2 (op2 (e21) (e21)) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 47.01/47.20 cut (((h2 (e10)) = (h2 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H16]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H16. apply refl_equal. % 47.01/47.20 apply zenon_H15. apply sym_equal. exact zenon_H14. % 47.01/47.20 (* end of lemma zenon_L1_ *) % 47.01/47.20 assert (zenon_L2_ : (~((e11) = (e11))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H17. % 47.01/47.20 apply zenon_H17. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L2_ *) % 47.01/47.20 assert (zenon_L3_ : (~((op1 (op1 (e11) (e11)) (e11)) = (op1 (e12) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H18 zenon_H19. % 47.01/47.20 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 47.01/47.20 cut (((op1 (e11) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H1a. apply sym_equal. exact zenon_H19. % 47.01/47.20 apply zenon_H17. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L3_ *) % 47.01/47.20 assert (zenon_L4_ : (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e10) (e11)) = (e10)) -> ((e12) = (op1 (e11) (e11))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H1b zenon_H1c zenon_H1d zenon_H19. % 47.01/47.20 cut (((e10) = (op1 (op1 (e11) (e11)) (e11))) = ((op1 (e10) (e11)) = (op1 (e12) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H1b. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H1c. % 47.01/47.20 cut (((op1 (op1 (e11) (e11)) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 47.01/47.20 cut (((e10) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e10) (e11)) = (op1 (e10) (e11)))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ]. % 47.01/47.20 cut (((op1 (e10) (e11)) = (op1 (e10) (e11))) = ((e10) = (op1 (e10) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H1e. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H1f. % 47.01/47.20 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 47.01/47.20 cut (((op1 (e10) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_H21 zenon_H1d). % 47.01/47.20 apply zenon_H20. apply refl_equal. % 47.01/47.20 apply zenon_H20. apply refl_equal. % 47.01/47.20 apply (zenon_L3_); trivial. % 47.01/47.20 (* end of lemma zenon_L4_ *) % 47.01/47.20 assert (zenon_L5_ : ((op1 (e10) (e12)) = (e10)) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H22 zenon_H23 zenon_H24. % 47.01/47.20 elim (classic ((op1 (e10) (e12)) = (op1 (e10) (e12)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 47.01/47.20 cut (((op1 (e10) (e12)) = (op1 (e10) (e12))) = ((op1 (e10) (e10)) = (op1 (e10) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H24. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H25. % 47.01/47.20 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 47.01/47.20 cut (((op1 (e10) (e12)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (e10) (e12)) = (e10)) = ((op1 (e10) (e12)) = (op1 (e10) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H27. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H22. % 47.01/47.20 cut (((e10) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 47.01/47.20 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H26. apply refl_equal. % 47.01/47.20 apply zenon_H28. apply sym_equal. exact zenon_H23. % 47.01/47.20 apply zenon_H26. apply refl_equal. % 47.01/47.20 apply zenon_H26. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L5_ *) % 47.01/47.20 assert (zenon_L6_ : (~((op1 (e11) (op1 (op1 (e11) (e11)) (e11))) = (op1 (e11) (e10)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H29 zenon_H1c. % 47.01/47.20 cut (((op1 (op1 (e11) (e11)) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 47.01/47.20 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H17. apply refl_equal. % 47.01/47.20 apply zenon_H2a. apply sym_equal. exact zenon_H1c. % 47.01/47.20 (* end of lemma zenon_L6_ *) % 47.01/47.20 assert (zenon_L7_ : (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((op1 (e10) (e10)) = (e13)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H2b zenon_H2c zenon_H2d zenon_H1c. % 47.01/47.20 cut (((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) = ((op1 (e10) (e10)) = (op1 (e11) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H2b. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H2c. % 47.01/47.20 cut (((op1 (e11) (op1 (op1 (e11) (e11)) (e11))) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 47.01/47.20 cut (((e13) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e10) (e10)) = (op1 (e10) (e10)))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 47.01/47.20 cut (((op1 (e10) (e10)) = (op1 (e10) (e10))) = ((e13) = (op1 (e10) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H2e. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H2f. % 47.01/47.20 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 47.01/47.20 cut (((op1 (e10) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_H31 zenon_H2d). % 47.01/47.20 apply zenon_H30. apply refl_equal. % 47.01/47.20 apply zenon_H30. apply refl_equal. % 47.01/47.20 apply (zenon_L6_); trivial. % 47.01/47.20 (* end of lemma zenon_L7_ *) % 47.01/47.20 assert (zenon_L8_ : (~((e10) = (e10))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H32. % 47.01/47.20 apply zenon_H32. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L8_ *) % 47.01/47.20 assert (zenon_L9_ : ((op1 (e11) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((e10) = (e13))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H33 zenon_H34 zenon_H35. % 47.01/47.20 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 47.01/47.20 cut (((e13) = (e13)) = ((e10) = (e13))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H35. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H36. % 47.01/47.20 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 47.01/47.20 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (e11) (e10)) = (e10)) = ((e13) = (e10))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H38. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H33. % 47.01/47.20 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 47.01/47.20 cut (((op1 (e11) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_H39 zenon_H34). % 47.01/47.20 apply zenon_H32. apply refl_equal. % 47.01/47.20 apply zenon_H37. apply refl_equal. % 47.01/47.20 apply zenon_H37. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L9_ *) % 47.01/47.20 assert (zenon_L10_ : ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((op1 (e12) (e10)) = (e13)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H2c zenon_H3a zenon_H1c zenon_H3b. % 47.01/47.20 elim (classic ((op1 (e12) (e10)) = (op1 (e12) (e10)))); [ zenon_intro zenon_H3c | zenon_intro zenon_H3d ]. % 47.01/47.20 cut (((op1 (e12) (e10)) = (op1 (e12) (e10))) = ((op1 (e11) (e10)) = (op1 (e12) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H3b. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H3c. % 47.01/47.20 cut (((op1 (e12) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 47.01/47.20 cut (((op1 (e12) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) = ((op1 (e12) (e10)) = (op1 (e11) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H3e. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H2c. % 47.01/47.20 cut (((op1 (e11) (op1 (op1 (e11) (e11)) (e11))) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 47.01/47.20 cut (((e13) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e12) (e10)) = (op1 (e12) (e10)))); [ zenon_intro zenon_H3c | zenon_intro zenon_H3d ]. % 47.01/47.20 cut (((op1 (e12) (e10)) = (op1 (e12) (e10))) = ((e13) = (op1 (e12) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H3f. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H3c. % 47.01/47.20 cut (((op1 (e12) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 47.01/47.20 cut (((op1 (e12) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_H40 zenon_H3a). % 47.01/47.20 apply zenon_H3d. apply refl_equal. % 47.01/47.20 apply zenon_H3d. apply refl_equal. % 47.01/47.20 apply (zenon_L6_); trivial. % 47.01/47.20 apply zenon_H3d. apply refl_equal. % 47.01/47.20 apply zenon_H3d. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L10_ *) % 47.01/47.20 assert (zenon_L11_ : ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((op1 (e13) (e10)) = (e13)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H2c zenon_H41 zenon_H1c zenon_H42. % 47.01/47.20 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H43 | zenon_intro zenon_H44 ]. % 47.01/47.20 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((op1 (e11) (e10)) = (op1 (e13) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H42. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H43. % 47.01/47.20 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 47.01/47.20 cut (((op1 (e13) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) = ((op1 (e13) (e10)) = (op1 (e11) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H45. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H2c. % 47.01/47.20 cut (((op1 (e11) (op1 (op1 (e11) (e11)) (e11))) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 47.01/47.20 cut (((e13) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H43 | zenon_intro zenon_H44 ]. % 47.01/47.20 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e13) = (op1 (e13) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H46. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H43. % 47.01/47.20 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 47.01/47.20 cut (((op1 (e13) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_H47 zenon_H41). % 47.01/47.20 apply zenon_H44. apply refl_equal. % 47.01/47.20 apply zenon_H44. apply refl_equal. % 47.01/47.20 apply (zenon_L6_); trivial. % 47.01/47.20 apply zenon_H44. apply refl_equal. % 47.01/47.20 apply zenon_H44. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L11_ *) % 47.01/47.20 assert (zenon_L12_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((e10) = (e13))) -> ((op1 (e11) (e10)) = (e10)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H48 zenon_H2b zenon_H35 zenon_H33 zenon_H3b zenon_H2c zenon_H1c zenon_H42. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.01/47.20 apply (zenon_L7_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.01/47.20 apply (zenon_L9_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.01/47.20 apply (zenon_L10_); trivial. % 47.01/47.20 apply (zenon_L11_); trivial. % 47.01/47.20 (* end of lemma zenon_L12_ *) % 47.01/47.20 assert (zenon_L13_ : (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e12) (e10)) = (e10)) -> ((e12) = (op1 (e11) (e11))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H4b zenon_H1c zenon_H4c zenon_H19. % 47.01/47.20 cut (((e10) = (op1 (op1 (e11) (e11)) (e11))) = ((op1 (e12) (e10)) = (op1 (e12) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H4b. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H1c. % 47.01/47.20 cut (((op1 (op1 (e11) (e11)) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 47.01/47.20 cut (((e10) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e12) (e10)) = (op1 (e12) (e10)))); [ zenon_intro zenon_H3c | zenon_intro zenon_H3d ]. % 47.01/47.20 cut (((op1 (e12) (e10)) = (op1 (e12) (e10))) = ((e10) = (op1 (e12) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H4d. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H3c. % 47.01/47.20 cut (((op1 (e12) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 47.01/47.20 cut (((op1 (e12) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_H4e zenon_H4c). % 47.01/47.20 apply zenon_H3d. apply refl_equal. % 47.01/47.20 apply zenon_H3d. apply refl_equal. % 47.01/47.20 apply (zenon_L3_); trivial. % 47.01/47.20 (* end of lemma zenon_L13_ *) % 47.01/47.20 assert (zenon_L14_ : ((op1 (e10) (e10)) = (e11)) -> ((op1 (e10) (e10)) = (e12)) -> (~((e11) = (e12))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H4f zenon_H50 zenon_H51. % 47.01/47.20 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 47.01/47.20 cut (((e12) = (e12)) = ((e11) = (e12))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H51. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H52. % 47.01/47.20 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.01/47.20 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (e10) (e10)) = (e11)) = ((e12) = (e11))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H54. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H4f. % 47.01/47.20 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 47.01/47.20 cut (((op1 (e10) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_H55 zenon_H50). % 47.01/47.20 apply zenon_H17. apply refl_equal. % 47.01/47.20 apply zenon_H53. apply refl_equal. % 47.01/47.20 apply zenon_H53. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L14_ *) % 47.01/47.20 assert (zenon_L15_ : (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e10) (e11)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H56 zenon_H19 zenon_H57. % 47.01/47.20 cut (((e12) = (op1 (e11) (e11))) = ((op1 (e10) (e11)) = (op1 (e11) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H56. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H19. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 47.01/47.20 cut (((e12) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e10) (e11)) = (op1 (e10) (e11)))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ]. % 47.01/47.20 cut (((op1 (e10) (e11)) = (op1 (e10) (e11))) = ((e12) = (op1 (e10) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H59. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H1f. % 47.01/47.20 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 47.01/47.20 cut (((op1 (e10) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_H5a zenon_H57). % 47.01/47.20 apply zenon_H20. apply refl_equal. % 47.01/47.20 apply zenon_H20. apply refl_equal. % 47.01/47.20 apply zenon_H58. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L15_ *) % 47.01/47.20 assert (zenon_L16_ : ((op1 (e10) (e12)) = (e10)) -> ((op1 (e10) (e12)) = (e12)) -> (~((e10) = (e12))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H22 zenon_H5b zenon_H5c. % 47.01/47.20 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 47.01/47.20 cut (((e12) = (e12)) = ((e10) = (e12))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H5c. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H52. % 47.01/47.20 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.01/47.20 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (e10) (e12)) = (e10)) = ((e12) = (e10))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H5d. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H22. % 47.01/47.20 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 47.01/47.20 cut (((op1 (e10) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_H5e zenon_H5b). % 47.01/47.20 apply zenon_H32. apply refl_equal. % 47.01/47.20 apply zenon_H53. apply refl_equal. % 47.01/47.20 apply zenon_H53. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L16_ *) % 47.01/47.20 assert (zenon_L17_ : (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e11)) = (e13)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H1b zenon_H5f zenon_H60. % 47.01/47.20 cut (((op1 (e10) (e11)) = (e13)) = ((op1 (e10) (e11)) = (op1 (e12) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H1b. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H5f. % 47.01/47.20 cut (((e13) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 47.01/47.20 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H20. apply refl_equal. % 47.01/47.20 apply zenon_H61. apply sym_equal. exact zenon_H60. % 47.01/47.20 (* end of lemma zenon_L17_ *) % 47.01/47.20 assert (zenon_L18_ : ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e12) (e13)) = (e10)) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H1c zenon_H62 zenon_H19 zenon_H63. % 47.01/47.20 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H64 | zenon_intro zenon_H65 ]. % 47.01/47.20 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((op1 (e12) (e11)) = (op1 (e12) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H63. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H64. % 47.01/47.20 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 47.01/47.20 cut (((op1 (e12) (e13)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e10) = (op1 (op1 (e11) (e11)) (e11))) = ((op1 (e12) (e13)) = (op1 (e12) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H66. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H1c. % 47.01/47.20 cut (((op1 (op1 (e11) (e11)) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 47.01/47.20 cut (((e10) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H64 | zenon_intro zenon_H65 ]. % 47.01/47.20 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e10) = (op1 (e12) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H67. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H64. % 47.01/47.20 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 47.01/47.20 cut (((op1 (e12) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H68]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_H68 zenon_H62). % 47.01/47.20 apply zenon_H65. apply refl_equal. % 47.01/47.20 apply zenon_H65. apply refl_equal. % 47.01/47.20 apply (zenon_L3_); trivial. % 47.01/47.20 apply zenon_H65. apply refl_equal. % 47.01/47.20 apply zenon_H65. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L18_ *) % 47.01/47.20 assert (zenon_L19_ : ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e13) (e11)) = (e10)) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H1c zenon_H69 zenon_H19 zenon_H6a. % 47.01/47.20 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ]. % 47.01/47.20 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((op1 (e12) (e11)) = (op1 (e13) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H6a. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H6b. % 47.01/47.20 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 47.01/47.20 cut (((op1 (e13) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e10) = (op1 (op1 (e11) (e11)) (e11))) = ((op1 (e13) (e11)) = (op1 (e12) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H6d. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H1c. % 47.01/47.20 cut (((op1 (op1 (e11) (e11)) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 47.01/47.20 cut (((e10) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ]. % 47.01/47.20 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((e10) = (op1 (e13) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H6e. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H6b. % 47.01/47.20 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 47.01/47.20 cut (((op1 (e13) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_H6f zenon_H69). % 47.01/47.20 apply zenon_H6c. apply refl_equal. % 47.01/47.20 apply zenon_H6c. apply refl_equal. % 47.01/47.20 apply (zenon_L3_); trivial. % 47.01/47.20 apply zenon_H6c. apply refl_equal. % 47.01/47.20 apply zenon_H6c. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L19_ *) % 47.01/47.20 assert (zenon_L20_ : (((op1 (op1 (e10) (e10)) (op1 (e10) (e10))) = (e10))/\(((op1 (op1 (e11) (e10)) (op1 (e11) (e10))) = (e11))/\(((op1 (op1 (e12) (e10)) (op1 (e12) (e10))) = (e12))/\((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H70 zenon_H2b zenon_H71 zenon_H34. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H73. zenon_intro zenon_H72. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H75. zenon_intro zenon_H74. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H74). zenon_intro zenon_H77. zenon_intro zenon_H76. % 47.01/47.20 cut (((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (e13)) = ((op1 (e10) (e10)) = (op1 (e11) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H2b. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H76. % 47.01/47.20 cut (((e13) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 47.01/47.20 cut (((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e10) (e10)) = (op1 (e10) (e10)))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 47.01/47.20 cut (((op1 (e10) (e10)) = (op1 (e10) (e10))) = ((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (op1 (e10) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H79. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H2f. % 47.01/47.20 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 47.01/47.20 cut (((op1 (e10) (e10)) = (op1 (op1 (e13) (e10)) (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e10) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 47.01/47.20 cut (((e10) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H7b. apply sym_equal. exact zenon_H71. % 47.01/47.20 apply zenon_H7b. apply sym_equal. exact zenon_H71. % 47.01/47.20 apply zenon_H30. apply refl_equal. % 47.01/47.20 apply zenon_H30. apply refl_equal. % 47.01/47.20 apply zenon_H78. apply sym_equal. exact zenon_H34. % 47.01/47.20 (* end of lemma zenon_L20_ *) % 47.01/47.20 assert (zenon_L21_ : (((op1 (op1 (e10) (e11)) (op1 (e10) (e11))) = (e10))/\(((op1 (op1 (e11) (e11)) (op1 (e11) (e11))) = (e11))/\(((op1 (op1 (e12) (e11)) (op1 (e12) (e11))) = (e12))/\((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (e13))))) -> ((op1 (e13) (e11)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H7c zenon_H7d zenon_H5f zenon_H56. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H7c). zenon_intro zenon_H7f. zenon_intro zenon_H7e. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H7e). zenon_intro zenon_H81. zenon_intro zenon_H80. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82. % 47.01/47.20 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H84 | zenon_intro zenon_H58 ]. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((op1 (e10) (e11)) = (op1 (e11) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H56. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H84. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (e13)) = ((op1 (e11) (e11)) = (op1 (e10) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H85. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H82. % 47.01/47.20 cut (((e13) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 47.01/47.20 cut (((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H84 | zenon_intro zenon_H58 ]. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (op1 (e11) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H87. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H84. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (op1 (e13) (e11)) (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e11) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 47.01/47.20 cut (((e11) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H89. apply sym_equal. exact zenon_H7d. % 47.01/47.20 apply zenon_H89. apply sym_equal. exact zenon_H7d. % 47.01/47.20 apply zenon_H58. apply refl_equal. % 47.01/47.20 apply zenon_H58. apply refl_equal. % 47.01/47.20 apply zenon_H86. apply sym_equal. exact zenon_H5f. % 47.01/47.20 apply zenon_H58. apply refl_equal. % 47.01/47.20 apply zenon_H58. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L21_ *) % 47.01/47.20 assert (zenon_L22_ : (~((op1 (e13) (e13)) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12))))) -> ((op1 (e12) (e12)) = (e13)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H8a zenon_H8b. % 47.01/47.20 cut (((e13) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 47.01/47.20 cut (((e13) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H8c. apply sym_equal. exact zenon_H8b. % 47.01/47.20 apply zenon_H8c. apply sym_equal. exact zenon_H8b. % 47.01/47.20 (* end of lemma zenon_L22_ *) % 47.01/47.20 assert (zenon_L23_ : (((op1 (op1 (e10) (e12)) (op1 (e10) (e12))) = (e10))/\(((op1 (op1 (e11) (e12)) (op1 (e11) (e12))) = (e11))/\(((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (e12))/\((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (e13))))) -> ((op1 (e12) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H8d zenon_H8b zenon_H8e zenon_H8f. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H91. zenon_intro zenon_H90. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H93. zenon_intro zenon_H92. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H92). zenon_intro zenon_H95. zenon_intro zenon_H94. % 47.01/47.20 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e10) (e13)) = (op1 (e13) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H8f. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H96. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (e12)) = ((op1 (e13) (e13)) = (op1 (e10) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H98. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H95. % 47.01/47.20 cut (((e12) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 47.01/47.20 cut (((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (e13) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H9a. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H96. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 47.01/47.20 congruence. % 47.01/47.20 apply (zenon_L22_); trivial. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 apply zenon_H99. apply sym_equal. exact zenon_H8e. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L23_ *) % 47.01/47.20 assert (zenon_L24_ : (((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (e10))/\(((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (e11))/\(((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e12))/\((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13))))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H9b zenon_H8e zenon_H22 zenon_H9c. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9e. zenon_intro zenon_H9d. % 47.01/47.20 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e10) (e12)) = (op1 (e12) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H9c. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H9f. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (e10)) = ((op1 (e12) (e12)) = (op1 (e10) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Ha1. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H9e. % 47.01/47.20 cut (((e10) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 47.01/47.20 cut (((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (op1 (e12) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Ha3. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H9f. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (op1 (e10) (e13)) (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e12) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 47.01/47.20 cut (((e12) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H99. apply sym_equal. exact zenon_H8e. % 47.01/47.20 apply zenon_H99. apply sym_equal. exact zenon_H8e. % 47.01/47.20 apply zenon_Ha0. apply refl_equal. % 47.01/47.20 apply zenon_Ha0. apply refl_equal. % 47.01/47.20 apply zenon_Ha2. apply sym_equal. exact zenon_H22. % 47.01/47.20 apply zenon_Ha0. apply refl_equal. % 47.01/47.20 apply zenon_Ha0. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L24_ *) % 47.01/47.20 assert (zenon_L25_ : ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H34 zenon_H71 zenon_H2b zenon_H56 zenon_H5f zenon_H7d zenon_H8f zenon_H8b zenon_H8e zenon_H22 zenon_H9c. % 47.01/47.20 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.01/47.20 apply (zenon_L20_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.01/47.20 apply (zenon_L21_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.01/47.20 apply (zenon_L23_); trivial. % 47.01/47.20 apply (zenon_L24_); trivial. % 47.01/47.20 (* end of lemma zenon_L25_ *) % 47.01/47.20 assert (zenon_L26_ : ((op1 (e12) (e13)) = (e11)) -> ((op1 (e12) (e13)) = (e13)) -> (~((e11) = (e13))) -> False). % 47.01/47.20 do 0 intro. intros zenon_Ha7 zenon_Ha8 zenon_Ha9. % 47.01/47.20 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 47.01/47.20 cut (((e13) = (e13)) = ((e11) = (e13))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Ha9. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H36. % 47.01/47.20 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 47.01/47.20 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (e12) (e13)) = (e11)) = ((e13) = (e11))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Haa. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_Ha7. % 47.01/47.20 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 47.01/47.20 cut (((op1 (e12) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_Hab zenon_Ha8). % 47.01/47.20 apply zenon_H17. apply refl_equal. % 47.01/47.20 apply zenon_H37. apply refl_equal. % 47.01/47.20 apply zenon_H37. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L26_ *) % 47.01/47.20 assert (zenon_L27_ : (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e10)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e11)) -> (~((e11) = (e13))) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hac zenon_H3b zenon_H1c zenon_H2c zenon_H1b zenon_H9c zenon_H22 zenon_H8e zenon_H8f zenon_H7d zenon_H5f zenon_H56 zenon_H2b zenon_H71 zenon_H34 zenon_Ha7 zenon_Ha9. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.01/47.20 apply (zenon_L10_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.01/47.20 apply (zenon_L17_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.01/47.20 apply (zenon_L25_); trivial. % 47.01/47.20 apply (zenon_L26_); trivial. % 47.01/47.20 (* end of lemma zenon_L27_ *) % 47.01/47.20 assert (zenon_L28_ : ((e12) = (op1 (e11) (e11))) -> ((op1 (e13) (e11)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H19 zenon_Haf zenon_Hb0. % 47.01/47.20 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ]. % 47.01/47.20 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((op1 (e11) (e11)) = (op1 (e13) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hb0. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H6b. % 47.01/47.20 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 47.01/47.20 cut (((op1 (e13) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e12) = (op1 (e11) (e11))) = ((op1 (e13) (e11)) = (op1 (e11) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hb1. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H19. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 47.01/47.20 cut (((e12) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ]. % 47.01/47.20 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((e12) = (op1 (e13) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hb2. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H6b. % 47.01/47.20 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 47.01/47.20 cut (((op1 (e13) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_Hb3 zenon_Haf). % 47.01/47.20 apply zenon_H6c. apply refl_equal. % 47.01/47.20 apply zenon_H6c. apply refl_equal. % 47.01/47.20 apply zenon_H58. apply refl_equal. % 47.01/47.20 apply zenon_H6c. apply refl_equal. % 47.01/47.20 apply zenon_H6c. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L28_ *) % 47.01/47.20 assert (zenon_L29_ : (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e13)) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hb4 zenon_H5f zenon_Hb5. % 47.01/47.20 cut (((op1 (e10) (e11)) = (e13)) = ((op1 (e10) (e11)) = (op1 (e13) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hb4. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H5f. % 47.01/47.20 cut (((e13) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 47.01/47.20 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H20. apply refl_equal. % 47.01/47.20 apply zenon_Hb6. apply sym_equal. exact zenon_Hb5. % 47.01/47.20 (* end of lemma zenon_L29_ *) % 47.01/47.20 assert (zenon_L30_ : (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e13)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hb7 zenon_H8e zenon_Hb8. % 47.01/47.20 cut (((op1 (e10) (e13)) = (e12)) = ((op1 (e10) (e13)) = (op1 (e12) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hb7. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H8e. % 47.01/47.20 cut (((e12) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 47.01/47.20 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_Hba. apply refl_equal. % 47.01/47.20 apply zenon_Hb9. apply sym_equal. exact zenon_Hb8. % 47.01/47.20 (* end of lemma zenon_L30_ *) % 47.01/47.20 assert (zenon_L31_ : ((op1 (e10) (e12)) = (e10)) -> ((op1 (e10) (e12)) = (e13)) -> (~((e10) = (e13))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H22 zenon_Hbb zenon_H35. % 47.01/47.20 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 47.01/47.20 cut (((e13) = (e13)) = ((e10) = (e13))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H35. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H36. % 47.01/47.20 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 47.01/47.20 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (e10) (e12)) = (e10)) = ((e13) = (e10))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H38. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H22. % 47.01/47.20 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 47.01/47.20 cut (((op1 (e10) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hbc]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_Hbc zenon_Hbb). % 47.01/47.20 apply zenon_H32. apply refl_equal. % 47.01/47.20 apply zenon_H37. apply refl_equal. % 47.01/47.20 apply zenon_H37. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L31_ *) % 47.01/47.20 assert (zenon_L32_ : ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((op1 (e11) (e12)) = (e13)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H2c zenon_Hbd zenon_H1c zenon_Hbe. % 47.01/47.20 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc0 ]. % 47.01/47.20 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((op1 (e11) (e10)) = (op1 (e11) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hbe. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_Hbf. % 47.01/47.20 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 47.01/47.20 cut (((op1 (e11) (e12)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) = ((op1 (e11) (e12)) = (op1 (e11) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hc1. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H2c. % 47.01/47.20 cut (((op1 (e11) (op1 (op1 (e11) (e11)) (e11))) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 47.01/47.20 cut (((e13) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hc2]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc0 ]. % 47.01/47.20 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((e13) = (op1 (e11) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hc2. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_Hbf. % 47.01/47.20 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 47.01/47.20 cut (((op1 (e11) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_Hc3 zenon_Hbd). % 47.01/47.20 apply zenon_Hc0. apply refl_equal. % 47.01/47.20 apply zenon_Hc0. apply refl_equal. % 47.01/47.20 apply (zenon_L6_); trivial. % 47.01/47.20 apply zenon_Hc0. apply refl_equal. % 47.01/47.20 apply zenon_Hc0. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L32_ *) % 47.01/47.20 assert (zenon_L33_ : (((op1 (op1 (e10) (e12)) (op1 (e10) (e12))) = (e10))/\(((op1 (op1 (e11) (e12)) (op1 (e11) (e12))) = (e11))/\(((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (e12))/\((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (e13))))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H8d zenon_Hc4 zenon_Ha8 zenon_Hc5. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H91. zenon_intro zenon_H90. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H93. zenon_intro zenon_H92. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H92). zenon_intro zenon_H95. zenon_intro zenon_H94. % 47.01/47.20 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e12) (e13)) = (op1 (e13) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hc5. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H96. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (e13)) = ((op1 (e13) (e13)) = (op1 (e12) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hc6. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H94. % 47.01/47.20 cut (((e13) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 47.01/47.20 cut (((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (op1 (e13) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hc8. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H96. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (op1 (e13) (e12)) (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e13) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 47.01/47.20 cut (((e13) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_Hca. apply sym_equal. exact zenon_Hc4. % 47.01/47.20 apply zenon_Hca. apply sym_equal. exact zenon_Hc4. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 apply zenon_Hc7. apply sym_equal. exact zenon_Ha8. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L33_ *) % 47.01/47.20 assert (zenon_L34_ : ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H34 zenon_H71 zenon_H2b zenon_H56 zenon_H5f zenon_H7d zenon_Hc5 zenon_Ha8 zenon_Hc4 zenon_H8e zenon_H22 zenon_H9c. % 47.01/47.20 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.01/47.20 apply (zenon_L20_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.01/47.20 apply (zenon_L21_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.01/47.20 apply (zenon_L33_); trivial. % 47.01/47.20 apply (zenon_L24_); trivial. % 47.01/47.20 (* end of lemma zenon_L34_ *) % 47.01/47.20 assert (zenon_L35_ : (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hcb zenon_H35 zenon_Hbe zenon_H1c zenon_H2c zenon_H8f zenon_H34 zenon_H71 zenon_H2b zenon_H56 zenon_H5f zenon_H7d zenon_Hc5 zenon_Ha8 zenon_H8e zenon_H22 zenon_H9c. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hcc ]. % 47.01/47.20 apply (zenon_L31_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hcd ]. % 47.01/47.20 apply (zenon_L32_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hc4 ]. % 47.01/47.20 apply (zenon_L25_); trivial. % 47.01/47.20 apply (zenon_L34_); trivial. % 47.01/47.20 (* end of lemma zenon_L35_ *) % 47.01/47.20 assert (zenon_L36_ : (~((op1 (e13) (e13)) = (op1 (op1 (e13) (e11)) (op1 (e13) (e11))))) -> ((op1 (e13) (e11)) = (e13)) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hce zenon_Hb5. % 47.01/47.20 cut (((e13) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 47.01/47.20 cut (((e13) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_Hb6. apply sym_equal. exact zenon_Hb5. % 47.01/47.20 apply zenon_Hb6. apply sym_equal. exact zenon_Hb5. % 47.01/47.20 (* end of lemma zenon_L36_ *) % 47.01/47.20 assert (zenon_L37_ : (((op1 (op1 (e10) (e11)) (op1 (e10) (e11))) = (e10))/\(((op1 (op1 (e11) (e11)) (op1 (e11) (e11))) = (e11))/\(((op1 (op1 (e12) (e11)) (op1 (e12) (e11))) = (e12))/\((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (e13))))) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H7c zenon_Hb5 zenon_Ha8 zenon_Hc5. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H7c). zenon_intro zenon_H7f. zenon_intro zenon_H7e. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H7e). zenon_intro zenon_H81. zenon_intro zenon_H80. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82. % 47.01/47.20 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e12) (e13)) = (op1 (e13) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hc5. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H96. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (e13)) = ((op1 (e13) (e13)) = (op1 (e12) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hc6. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H82. % 47.01/47.20 cut (((e13) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 47.01/47.20 cut (((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (op1 (e13) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hcf. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H96. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (op1 (e13) (e11)) (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 47.01/47.20 congruence. % 47.01/47.20 apply (zenon_L36_); trivial. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 apply zenon_Hc7. apply sym_equal. exact zenon_Ha8. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L37_ *) % 47.01/47.20 assert (zenon_L38_ : ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H34 zenon_H71 zenon_H2b zenon_Hc5 zenon_Ha8 zenon_Hb5 zenon_H8f zenon_H8b zenon_H8e zenon_H22 zenon_H9c. % 47.01/47.20 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.01/47.20 apply (zenon_L20_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.01/47.20 apply (zenon_L37_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.01/47.20 apply (zenon_L23_); trivial. % 47.01/47.20 apply (zenon_L24_); trivial. % 47.01/47.20 (* end of lemma zenon_L38_ *) % 47.01/47.20 assert (zenon_L39_ : (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hd0 zenon_H6a zenon_H5f zenon_H56 zenon_H2c zenon_H1c zenon_Hbe zenon_H35 zenon_Hcb zenon_Hb0 zenon_H19 zenon_H34 zenon_H71 zenon_H2b zenon_Hc5 zenon_Ha8 zenon_H8f zenon_H8b zenon_H8e zenon_H22 zenon_H9c. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.01/47.20 apply (zenon_L19_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.01/47.20 apply (zenon_L35_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.01/47.20 apply (zenon_L28_); trivial. % 47.01/47.20 apply (zenon_L38_); trivial. % 47.01/47.20 (* end of lemma zenon_L39_ *) % 47.01/47.20 assert (zenon_L40_ : (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> ((op1 (e13) (e11)) = (e11)) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hb4 zenon_Hd3 zenon_H7d. % 47.01/47.20 cut (((op1 (e10) (e11)) = (e11)) = ((op1 (e10) (e11)) = (op1 (e13) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hb4. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_Hd3. % 47.01/47.20 cut (((e11) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 47.01/47.20 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H20. apply refl_equal. % 47.01/47.20 apply zenon_H89. apply sym_equal. exact zenon_H7d. % 47.01/47.20 (* end of lemma zenon_L40_ *) % 47.01/47.20 assert (zenon_L41_ : (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e11)) = (e13)) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hd4 zenon_H1c zenon_H7d zenon_Hb4 zenon_H19 zenon_H56 zenon_H1b zenon_H60. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H1d | zenon_intro zenon_Hd5 ]. % 47.01/47.20 apply (zenon_L4_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd6 ]. % 47.01/47.20 apply (zenon_L40_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H57 | zenon_intro zenon_H5f ]. % 47.01/47.20 apply (zenon_L15_); trivial. % 47.01/47.20 apply (zenon_L17_); trivial. % 47.01/47.20 (* end of lemma zenon_L41_ *) % 47.01/47.20 assert (zenon_L42_ : (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hac zenon_H3b zenon_H1b zenon_H19 zenon_Hb4 zenon_Hd4 zenon_Hcb zenon_H35 zenon_Hbe zenon_H1c zenon_H2c zenon_H8f zenon_H34 zenon_H71 zenon_H2b zenon_H56 zenon_H5f zenon_H7d zenon_Hc5 zenon_H8e zenon_H22 zenon_H9c. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.01/47.20 apply (zenon_L10_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.01/47.20 apply (zenon_L41_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.01/47.20 apply (zenon_L25_); trivial. % 47.01/47.20 apply (zenon_L35_); trivial. % 47.01/47.20 (* end of lemma zenon_L42_ *) % 47.01/47.20 assert (zenon_L43_ : (~((e12) = (e12))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H53. % 47.01/47.20 apply zenon_H53. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L43_ *) % 47.01/47.20 assert (zenon_L44_ : ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e13)) = (e13)) -> (~((e12) = (e13))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H8e zenon_Hd7 zenon_Hd8. % 47.01/47.20 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 47.01/47.20 cut (((e13) = (e13)) = ((e12) = (e13))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hd8. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H36. % 47.01/47.20 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 47.01/47.20 cut (((e13) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (e10) (e13)) = (e12)) = ((e13) = (e12))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hd9. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H8e. % 47.01/47.20 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.01/47.20 cut (((op1 (e10) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_Hda zenon_Hd7). % 47.01/47.20 apply zenon_H53. apply refl_equal. % 47.01/47.20 apply zenon_H37. apply refl_equal. % 47.01/47.20 apply zenon_H37. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L44_ *) % 47.01/47.20 assert (zenon_L45_ : ((op1 (e10) (e11)) = (e11)) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hd3 zenon_H4f zenon_Hdb. % 47.01/47.20 elim (classic ((op1 (e10) (e11)) = (op1 (e10) (e11)))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ]. % 47.01/47.20 cut (((op1 (e10) (e11)) = (op1 (e10) (e11))) = ((op1 (e10) (e10)) = (op1 (e10) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hdb. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H1f. % 47.01/47.20 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 47.01/47.20 cut (((op1 (e10) (e11)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hdc]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (e10) (e11)) = (e11)) = ((op1 (e10) (e11)) = (op1 (e10) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hdc. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_Hd3. % 47.01/47.20 cut (((e11) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 47.01/47.20 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H20. apply refl_equal. % 47.01/47.20 apply zenon_Hdd. apply sym_equal. exact zenon_H4f. % 47.01/47.20 apply zenon_H20. apply refl_equal. % 47.01/47.20 apply zenon_H20. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L45_ *) % 47.01/47.20 assert (zenon_L46_ : (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e12)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hde zenon_H22 zenon_Hdf. % 47.01/47.20 cut (((op1 (e10) (e12)) = (e10)) = ((op1 (e10) (e12)) = (op1 (e11) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hde. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H22. % 47.01/47.20 cut (((e10) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_He0]. % 47.01/47.20 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H26. apply refl_equal. % 47.01/47.20 apply zenon_He0. apply sym_equal. exact zenon_Hdf. % 47.01/47.20 (* end of lemma zenon_L46_ *) % 47.01/47.20 assert (zenon_L47_ : (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e11) (e12)) = (e11)) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hbe zenon_He1 zenon_He2. % 47.01/47.20 cut (((op1 (e11) (e10)) = (e11)) = ((op1 (e11) (e10)) = (op1 (e11) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hbe. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_He1. % 47.01/47.20 cut (((e11) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_He3]. % 47.01/47.20 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_He4. apply refl_equal. % 47.01/47.20 apply zenon_He3. apply sym_equal. exact zenon_He2. % 47.01/47.20 (* end of lemma zenon_L47_ *) % 47.01/47.20 assert (zenon_L48_ : ((e12) = (op1 (e11) (e11))) -> ((op1 (e11) (e12)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H19 zenon_He5 zenon_He6. % 47.01/47.20 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc0 ]. % 47.01/47.20 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((op1 (e11) (e11)) = (op1 (e11) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_He6. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_Hbf. % 47.01/47.20 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 47.01/47.20 cut (((op1 (e11) (e12)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e12) = (op1 (e11) (e11))) = ((op1 (e11) (e12)) = (op1 (e11) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_He7. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H19. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 47.01/47.20 cut (((e12) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc0 ]. % 47.01/47.20 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((e12) = (op1 (e11) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_He8. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_Hbf. % 47.01/47.20 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 47.01/47.20 cut (((op1 (e11) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_He9]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_He9 zenon_He5). % 47.01/47.20 apply zenon_Hc0. apply refl_equal. % 47.01/47.20 apply zenon_Hc0. apply refl_equal. % 47.01/47.20 apply zenon_H58. apply refl_equal. % 47.01/47.20 apply zenon_Hc0. apply refl_equal. % 47.01/47.20 apply zenon_Hc0. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L48_ *) % 47.01/47.20 assert (zenon_L49_ : (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e10) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((e12) = (op1 (e11) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hea zenon_H22 zenon_Hde zenon_He1 zenon_He6 zenon_H19 zenon_H2c zenon_H1c zenon_Hbe. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hdf | zenon_intro zenon_Heb ]. % 47.01/47.20 apply (zenon_L46_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_He2 | zenon_intro zenon_Hec ]. % 47.01/47.20 apply (zenon_L47_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_He5 | zenon_intro zenon_Hbd ]. % 47.01/47.20 apply (zenon_L48_); trivial. % 47.01/47.20 apply (zenon_L32_); trivial. % 47.01/47.20 (* end of lemma zenon_L49_ *) % 47.01/47.20 assert (zenon_L50_ : ((op1 (e12) (e10)) = (e11)) -> ((op1 (e12) (e10)) = (e12)) -> (~((e11) = (e12))) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hed zenon_Hee zenon_H51. % 47.01/47.20 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 47.01/47.20 cut (((e12) = (e12)) = ((e11) = (e12))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H51. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H52. % 47.01/47.20 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.01/47.20 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (e12) (e10)) = (e11)) = ((e12) = (e11))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H54. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_Hed. % 47.01/47.20 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 47.01/47.20 cut (((op1 (e12) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_Hef zenon_Hee). % 47.01/47.20 apply zenon_H17. apply refl_equal. % 47.01/47.20 apply zenon_H53. apply refl_equal. % 47.01/47.20 apply zenon_H53. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L50_ *) % 47.01/47.20 assert (zenon_L51_ : ((e12) = (op1 (e11) (e11))) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H19 zenon_Hf0 zenon_Hf1. % 47.01/47.20 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf3 ]. % 47.01/47.20 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((op1 (e11) (e11)) = (op1 (e12) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hf1. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_Hf2. % 47.01/47.20 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 47.01/47.20 cut (((op1 (e12) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hf4]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e12) = (op1 (e11) (e11))) = ((op1 (e12) (e11)) = (op1 (e11) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hf4. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H19. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 47.01/47.20 cut (((e12) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf3 ]. % 47.01/47.20 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((e12) = (op1 (e12) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hf5. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_Hf2. % 47.01/47.20 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 47.01/47.20 cut (((op1 (e12) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hf6]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_Hf6 zenon_Hf0). % 47.01/47.20 apply zenon_Hf3. apply refl_equal. % 47.01/47.20 apply zenon_Hf3. apply refl_equal. % 47.01/47.20 apply zenon_H58. apply refl_equal. % 47.01/47.20 apply zenon_Hf3. apply refl_equal. % 47.01/47.20 apply zenon_Hf3. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L51_ *) % 47.01/47.20 assert (zenon_L52_ : ((op1 (e13) (e10)) = (e10)) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e12))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H71 zenon_Hf7 zenon_H5c. % 47.01/47.20 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 47.01/47.20 cut (((e12) = (e12)) = ((e10) = (e12))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H5c. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H52. % 47.01/47.20 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.01/47.20 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (e13) (e10)) = (e10)) = ((e12) = (e10))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H5d. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H71. % 47.01/47.20 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 47.01/47.20 cut (((op1 (e13) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_Hf8 zenon_Hf7). % 47.01/47.20 apply zenon_H32. apply refl_equal. % 47.01/47.20 apply zenon_H53. apply refl_equal. % 47.01/47.20 apply zenon_H53. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L52_ *) % 47.01/47.20 assert (zenon_L53_ : (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hf9 zenon_Hfa zenon_Hfb. % 47.01/47.20 cut (((op1 (e12) (e12)) = (e12)) = ((op1 (e12) (e12)) = (op1 (e13) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hf9. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_Hfa. % 47.01/47.20 cut (((e12) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_Ha0. apply refl_equal. % 47.01/47.20 apply zenon_Hfc. apply sym_equal. exact zenon_Hfb. % 47.01/47.20 (* end of lemma zenon_L53_ *) % 47.01/47.20 assert (zenon_L54_ : (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e12) (e13)) = (e11)) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hfd zenon_Hed zenon_Ha7. % 47.01/47.20 cut (((op1 (e12) (e10)) = (e11)) = ((op1 (e12) (e10)) = (op1 (e12) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hfd. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_Hed. % 47.01/47.20 cut (((e11) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 47.01/47.20 cut (((op1 (e12) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H3d. apply refl_equal. % 47.01/47.20 apply zenon_Hfe. apply sym_equal. exact zenon_Ha7. % 47.01/47.20 (* end of lemma zenon_L54_ *) % 47.01/47.20 assert (zenon_L55_ : (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e12)) -> ((op1 (e13) (e13)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hc5 zenon_Hb8 zenon_Hff. % 47.01/47.20 cut (((op1 (e12) (e13)) = (e12)) = ((op1 (e12) (e13)) = (op1 (e13) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hc5. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_Hb8. % 47.01/47.20 cut (((e12) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 47.01/47.20 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H65. apply refl_equal. % 47.01/47.20 apply zenon_H100. apply sym_equal. exact zenon_Hff. % 47.01/47.20 (* end of lemma zenon_L55_ *) % 47.01/47.20 assert (zenon_L56_ : (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e10)) -> ((op1 (e13) (e12)) = (e10)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H101 zenon_H71 zenon_H102. % 47.01/47.20 cut (((op1 (e13) (e10)) = (e10)) = ((op1 (e13) (e10)) = (op1 (e13) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H101. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H71. % 47.01/47.20 cut (((e10) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 47.01/47.20 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H44. apply refl_equal. % 47.01/47.20 apply zenon_H103. apply sym_equal. exact zenon_H102. % 47.01/47.20 (* end of lemma zenon_L56_ *) % 47.01/47.20 assert (zenon_L57_ : (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e11)) -> ((op1 (e13) (e12)) = (e11)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H104 zenon_H7d zenon_H105. % 47.01/47.20 cut (((op1 (e13) (e11)) = (e11)) = ((op1 (e13) (e11)) = (op1 (e13) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H104. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H7d. % 47.01/47.20 cut (((e11) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 47.01/47.20 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H6c. apply refl_equal. % 47.01/47.20 apply zenon_H106. apply sym_equal. exact zenon_H105. % 47.01/47.20 (* end of lemma zenon_L57_ *) % 47.01/47.20 assert (zenon_L58_ : (~((op1 (e12) (e12)) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((op1 (e13) (e13)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H107 zenon_Hff. % 47.01/47.20 cut (((e12) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 47.01/47.20 cut (((e12) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H100. apply sym_equal. exact zenon_Hff. % 47.01/47.20 apply zenon_H100. apply sym_equal. exact zenon_Hff. % 47.01/47.20 (* end of lemma zenon_L58_ *) % 47.01/47.20 assert (zenon_L59_ : (((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (e10))/\(((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (e11))/\(((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e12))/\((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e13)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H9b zenon_Hf9 zenon_Hff zenon_Hc4. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9e. zenon_intro zenon_H9d. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H9d). zenon_intro zenon_H109. zenon_intro zenon_H108. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H10b. zenon_intro zenon_H10a. % 47.01/47.20 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13)) = ((op1 (e12) (e12)) = (op1 (e13) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hf9. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H10a. % 47.01/47.20 cut (((e13) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 47.01/47.20 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e12) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H10c. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H9f. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 47.01/47.20 congruence. % 47.01/47.20 apply (zenon_L58_); trivial. % 47.01/47.20 apply zenon_Ha0. apply refl_equal. % 47.01/47.20 apply zenon_Ha0. apply refl_equal. % 47.01/47.20 apply zenon_Hca. apply sym_equal. exact zenon_Hc4. % 47.01/47.20 (* end of lemma zenon_L59_ *) % 47.01/47.20 assert (zenon_L60_ : ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e13)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H34 zenon_H71 zenon_H2b zenon_H56 zenon_H5f zenon_H7d zenon_Hc5 zenon_Ha8 zenon_Hf9 zenon_Hff zenon_Hc4. % 47.01/47.20 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.01/47.20 apply (zenon_L20_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.01/47.20 apply (zenon_L21_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.01/47.20 apply (zenon_L33_); trivial. % 47.01/47.20 apply (zenon_L59_); trivial. % 47.01/47.20 (* end of lemma zenon_L60_ *) % 47.01/47.20 assert (zenon_L61_ : (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e13)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H10d zenon_H101 zenon_H104 zenon_Hfa zenon_H34 zenon_H71 zenon_H2b zenon_H56 zenon_H5f zenon_H7d zenon_Hc5 zenon_Ha8 zenon_Hf9 zenon_Hff. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H102 | zenon_intro zenon_H10e ]. % 47.01/47.20 apply (zenon_L56_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H105 | zenon_intro zenon_H10f ]. % 47.01/47.20 apply (zenon_L57_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hc4 ]. % 47.01/47.20 apply (zenon_L53_); trivial. % 47.01/47.20 apply (zenon_L60_); trivial. % 47.01/47.20 (* end of lemma zenon_L61_ *) % 47.01/47.20 assert (zenon_L62_ : (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (e11) (e11))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e13)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H110 zenon_H63 zenon_H19 zenon_H1c zenon_Hed zenon_Hfd zenon_H10d zenon_H101 zenon_H104 zenon_Hfa zenon_H34 zenon_H71 zenon_H2b zenon_H56 zenon_H5f zenon_H7d zenon_Hc5 zenon_Hf9 zenon_Hff. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H62 | zenon_intro zenon_H111 ]. % 47.01/47.20 apply (zenon_L18_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H112 ]. % 47.01/47.20 apply (zenon_L54_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Ha8 ]. % 47.01/47.20 apply (zenon_L55_); trivial. % 47.01/47.20 apply (zenon_L61_); trivial. % 47.01/47.20 (* end of lemma zenon_L62_ *) % 47.01/47.20 assert (zenon_L63_ : (((op1 (op1 (e10) (e12)) (op1 (e10) (e12))) = (e10))/\(((op1 (op1 (e11) (e12)) (op1 (e11) (e12))) = (e11))/\(((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (e12))/\((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e12)) = (e11)) -> ((op1 (e13) (e11)) = (e13)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H8d zenon_Hb0 zenon_H105 zenon_Hb5. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H91. zenon_intro zenon_H90. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H93. zenon_intro zenon_H92. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H92). zenon_intro zenon_H95. zenon_intro zenon_H94. % 47.01/47.20 cut (((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (e13)) = ((op1 (e11) (e11)) = (op1 (e13) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hb0. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H94. % 47.01/47.20 cut (((e13) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 47.01/47.20 cut (((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H84 | zenon_intro zenon_H58 ]. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (op1 (e11) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H113. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H84. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (op1 (e13) (e12)) (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e11) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 47.01/47.20 cut (((e11) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H106. apply sym_equal. exact zenon_H105. % 47.01/47.20 apply zenon_H106. apply sym_equal. exact zenon_H105. % 47.01/47.20 apply zenon_H58. apply refl_equal. % 47.01/47.20 apply zenon_H58. apply refl_equal. % 47.01/47.20 apply zenon_Hb6. apply sym_equal. exact zenon_Hb5. % 47.01/47.20 (* end of lemma zenon_L63_ *) % 47.01/47.20 assert (zenon_L64_ : (((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (e10))/\(((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (e11))/\(((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e12))/\((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e13)) = (e12)) -> ((op1 (e12) (e13)) = (e13)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H9b zenon_H115 zenon_Hff zenon_Ha8. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9e. zenon_intro zenon_H9d. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H9d). zenon_intro zenon_H109. zenon_intro zenon_H108. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H10b. zenon_intro zenon_H10a. % 47.01/47.20 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13)) = ((op1 (e12) (e12)) = (op1 (e12) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H115. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H10a. % 47.01/47.20 cut (((e13) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 47.01/47.20 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e12) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H10c. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H9f. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 47.01/47.20 congruence. % 47.01/47.20 apply (zenon_L58_); trivial. % 47.01/47.20 apply zenon_Ha0. apply refl_equal. % 47.01/47.20 apply zenon_Ha0. apply refl_equal. % 47.01/47.20 apply zenon_Hc7. apply sym_equal. exact zenon_Ha8. % 47.01/47.20 (* end of lemma zenon_L64_ *) % 47.01/47.20 assert (zenon_L65_ : ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e13) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e13)) = (e12)) -> ((op1 (e12) (e13)) = (e13)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H34 zenon_H71 zenon_H2b zenon_Hc5 zenon_Hb5 zenon_H105 zenon_Hb0 zenon_H115 zenon_Hff zenon_Ha8. % 47.01/47.20 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.01/47.20 apply (zenon_L20_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.01/47.20 apply (zenon_L37_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.01/47.20 apply (zenon_L63_); trivial. % 47.01/47.20 apply (zenon_L64_); trivial. % 47.01/47.20 (* end of lemma zenon_L65_ *) % 47.01/47.20 assert (zenon_L66_ : ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e13)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H34 zenon_H71 zenon_H2b zenon_Hb5 zenon_Hc5 zenon_Ha8 zenon_Hf9 zenon_Hff zenon_Hc4. % 47.01/47.20 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.01/47.20 apply (zenon_L20_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.01/47.20 apply (zenon_L37_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.01/47.20 apply (zenon_L33_); trivial. % 47.01/47.20 apply (zenon_L59_); trivial. % 47.01/47.20 (* end of lemma zenon_L66_ *) % 47.01/47.20 assert (zenon_L67_ : (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e13)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H10d zenon_H101 zenon_H115 zenon_Hb0 zenon_Hfa zenon_H34 zenon_H71 zenon_H2b zenon_Hb5 zenon_Hc5 zenon_Ha8 zenon_Hf9 zenon_Hff. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H102 | zenon_intro zenon_H10e ]. % 47.01/47.20 apply (zenon_L56_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H105 | zenon_intro zenon_H10f ]. % 47.01/47.20 apply (zenon_L65_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hc4 ]. % 47.01/47.20 apply (zenon_L53_); trivial. % 47.01/47.20 apply (zenon_L66_); trivial. % 47.01/47.20 (* end of lemma zenon_L67_ *) % 47.01/47.20 assert (zenon_L68_ : (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (e11) (e11))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e13)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H110 zenon_H63 zenon_H19 zenon_H1c zenon_Hed zenon_Hfd zenon_H10d zenon_H101 zenon_H115 zenon_Hb0 zenon_Hfa zenon_H34 zenon_H71 zenon_H2b zenon_Hb5 zenon_Hc5 zenon_Hf9 zenon_Hff. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H62 | zenon_intro zenon_H111 ]. % 47.01/47.20 apply (zenon_L18_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H112 ]. % 47.01/47.20 apply (zenon_L54_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Ha8 ]. % 47.01/47.20 apply (zenon_L55_); trivial. % 47.01/47.20 apply (zenon_L67_); trivial. % 47.01/47.20 (* end of lemma zenon_L68_ *) % 47.01/47.20 assert (zenon_L69_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (e11) (e11))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H116 zenon_H5c zenon_Hd0 zenon_H6a zenon_H5f zenon_H56 zenon_H104 zenon_H110 zenon_H63 zenon_H19 zenon_H1c zenon_Hed zenon_Hfd zenon_H10d zenon_H101 zenon_H115 zenon_Hb0 zenon_Hfa zenon_H34 zenon_H71 zenon_H2b zenon_Hc5 zenon_Hf9. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.01/47.20 apply (zenon_L52_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.01/47.20 apply (zenon_L28_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.01/47.20 apply (zenon_L53_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.01/47.20 apply (zenon_L19_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.01/47.20 apply (zenon_L62_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.01/47.20 apply (zenon_L28_); trivial. % 47.01/47.20 apply (zenon_L68_); trivial. % 47.01/47.20 (* end of lemma zenon_L69_ *) % 47.01/47.20 assert (zenon_L70_ : (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H119 zenon_H5b zenon_Hfb. % 47.01/47.20 cut (((op1 (e10) (e12)) = (e12)) = ((op1 (e10) (e12)) = (op1 (e13) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H119. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H5b. % 47.01/47.20 cut (((e12) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 47.01/47.20 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H26. apply refl_equal. % 47.01/47.20 apply zenon_Hfc. apply sym_equal. exact zenon_Hfb. % 47.01/47.20 (* end of lemma zenon_L70_ *) % 47.01/47.20 assert (zenon_L71_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H116 zenon_H5c zenon_H71 zenon_Hb0 zenon_H19 zenon_H5b zenon_H119 zenon_Hc5 zenon_Hb8. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.01/47.20 apply (zenon_L52_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.01/47.20 apply (zenon_L28_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.01/47.20 apply (zenon_L70_); trivial. % 47.01/47.20 apply (zenon_L55_); trivial. % 47.01/47.20 (* end of lemma zenon_L71_ *) % 47.01/47.20 assert (zenon_L72_ : ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e12) (e12)) = (e10)) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H1c zenon_H11a zenon_H19 zenon_H11b. % 47.01/47.20 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e12) (e11)) = (op1 (e12) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H11b. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H9f. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e10) = (op1 (op1 (e11) (e11)) (e11))) = ((op1 (e12) (e12)) = (op1 (e12) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H11c. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H1c. % 47.01/47.20 cut (((op1 (op1 (e11) (e11)) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 47.01/47.20 cut (((e10) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((e10) = (op1 (e12) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H11d. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H9f. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 47.01/47.20 cut (((op1 (e12) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_H11e zenon_H11a). % 47.01/47.20 apply zenon_Ha0. apply refl_equal. % 47.01/47.20 apply zenon_Ha0. apply refl_equal. % 47.01/47.20 apply (zenon_L3_); trivial. % 47.01/47.20 apply zenon_Ha0. apply refl_equal. % 47.01/47.20 apply zenon_Ha0. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L72_ *) % 47.01/47.20 assert (zenon_L73_ : (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e12) (e12)) = (e11)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H11f zenon_Hed zenon_H120. % 47.01/47.20 cut (((op1 (e12) (e10)) = (e11)) = ((op1 (e12) (e10)) = (op1 (e12) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H11f. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_Hed. % 47.01/47.20 cut (((e11) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 47.01/47.20 cut (((op1 (e12) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_H3d. apply refl_equal. % 47.01/47.20 apply zenon_H121. apply sym_equal. exact zenon_H120. % 47.01/47.20 (* end of lemma zenon_L73_ *) % 47.01/47.20 assert (zenon_L74_ : (((op1 (op1 (e10) (e12)) (op1 (e10) (e12))) = (e10))/\(((op1 (op1 (e11) (e12)) (op1 (e11) (e12))) = (e11))/\(((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (e12))/\((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (e13))))) -> ((op1 (e12) (e12)) = (e13)) -> ((op1 (e12) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H8d zenon_H8b zenon_Hb8 zenon_Hc5. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H91. zenon_intro zenon_H90. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H93. zenon_intro zenon_H92. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H92). zenon_intro zenon_H95. zenon_intro zenon_H94. % 47.01/47.20 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e12) (e13)) = (op1 (e13) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hc5. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H96. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (e12)) = ((op1 (e13) (e13)) = (op1 (e12) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hc6. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H95. % 47.01/47.20 cut (((e12) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 47.01/47.20 cut (((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (e13) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H9a. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H96. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 47.01/47.20 congruence. % 47.01/47.20 apply (zenon_L22_); trivial. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 apply zenon_Hb9. apply sym_equal. exact zenon_Hb8. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L74_ *) % 47.01/47.20 assert (zenon_L75_ : (~((op1 (e12) (e12)) = (op1 (op1 (e12) (e13)) (op1 (e12) (e13))))) -> ((op1 (e12) (e13)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H122 zenon_Hb8. % 47.01/47.20 cut (((e12) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 47.01/47.20 cut (((e12) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 47.01/47.20 congruence. % 47.01/47.20 apply zenon_Hb9. apply sym_equal. exact zenon_Hb8. % 47.01/47.20 apply zenon_Hb9. apply sym_equal. exact zenon_Hb8. % 47.01/47.20 (* end of lemma zenon_L75_ *) % 47.01/47.20 assert (zenon_L76_ : (((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (e10))/\(((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (e11))/\(((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e12))/\((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H9b zenon_Hf9 zenon_Hb8 zenon_Hfb. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9e. zenon_intro zenon_H9d. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H9d). zenon_intro zenon_H109. zenon_intro zenon_H108. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H10b. zenon_intro zenon_H10a. % 47.01/47.20 cut (((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e12)) = ((op1 (e12) (e12)) = (op1 (e13) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hf9. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H10b. % 47.01/47.20 cut (((e12) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 47.01/47.20 cut (((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (op1 (e12) (e12)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H123. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H9f. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 47.01/47.20 cut (((op1 (e12) (e12)) = (op1 (op1 (e12) (e13)) (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 47.01/47.20 congruence. % 47.01/47.20 apply (zenon_L75_); trivial. % 47.01/47.20 apply zenon_Ha0. apply refl_equal. % 47.01/47.20 apply zenon_Ha0. apply refl_equal. % 47.01/47.20 apply zenon_Hfc. apply sym_equal. exact zenon_Hfb. % 47.01/47.20 (* end of lemma zenon_L76_ *) % 47.01/47.20 assert (zenon_L77_ : ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H34 zenon_H71 zenon_H2b zenon_H56 zenon_H5f zenon_H7d zenon_Hc5 zenon_H8b zenon_Hf9 zenon_Hb8 zenon_Hfb. % 47.01/47.20 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.01/47.20 apply (zenon_L20_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.01/47.20 apply (zenon_L21_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.01/47.20 apply (zenon_L74_); trivial. % 47.01/47.20 apply (zenon_L76_); trivial. % 47.01/47.20 (* end of lemma zenon_L77_ *) % 47.01/47.20 assert (zenon_L78_ : (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hd4 zenon_H1c zenon_H1b zenon_Hb4 zenon_H19 zenon_H34 zenon_H71 zenon_H2b zenon_H56 zenon_H7d zenon_Hc5 zenon_H8b zenon_Hf9 zenon_Hb8 zenon_Hfb. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H1d | zenon_intro zenon_Hd5 ]. % 47.01/47.20 apply (zenon_L4_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd6 ]. % 47.01/47.20 apply (zenon_L40_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H57 | zenon_intro zenon_H5f ]. % 47.01/47.20 apply (zenon_L15_); trivial. % 47.01/47.20 apply (zenon_L77_); trivial. % 47.01/47.20 (* end of lemma zenon_L78_ *) % 47.01/47.20 assert (zenon_L79_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((e12) = (op1 (e11) (e11))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H116 zenon_H5c zenon_H19 zenon_H10d zenon_H101 zenon_H115 zenon_Hb0 zenon_Hfa zenon_H34 zenon_H71 zenon_H2b zenon_Hb5 zenon_Hc5 zenon_Ha8 zenon_Hf9. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.01/47.20 apply (zenon_L52_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.01/47.20 apply (zenon_L28_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.01/47.20 apply (zenon_L53_); trivial. % 47.01/47.20 apply (zenon_L67_); trivial. % 47.01/47.20 (* end of lemma zenon_L79_ *) % 47.01/47.20 assert (zenon_L80_ : (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((e12) = (op1 (e11) (e11))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hd0 zenon_H6a zenon_H60 zenon_H1b zenon_H56 zenon_Hb4 zenon_H1c zenon_Hd4 zenon_H116 zenon_H5c zenon_H19 zenon_H10d zenon_H101 zenon_H115 zenon_Hb0 zenon_Hfa zenon_H34 zenon_H71 zenon_H2b zenon_Hc5 zenon_Ha8 zenon_Hf9. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.01/47.20 apply (zenon_L19_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.01/47.20 apply (zenon_L41_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.01/47.20 apply (zenon_L28_); trivial. % 47.01/47.20 apply (zenon_L79_); trivial. % 47.01/47.20 (* end of lemma zenon_L80_ *) % 47.01/47.20 assert (zenon_L81_ : (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((e12) = (op1 (e11) (e11))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H110 zenon_H63 zenon_Hed zenon_Hfd zenon_Hd0 zenon_H6a zenon_H60 zenon_H1b zenon_H56 zenon_Hb4 zenon_H1c zenon_Hd4 zenon_H116 zenon_H5c zenon_H19 zenon_H10d zenon_H101 zenon_H115 zenon_Hb0 zenon_Hfa zenon_H34 zenon_H71 zenon_H2b zenon_Hc5 zenon_Hf9. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.01/47.20 apply (zenon_L52_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.01/47.20 apply (zenon_L28_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.01/47.20 apply (zenon_L53_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H62 | zenon_intro zenon_H111 ]. % 47.01/47.20 apply (zenon_L18_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H112 ]. % 47.01/47.20 apply (zenon_L54_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Ha8 ]. % 47.01/47.20 apply (zenon_L55_); trivial. % 47.01/47.20 apply (zenon_L80_); trivial. % 47.01/47.20 (* end of lemma zenon_L81_ *) % 47.01/47.20 assert (zenon_L82_ : (((op1 (op1 (e10) (e11)) (op1 (e10) (e11))) = (e10))/\(((op1 (op1 (e11) (e11)) (op1 (e11) (e11))) = (e11))/\(((op1 (op1 (e12) (e11)) (op1 (e12) (e11))) = (e12))/\((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (e13))))) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H7c zenon_Hb5 zenon_Hd7 zenon_H8f. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H7c). zenon_intro zenon_H7f. zenon_intro zenon_H7e. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H7e). zenon_intro zenon_H81. zenon_intro zenon_H80. % 47.01/47.20 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82. % 47.01/47.20 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e10) (e13)) = (op1 (e13) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H8f. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H96. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (e13)) = ((op1 (e13) (e13)) = (op1 (e10) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H98. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H82. % 47.01/47.20 cut (((e13) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 47.01/47.20 cut (((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (op1 (e13) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hcf. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H96. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 47.01/47.20 cut (((op1 (e13) (e13)) = (op1 (op1 (e13) (e11)) (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 47.01/47.20 congruence. % 47.01/47.20 apply (zenon_L36_); trivial. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 apply zenon_H124. apply sym_equal. exact zenon_Hd7. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 apply zenon_H97. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L82_ *) % 47.01/47.20 assert (zenon_L83_ : ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> False). % 47.01/47.20 do 0 intro. intros zenon_H34 zenon_H71 zenon_H2b zenon_H8f zenon_Hd7 zenon_Hb5 zenon_Hc5 zenon_H8b zenon_Hf9 zenon_Hb8 zenon_Hfb. % 47.01/47.20 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.01/47.20 apply (zenon_L20_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.01/47.20 apply (zenon_L82_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.01/47.20 apply (zenon_L74_); trivial. % 47.01/47.20 apply (zenon_L76_); trivial. % 47.01/47.20 (* end of lemma zenon_L83_ *) % 47.01/47.20 assert (zenon_L84_ : ((op1 (e12) (e13)) = (e12)) -> ((op1 (e12) (e13)) = (e13)) -> (~((e12) = (e13))) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hb8 zenon_Ha8 zenon_Hd8. % 47.01/47.20 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 47.01/47.20 cut (((e13) = (e13)) = ((e12) = (e13))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hd8. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H36. % 47.01/47.20 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 47.01/47.20 cut (((e13) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((op1 (e12) (e13)) = (e12)) = ((e13) = (e12))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_Hd9. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_Hb8. % 47.01/47.20 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.01/47.20 cut (((op1 (e12) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_Hab zenon_Ha8). % 47.01/47.20 apply zenon_H53. apply refl_equal. % 47.01/47.20 apply zenon_H37. apply refl_equal. % 47.01/47.20 apply zenon_H37. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L84_ *) % 47.01/47.20 assert (zenon_L85_ : (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((e12) = (op1 (e11) (e11))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e12)) -> (~((e12) = (e13))) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hac zenon_H3b zenon_H2c zenon_H110 zenon_H63 zenon_Hed zenon_Hfd zenon_Hd0 zenon_H6a zenon_H1b zenon_H56 zenon_Hb4 zenon_H1c zenon_Hd4 zenon_H116 zenon_H5c zenon_H19 zenon_H10d zenon_H101 zenon_H115 zenon_Hb0 zenon_H11f zenon_H11b zenon_H125 zenon_Hfb zenon_Hf9 zenon_Hc5 zenon_Hb5 zenon_Hd7 zenon_H8f zenon_H2b zenon_H71 zenon_H34 zenon_Hb8 zenon_Hd8. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.01/47.20 apply (zenon_L10_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H11a | zenon_intro zenon_H126 ]. % 47.01/47.20 apply (zenon_L72_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 47.01/47.20 apply (zenon_L73_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hfa | zenon_intro zenon_H8b ]. % 47.01/47.20 apply (zenon_L81_); trivial. % 47.01/47.20 apply (zenon_L83_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.01/47.20 apply (zenon_L83_); trivial. % 47.01/47.20 apply (zenon_L84_); trivial. % 47.01/47.20 (* end of lemma zenon_L85_ *) % 47.01/47.20 assert (zenon_L86_ : (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((e12) = (op1 (e11) (e11))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e12)) -> (~((e12) = (e13))) -> False). % 47.01/47.20 do 0 intro. intros zenon_Hac zenon_H3b zenon_H2c zenon_H110 zenon_H63 zenon_Hed zenon_Hfd zenon_Hd0 zenon_H6a zenon_H1b zenon_H56 zenon_Hb4 zenon_H1c zenon_Hd4 zenon_H116 zenon_H5c zenon_H19 zenon_H10d zenon_H101 zenon_H115 zenon_Hb0 zenon_H11f zenon_H11b zenon_H125 zenon_Hfb zenon_Hf9 zenon_Hc5 zenon_Hd7 zenon_H8f zenon_H2b zenon_H71 zenon_H34 zenon_Hb8 zenon_Hd8. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H11a | zenon_intro zenon_H126 ]. % 47.01/47.20 apply (zenon_L72_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 47.01/47.20 apply (zenon_L73_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hfa | zenon_intro zenon_H8b ]. % 47.01/47.20 apply (zenon_L53_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.01/47.20 apply (zenon_L19_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.01/47.20 apply (zenon_L78_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.01/47.20 apply (zenon_L28_); trivial. % 47.01/47.20 apply (zenon_L85_); trivial. % 47.01/47.20 (* end of lemma zenon_L86_ *) % 47.01/47.20 assert (zenon_L87_ : ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((op1 (e11) (e11)) = (e13)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H2c zenon_H128 zenon_H1c zenon_H129. % 47.01/47.20 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H84 | zenon_intro zenon_H58 ]. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((op1 (e11) (e10)) = (op1 (e11) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H129. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H84. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H12a]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) = ((op1 (e11) (e11)) = (op1 (e11) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H12a. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H2c. % 47.01/47.20 cut (((op1 (e11) (op1 (op1 (e11) (e11)) (e11))) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 47.01/47.20 cut (((e13) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H84 | zenon_intro zenon_H58 ]. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((e13) = (op1 (e11) (e11)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H12b. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H84. % 47.01/47.20 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 47.01/47.20 cut (((op1 (e11) (e11)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 47.01/47.20 congruence. % 47.01/47.20 exact (zenon_H12c zenon_H128). % 47.01/47.20 apply zenon_H58. apply refl_equal. % 47.01/47.20 apply zenon_H58. apply refl_equal. % 47.01/47.20 apply (zenon_L6_); trivial. % 47.01/47.20 apply zenon_H58. apply refl_equal. % 47.01/47.20 apply zenon_H58. apply refl_equal. % 47.01/47.20 (* end of lemma zenon_L87_ *) % 47.01/47.20 assert (zenon_L88_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (e11) (e11))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H116 zenon_H5c zenon_H110 zenon_H63 zenon_H19 zenon_H1c zenon_Hed zenon_Hfd zenon_H10d zenon_H101 zenon_H115 zenon_Hb0 zenon_Hfa zenon_H34 zenon_H71 zenon_H2b zenon_Hb5 zenon_Hc5 zenon_Hf9. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.01/47.20 apply (zenon_L52_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.01/47.20 apply (zenon_L28_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.01/47.20 apply (zenon_L53_); trivial. % 47.01/47.20 apply (zenon_L68_); trivial. % 47.01/47.20 (* end of lemma zenon_L88_ *) % 47.01/47.20 assert (zenon_L89_ : (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((e12) = (op1 (e11) (e11))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e12)) -> (~((e12) = (e13))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H12d zenon_H119 zenon_He6 zenon_Hac zenon_H3b zenon_H2c zenon_H110 zenon_H63 zenon_Hed zenon_Hfd zenon_Hd0 zenon_H6a zenon_H1b zenon_H56 zenon_Hb4 zenon_H1c zenon_Hd4 zenon_H116 zenon_H5c zenon_H19 zenon_H10d zenon_H101 zenon_H115 zenon_Hb0 zenon_H11f zenon_H11b zenon_H125 zenon_Hf9 zenon_Hc5 zenon_Hb5 zenon_Hd7 zenon_H8f zenon_H2b zenon_H71 zenon_H34 zenon_Hb8 zenon_Hd8. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H5b | zenon_intro zenon_H12e ]. % 47.01/47.20 apply (zenon_L71_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_He5 | zenon_intro zenon_H12f ]. % 47.01/47.20 apply (zenon_L48_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 47.01/47.20 apply (zenon_L88_); trivial. % 47.01/47.20 apply (zenon_L85_); trivial. % 47.01/47.20 (* end of lemma zenon_L89_ *) % 47.01/47.20 assert (zenon_L90_ : (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((e12) = (op1 (e11) (e11))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((e12) = (e13))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H130 zenon_H51 zenon_Hf1 zenon_H12d zenon_H119 zenon_He6 zenon_Hac zenon_H3b zenon_H2c zenon_H110 zenon_H63 zenon_Hed zenon_Hfd zenon_Hd0 zenon_H6a zenon_H1b zenon_H56 zenon_Hb4 zenon_H1c zenon_Hd4 zenon_H116 zenon_H5c zenon_H19 zenon_H10d zenon_H101 zenon_H115 zenon_Hb0 zenon_H11f zenon_H11b zenon_H125 zenon_Hf9 zenon_Hc5 zenon_Hb5 zenon_Hd7 zenon_H8f zenon_H2b zenon_H71 zenon_H34 zenon_Hd8. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.01/47.20 apply (zenon_L50_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.01/47.20 apply (zenon_L51_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.01/47.20 apply (zenon_L88_); trivial. % 47.01/47.20 apply (zenon_L89_); trivial. % 47.01/47.20 (* end of lemma zenon_L90_ *) % 47.01/47.20 assert (zenon_L91_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((e12) = (op1 (e11) (e11))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H48 zenon_Hd8 zenon_H71 zenon_H2b zenon_H8f zenon_Hd7 zenon_Hc5 zenon_Hf9 zenon_H125 zenon_H11b zenon_H11f zenon_Hb0 zenon_H115 zenon_H101 zenon_H10d zenon_H19 zenon_H5c zenon_H116 zenon_Hd4 zenon_Hb4 zenon_H56 zenon_H1b zenon_H6a zenon_Hd0 zenon_Hfd zenon_Hed zenon_H63 zenon_H110 zenon_Hac zenon_He6 zenon_H119 zenon_H12d zenon_Hf1 zenon_H51 zenon_H130 zenon_H129 zenon_H104 zenon_H133 zenon_H3b zenon_H2c zenon_H1c zenon_H42. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.01/47.20 apply (zenon_L7_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H5f | zenon_intro zenon_H134 ]. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.01/47.20 apply (zenon_L50_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.01/47.20 apply (zenon_L51_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.01/47.20 apply (zenon_L69_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H5b | zenon_intro zenon_H12e ]. % 47.01/47.20 apply (zenon_L71_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_He5 | zenon_intro zenon_H12f ]. % 47.01/47.20 apply (zenon_L48_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 47.01/47.20 apply (zenon_L69_); trivial. % 47.01/47.20 apply (zenon_L86_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H128 | zenon_intro zenon_H135 ]. % 47.01/47.20 apply (zenon_L87_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H60 | zenon_intro zenon_Hb5 ]. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.01/47.20 apply (zenon_L50_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.01/47.20 apply (zenon_L51_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.01/47.20 apply (zenon_L81_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H5b | zenon_intro zenon_H12e ]. % 47.01/47.20 apply (zenon_L71_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_He5 | zenon_intro zenon_H12f ]. % 47.01/47.20 apply (zenon_L48_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 47.01/47.20 apply (zenon_L81_); trivial. % 47.01/47.20 apply (zenon_L86_); trivial. % 47.01/47.20 apply (zenon_L90_); trivial. % 47.01/47.20 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.01/47.20 apply (zenon_L10_); trivial. % 47.01/47.20 apply (zenon_L11_); trivial. % 47.01/47.20 (* end of lemma zenon_L91_ *) % 47.01/47.20 assert (zenon_L92_ : ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((op1 (e11) (e13)) = (e13)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> False). % 47.01/47.20 do 0 intro. intros zenon_H2c zenon_H136 zenon_H1c zenon_H137. % 47.01/47.20 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 47.01/47.20 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((op1 (e11) (e10)) = (op1 (e11) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H137. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H138. % 47.01/47.20 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 47.01/47.20 cut (((op1 (e11) (e13)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 47.01/47.20 congruence. % 47.01/47.20 cut (((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) = ((op1 (e11) (e13)) = (op1 (e11) (e10)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H13a. % 47.01/47.20 rewrite <- zenon_D_pnotp. % 47.01/47.20 exact zenon_H2c. % 47.01/47.20 cut (((op1 (e11) (op1 (op1 (e11) (e11)) (e11))) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 47.01/47.20 cut (((e13) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 47.01/47.20 congruence. % 47.01/47.20 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 47.01/47.20 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e13) = (op1 (e11) (e13)))). % 47.01/47.20 intro zenon_D_pnotp. % 47.01/47.20 apply zenon_H13b. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H138. % 47.01/47.21 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 47.01/47.21 cut (((op1 (e11) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H13c]. % 47.01/47.21 congruence. % 47.01/47.21 exact (zenon_H13c zenon_H136). % 47.01/47.21 apply zenon_H139. apply refl_equal. % 47.01/47.21 apply zenon_H139. apply refl_equal. % 47.01/47.21 apply (zenon_L6_); trivial. % 47.01/47.21 apply zenon_H139. apply refl_equal. % 47.01/47.21 apply zenon_H139. apply refl_equal. % 47.01/47.21 (* end of lemma zenon_L92_ *) % 47.01/47.21 assert (zenon_L93_ : ((op1 (e10) (e13)) = (e10)) -> ((op1 (e10) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H13d zenon_H22 zenon_H13e. % 47.01/47.21 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_H13f | zenon_intro zenon_Hba ]. % 47.01/47.21 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((op1 (e10) (e12)) = (op1 (e10) (e13)))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H13e. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H13f. % 47.01/47.21 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 47.01/47.21 cut (((op1 (e10) (e13)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 47.01/47.21 congruence. % 47.01/47.21 cut (((op1 (e10) (e13)) = (e10)) = ((op1 (e10) (e13)) = (op1 (e10) (e12)))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H140. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H13d. % 47.01/47.21 cut (((e10) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 47.01/47.21 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 47.01/47.21 congruence. % 47.01/47.21 apply zenon_Hba. apply refl_equal. % 47.01/47.21 apply zenon_Ha2. apply sym_equal. exact zenon_H22. % 47.01/47.21 apply zenon_Hba. apply refl_equal. % 47.01/47.21 apply zenon_Hba. apply refl_equal. % 47.01/47.21 (* end of lemma zenon_L93_ *) % 47.01/47.21 assert (zenon_L94_ : ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H141 zenon_Hd3 zenon_H142. % 47.01/47.21 elim (classic ((op1 (e10) (e12)) = (op1 (e10) (e12)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 47.01/47.21 cut (((op1 (e10) (e12)) = (op1 (e10) (e12))) = ((op1 (e10) (e11)) = (op1 (e10) (e12)))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H142. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H25. % 47.01/47.21 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 47.01/47.21 cut (((op1 (e10) (e12)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H143]. % 47.01/47.21 congruence. % 47.01/47.21 cut (((op1 (e10) (e12)) = (e11)) = ((op1 (e10) (e12)) = (op1 (e10) (e11)))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H143. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H141. % 47.01/47.21 cut (((e11) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H144]. % 47.01/47.21 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 47.01/47.21 congruence. % 47.01/47.21 apply zenon_H26. apply refl_equal. % 47.01/47.21 apply zenon_H144. apply sym_equal. exact zenon_Hd3. % 47.01/47.21 apply zenon_H26. apply refl_equal. % 47.01/47.21 apply zenon_H26. apply refl_equal. % 47.01/47.21 (* end of lemma zenon_L94_ *) % 47.01/47.21 assert (zenon_L95_ : ((e12) = (op1 (e11) (e11))) -> ((op1 (e11) (e11)) = (e11)) -> (~((e11) = (e12))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H19 zenon_H145 zenon_H51. % 47.01/47.21 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 47.01/47.21 cut (((e12) = (e12)) = ((e11) = (e12))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H51. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H52. % 47.01/47.21 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.01/47.21 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 47.01/47.21 congruence. % 47.01/47.21 cut (((e12) = (op1 (e11) (e11))) = ((e12) = (e11))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H54. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H19. % 47.01/47.21 cut (((op1 (e11) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 47.01/47.21 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.01/47.21 congruence. % 47.01/47.21 apply zenon_H53. apply refl_equal. % 47.01/47.21 exact (zenon_H146 zenon_H145). % 47.01/47.21 apply zenon_H53. apply refl_equal. % 47.01/47.21 apply zenon_H53. apply refl_equal. % 47.01/47.21 (* end of lemma zenon_L95_ *) % 47.01/47.21 assert (zenon_L96_ : (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e12) (e11)) = (e11)) -> False). % 47.01/47.21 do 0 intro. intros zenon_H4b zenon_Hed zenon_H147. % 47.01/47.21 cut (((op1 (e12) (e10)) = (e11)) = ((op1 (e12) (e10)) = (op1 (e12) (e11)))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H4b. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_Hed. % 47.01/47.21 cut (((e11) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H148]. % 47.01/47.21 cut (((op1 (e12) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 47.01/47.21 congruence. % 47.01/47.21 apply zenon_H3d. apply refl_equal. % 47.01/47.21 apply zenon_H148. apply sym_equal. exact zenon_H147. % 47.01/47.21 (* end of lemma zenon_L96_ *) % 47.01/47.21 assert (zenon_L97_ : (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e13) (e12)) = (e11)) -> False). % 47.01/47.21 do 0 intro. intros zenon_H119 zenon_H141 zenon_H105. % 47.01/47.21 cut (((op1 (e10) (e12)) = (e11)) = ((op1 (e10) (e12)) = (op1 (e13) (e12)))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H119. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H141. % 47.01/47.21 cut (((e11) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 47.01/47.21 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 47.01/47.21 congruence. % 47.01/47.21 apply zenon_H26. apply refl_equal. % 47.01/47.21 apply zenon_H106. apply sym_equal. exact zenon_H105. % 47.01/47.21 (* end of lemma zenon_L97_ *) % 47.01/47.21 assert (zenon_L98_ : (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e13)) = (e12)) -> False). % 47.01/47.21 do 0 intro. intros zenon_H10d zenon_H101 zenon_H141 zenon_H119 zenon_Hfa zenon_H34 zenon_H71 zenon_H2b zenon_H56 zenon_H5f zenon_H7d zenon_Hc5 zenon_Ha8 zenon_Hf9 zenon_Hff. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H102 | zenon_intro zenon_H10e ]. % 47.01/47.21 apply (zenon_L56_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H105 | zenon_intro zenon_H10f ]. % 47.01/47.21 apply (zenon_L97_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hc4 ]. % 47.01/47.21 apply (zenon_L53_); trivial. % 47.01/47.21 apply (zenon_L60_); trivial. % 47.01/47.21 (* end of lemma zenon_L98_ *) % 47.01/47.21 assert (zenon_L99_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e12)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e12)) -> False). % 47.01/47.21 do 0 intro. intros zenon_H116 zenon_H5c zenon_Hb0 zenon_H19 zenon_Hf9 zenon_H8b zenon_H7d zenon_H5f zenon_H56 zenon_H2b zenon_H71 zenon_H34 zenon_Hc5 zenon_Hb8. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.01/47.21 apply (zenon_L52_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.01/47.21 apply (zenon_L28_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.01/47.21 apply (zenon_L77_); trivial. % 47.01/47.21 apply (zenon_L55_); trivial. % 47.01/47.21 (* end of lemma zenon_L99_ *) % 47.01/47.21 assert (zenon_L100_ : (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e12) (e13)) = (e12)) -> (~((e12) = (e13))) -> False). % 47.01/47.21 do 0 intro. intros zenon_Hac zenon_H3b zenon_H1c zenon_H2c zenon_H1b zenon_Hc5 zenon_H34 zenon_H71 zenon_H2b zenon_H56 zenon_H5f zenon_H7d zenon_Hf9 zenon_H19 zenon_Hb0 zenon_H5c zenon_H116 zenon_Hb8 zenon_Hd8. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.01/47.21 apply (zenon_L10_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.01/47.21 apply (zenon_L17_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.01/47.21 apply (zenon_L99_); trivial. % 47.01/47.21 apply (zenon_L84_); trivial. % 47.01/47.21 (* end of lemma zenon_L100_ *) % 47.01/47.21 assert (zenon_L101_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H48 zenon_Hd8 zenon_H116 zenon_H5c zenon_Hb0 zenon_H19 zenon_Hf9 zenon_H5f zenon_H56 zenon_H2b zenon_H71 zenon_Hc5 zenon_H1b zenon_Hac zenon_H110 zenon_H63 zenon_Hed zenon_Hfd zenon_H10d zenon_H101 zenon_H141 zenon_H119 zenon_Hf1 zenon_H51 zenon_H130 zenon_H4b zenon_H142 zenon_H149 zenon_H3b zenon_H2c zenon_H1c zenon_H42. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.01/47.21 apply (zenon_L7_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H14a ]. % 47.01/47.21 apply (zenon_L94_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H145 | zenon_intro zenon_H14b ]. % 47.01/47.21 apply (zenon_L95_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H147 | zenon_intro zenon_H7d ]. % 47.01/47.21 apply (zenon_L96_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.01/47.21 apply (zenon_L50_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.01/47.21 apply (zenon_L51_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.01/47.21 apply (zenon_L52_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.01/47.21 apply (zenon_L28_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.01/47.21 apply (zenon_L53_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H62 | zenon_intro zenon_H111 ]. % 47.01/47.21 apply (zenon_L18_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H112 ]. % 47.01/47.21 apply (zenon_L54_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Ha8 ]. % 47.01/47.21 apply (zenon_L55_); trivial. % 47.01/47.21 apply (zenon_L98_); trivial. % 47.01/47.21 apply (zenon_L100_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.01/47.21 apply (zenon_L10_); trivial. % 47.01/47.21 apply (zenon_L11_); trivial. % 47.01/47.21 (* end of lemma zenon_L101_ *) % 47.01/47.21 assert (zenon_L102_ : (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> ((op1 (e12) (e12)) = (e13)) -> False). % 47.01/47.21 do 0 intro. intros zenon_H9c zenon_Hbb zenon_H8b. % 47.01/47.21 cut (((op1 (e10) (e12)) = (e13)) = ((op1 (e10) (e12)) = (op1 (e12) (e12)))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H9c. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_Hbb. % 47.01/47.21 cut (((e13) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 47.01/47.21 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 47.01/47.21 congruence. % 47.01/47.21 apply zenon_H26. apply refl_equal. % 47.01/47.21 apply zenon_H8c. apply sym_equal. exact zenon_H8b. % 47.01/47.21 (* end of lemma zenon_L102_ *) % 47.01/47.21 assert (zenon_L103_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e13)) = (e10)) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e13)) -> False). % 47.01/47.21 do 0 intro. intros zenon_H14c zenon_H13e zenon_H13d zenon_H42 zenon_H1c zenon_H2c zenon_H3b zenon_H149 zenon_H142 zenon_H4b zenon_H130 zenon_H51 zenon_Hf1 zenon_H101 zenon_H10d zenon_Hfd zenon_Hed zenon_H63 zenon_H110 zenon_Hac zenon_H1b zenon_Hc5 zenon_H71 zenon_H2b zenon_H56 zenon_H5f zenon_Hf9 zenon_H19 zenon_Hb0 zenon_H5c zenon_H116 zenon_Hd8 zenon_H48 zenon_Hfb zenon_H119 zenon_H9c zenon_H8b. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H22 | zenon_intro zenon_H14d ]. % 47.01/47.21 apply (zenon_L93_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H141 | zenon_intro zenon_H14e ]. % 47.01/47.21 apply (zenon_L101_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbb ]. % 47.01/47.21 apply (zenon_L70_); trivial. % 47.01/47.21 apply (zenon_L102_); trivial. % 47.01/47.21 (* end of lemma zenon_L103_ *) % 47.01/47.21 assert (zenon_L104_ : ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e13)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e12)) -> False). % 47.01/47.21 do 0 intro. intros zenon_H8b zenon_H9c zenon_H119 zenon_H48 zenon_Hd8 zenon_H116 zenon_H5c zenon_Hb0 zenon_H19 zenon_Hf9 zenon_H5f zenon_H56 zenon_H2b zenon_H71 zenon_H1b zenon_Hac zenon_H110 zenon_H63 zenon_Hed zenon_Hfd zenon_H10d zenon_H101 zenon_Hf1 zenon_H51 zenon_H130 zenon_H4b zenon_H142 zenon_H149 zenon_H3b zenon_H2c zenon_H1c zenon_H42 zenon_H13d zenon_H13e zenon_H14c zenon_Hc5 zenon_Hb8. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.01/47.21 apply (zenon_L52_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.01/47.21 apply (zenon_L28_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.01/47.21 apply (zenon_L103_); trivial. % 47.01/47.21 apply (zenon_L55_); trivial. % 47.01/47.21 (* end of lemma zenon_L104_ *) % 47.01/47.21 assert (zenon_L105_ : ((op1 (e10) (e13)) = (e11)) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H14f zenon_Hd3 zenon_H150. % 47.01/47.21 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_H13f | zenon_intro zenon_Hba ]. % 47.01/47.21 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((op1 (e10) (e11)) = (op1 (e10) (e13)))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H150. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H13f. % 47.01/47.21 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 47.01/47.21 cut (((op1 (e10) (e13)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 47.01/47.21 congruence. % 47.01/47.21 cut (((op1 (e10) (e13)) = (e11)) = ((op1 (e10) (e13)) = (op1 (e10) (e11)))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H151. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H14f. % 47.01/47.21 cut (((e11) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H144]. % 47.01/47.21 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 47.01/47.21 congruence. % 47.01/47.21 apply zenon_Hba. apply refl_equal. % 47.01/47.21 apply zenon_H144. apply sym_equal. exact zenon_Hd3. % 47.01/47.21 apply zenon_Hba. apply refl_equal. % 47.01/47.21 apply zenon_Hba. apply refl_equal. % 47.01/47.21 (* end of lemma zenon_L105_ *) % 47.01/47.21 assert (zenon_L106_ : (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H130 zenon_H51 zenon_Hf1 zenon_H104 zenon_H101 zenon_H10d zenon_Hfd zenon_Hed zenon_H63 zenon_H110 zenon_Hac zenon_H3b zenon_H1c zenon_H2c zenon_H1b zenon_Hc5 zenon_H34 zenon_H71 zenon_H2b zenon_H56 zenon_H5f zenon_H7d zenon_Hf9 zenon_H19 zenon_Hb0 zenon_H5c zenon_H116 zenon_Hd8. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.01/47.21 apply (zenon_L50_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.01/47.21 apply (zenon_L51_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.01/47.21 apply (zenon_L52_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.01/47.21 apply (zenon_L28_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.01/47.21 apply (zenon_L53_); trivial. % 47.01/47.21 apply (zenon_L62_); trivial. % 47.01/47.21 apply (zenon_L100_); trivial. % 47.01/47.21 (* end of lemma zenon_L106_ *) % 47.01/47.21 assert (zenon_L107_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e13)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H48 zenon_Hd8 zenon_H116 zenon_H5c zenon_Hb0 zenon_H19 zenon_Hf9 zenon_H5f zenon_H56 zenon_H2b zenon_H71 zenon_Hc5 zenon_H1b zenon_Hac zenon_H110 zenon_H63 zenon_Hed zenon_Hfd zenon_H10d zenon_H101 zenon_H104 zenon_Hf1 zenon_H51 zenon_H130 zenon_H4b zenon_H14f zenon_H150 zenon_H149 zenon_H3b zenon_H2c zenon_H1c zenon_H42. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.01/47.21 apply (zenon_L7_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H14a ]. % 47.01/47.21 apply (zenon_L105_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H145 | zenon_intro zenon_H14b ]. % 47.01/47.21 apply (zenon_L95_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H147 | zenon_intro zenon_H7d ]. % 47.01/47.21 apply (zenon_L96_); trivial. % 47.01/47.21 apply (zenon_L106_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.01/47.21 apply (zenon_L10_); trivial. % 47.01/47.21 apply (zenon_L11_); trivial. % 47.01/47.21 (* end of lemma zenon_L107_ *) % 47.01/47.21 assert (zenon_L108_ : (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> False). % 47.01/47.21 do 0 intro. intros zenon_H130 zenon_H51 zenon_Hf1 zenon_Hf9 zenon_Hc5 zenon_H2b zenon_H71 zenon_H34 zenon_Hb0 zenon_H115 zenon_H101 zenon_H10d zenon_Hfd zenon_Hed zenon_H1c zenon_H19 zenon_H63 zenon_H110 zenon_H104 zenon_H56 zenon_H5f zenon_H6a zenon_Hd0 zenon_H5c zenon_H116 zenon_Hb7 zenon_H8e. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.01/47.21 apply (zenon_L50_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.01/47.21 apply (zenon_L51_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.01/47.21 apply (zenon_L69_); trivial. % 47.01/47.21 apply (zenon_L30_); trivial. % 47.01/47.21 (* end of lemma zenon_L108_ *) % 47.01/47.21 assert (zenon_L109_ : (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> False). % 47.01/47.21 do 0 intro. intros zenon_H130 zenon_H51 zenon_Hf1 zenon_Hf9 zenon_Hc5 zenon_Hb5 zenon_H2b zenon_H71 zenon_H34 zenon_Hb0 zenon_H115 zenon_H101 zenon_H10d zenon_Hfd zenon_Hed zenon_H1c zenon_H19 zenon_H63 zenon_H110 zenon_H5c zenon_H116 zenon_Hb7 zenon_H8e. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.01/47.21 apply (zenon_L50_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.01/47.21 apply (zenon_L51_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.01/47.21 apply (zenon_L88_); trivial. % 47.01/47.21 apply (zenon_L30_); trivial. % 47.01/47.21 (* end of lemma zenon_L109_ *) % 47.01/47.21 assert (zenon_L110_ : (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> False). % 47.01/47.21 do 0 intro. intros zenon_H133 zenon_H104 zenon_H129 zenon_H2c zenon_Hd0 zenon_H6a zenon_H1b zenon_H56 zenon_Hb4 zenon_Hd4 zenon_H130 zenon_H51 zenon_Hf1 zenon_Hf9 zenon_Hc5 zenon_H2b zenon_H71 zenon_H34 zenon_Hb0 zenon_H115 zenon_H101 zenon_H10d zenon_Hfd zenon_Hed zenon_H1c zenon_H19 zenon_H63 zenon_H110 zenon_H5c zenon_H116 zenon_Hb7 zenon_H8e. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H5f | zenon_intro zenon_H134 ]. % 47.01/47.21 apply (zenon_L108_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H128 | zenon_intro zenon_H135 ]. % 47.01/47.21 apply (zenon_L87_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H60 | zenon_intro zenon_Hb5 ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.01/47.21 apply (zenon_L50_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.01/47.21 apply (zenon_L51_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.01/47.21 apply (zenon_L81_); trivial. % 47.01/47.21 apply (zenon_L30_); trivial. % 47.01/47.21 apply (zenon_L109_); trivial. % 47.01/47.21 (* end of lemma zenon_L110_ *) % 47.01/47.21 assert (zenon_L111_ : (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> ((op1 (e13) (e13)) = (e13)) -> False). % 47.01/47.21 do 0 intro. intros zenon_H8f zenon_Hd7 zenon_H152. % 47.01/47.21 cut (((op1 (e10) (e13)) = (e13)) = ((op1 (e10) (e13)) = (op1 (e13) (e13)))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H8f. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_Hd7. % 47.01/47.21 cut (((e13) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 47.01/47.21 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 47.01/47.21 congruence. % 47.01/47.21 apply zenon_Hba. apply refl_equal. % 47.01/47.21 apply zenon_H153. apply sym_equal. exact zenon_H152. % 47.01/47.21 (* end of lemma zenon_L111_ *) % 47.01/47.21 assert (zenon_L112_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e12) (e13)) = (e12)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((e12) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (e11) (e11))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e13)) = (e13)) -> False). % 47.01/47.21 do 0 intro. intros zenon_H154 zenon_Hb8 zenon_H14c zenon_H13e zenon_H142 zenon_H119 zenon_H9c zenon_H8b zenon_H42 zenon_H3b zenon_H149 zenon_H150 zenon_H4b zenon_Hac zenon_H5f zenon_Hd8 zenon_H48 zenon_Hb7 zenon_H116 zenon_H5c zenon_H110 zenon_H63 zenon_H19 zenon_H1c zenon_Hed zenon_Hfd zenon_H10d zenon_H101 zenon_H115 zenon_Hb0 zenon_H34 zenon_H71 zenon_H2b zenon_Hc5 zenon_Hf9 zenon_Hf1 zenon_H51 zenon_H130 zenon_Hd4 zenon_Hb4 zenon_H56 zenon_H1b zenon_H6a zenon_Hd0 zenon_H2c zenon_H129 zenon_H104 zenon_H133 zenon_H8f zenon_H152. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H13d | zenon_intro zenon_H155 ]. % 47.01/47.21 apply (zenon_L104_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H14f | zenon_intro zenon_H156 ]. % 47.01/47.21 apply (zenon_L107_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H8e | zenon_intro zenon_Hd7 ]. % 47.01/47.21 apply (zenon_L110_); trivial. % 47.01/47.21 apply (zenon_L111_); trivial. % 47.01/47.21 (* end of lemma zenon_L112_ *) % 47.01/47.21 assert (zenon_L113_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e12) (e13)) = (e12)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((e12) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (e11) (e11))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H157 zenon_H12d zenon_He6 zenon_H11f zenon_H11b zenon_H125 zenon_H137 zenon_H154 zenon_Hb8 zenon_H14c zenon_H13e zenon_H142 zenon_H119 zenon_H9c zenon_H8b zenon_H42 zenon_H3b zenon_H149 zenon_H150 zenon_H4b zenon_Hac zenon_H5f zenon_Hd8 zenon_H48 zenon_Hb7 zenon_H116 zenon_H5c zenon_H110 zenon_H63 zenon_H19 zenon_H1c zenon_Hed zenon_Hfd zenon_H10d zenon_H101 zenon_H115 zenon_Hb0 zenon_H34 zenon_H71 zenon_H2b zenon_Hc5 zenon_Hf9 zenon_Hf1 zenon_H51 zenon_H130 zenon_Hd4 zenon_Hb4 zenon_H56 zenon_H1b zenon_H6a zenon_Hd0 zenon_H2c zenon_H129 zenon_H104 zenon_H133 zenon_H8f. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H158 ]. % 47.01/47.21 apply (zenon_L91_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H136 | zenon_intro zenon_H159 ]. % 47.01/47.21 apply (zenon_L92_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H152 ]. % 47.01/47.21 apply (zenon_L84_); trivial. % 47.01/47.21 apply (zenon_L112_); trivial. % 47.01/47.21 (* end of lemma zenon_L113_ *) % 47.01/47.21 assert (zenon_L114_ : (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((e12) = (op1 (e11) (e11))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> False). % 47.01/47.21 do 0 intro. intros zenon_H125 zenon_H11b zenon_H19 zenon_H1c zenon_Hed zenon_H11f zenon_Hfb zenon_Hf9 zenon_H9c zenon_Hbb. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H11a | zenon_intro zenon_H126 ]. % 47.01/47.21 apply (zenon_L72_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 47.01/47.21 apply (zenon_L73_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hfa | zenon_intro zenon_H8b ]. % 47.01/47.21 apply (zenon_L53_); trivial. % 47.01/47.21 apply (zenon_L102_); trivial. % 47.01/47.21 (* end of lemma zenon_L114_ *) % 47.01/47.21 assert (zenon_L115_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e12)) -> False). % 47.01/47.21 do 0 intro. intros zenon_H116 zenon_H5c zenon_H71 zenon_Hb0 zenon_Hbb zenon_H9c zenon_Hf9 zenon_H11f zenon_Hed zenon_H1c zenon_H19 zenon_H11b zenon_H125 zenon_Hc5 zenon_Hb8. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.01/47.21 apply (zenon_L52_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.01/47.21 apply (zenon_L28_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.01/47.21 apply (zenon_L114_); trivial. % 47.01/47.21 apply (zenon_L55_); trivial. % 47.01/47.21 (* end of lemma zenon_L115_ *) % 47.01/47.21 assert (zenon_L116_ : (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H130 zenon_H51 zenon_Hf1 zenon_Hb5 zenon_H2b zenon_H34 zenon_H115 zenon_H101 zenon_H10d zenon_Hfd zenon_H63 zenon_H110 zenon_H116 zenon_H5c zenon_H71 zenon_Hb0 zenon_Hbb zenon_H9c zenon_Hf9 zenon_H11f zenon_Hed zenon_H1c zenon_H19 zenon_H11b zenon_H125 zenon_Hc5. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.01/47.21 apply (zenon_L50_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.01/47.21 apply (zenon_L51_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.01/47.21 apply (zenon_L52_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.01/47.21 apply (zenon_L28_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.01/47.21 apply (zenon_L114_); trivial. % 47.01/47.21 apply (zenon_L68_); trivial. % 47.01/47.21 apply (zenon_L115_); trivial. % 47.01/47.21 (* end of lemma zenon_L116_ *) % 47.01/47.21 assert (zenon_L117_ : (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> False). % 47.01/47.21 do 0 intro. intros zenon_Hd0 zenon_H6a zenon_Hd3 zenon_Hb4 zenon_H130 zenon_H51 zenon_Hf1 zenon_H2b zenon_H34 zenon_H115 zenon_H101 zenon_H10d zenon_Hfd zenon_H63 zenon_H110 zenon_H116 zenon_H5c zenon_H71 zenon_Hb0 zenon_Hbb zenon_H9c zenon_Hf9 zenon_H11f zenon_Hed zenon_H1c zenon_H19 zenon_H11b zenon_H125 zenon_Hc5. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.01/47.21 apply (zenon_L19_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.01/47.21 apply (zenon_L40_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.01/47.21 apply (zenon_L28_); trivial. % 47.01/47.21 apply (zenon_L116_); trivial. % 47.01/47.21 (* end of lemma zenon_L117_ *) % 47.01/47.21 assert (zenon_L118_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e10)) = (e10)) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H48 zenon_Hc5 zenon_H125 zenon_H11b zenon_H19 zenon_Hed zenon_H11f zenon_Hf9 zenon_H9c zenon_Hbb zenon_Hb0 zenon_H71 zenon_H5c zenon_H116 zenon_H110 zenon_H63 zenon_Hfd zenon_H10d zenon_H101 zenon_H115 zenon_H2b zenon_Hf1 zenon_H51 zenon_H130 zenon_Hb4 zenon_Hd3 zenon_H6a zenon_Hd0 zenon_H3b zenon_H2c zenon_H1c zenon_H42. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.01/47.21 apply (zenon_L7_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.01/47.21 apply (zenon_L117_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.01/47.21 apply (zenon_L10_); trivial. % 47.01/47.21 apply (zenon_L11_); trivial. % 47.01/47.21 (* end of lemma zenon_L118_ *) % 47.01/47.21 assert (zenon_L119_ : ((op1 (e13) (e10)) = (e10)) -> ((op1 (e13) (e10)) = (e11)) -> (~((e10) = (e11))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H71 zenon_H15a zenon_H15b. % 47.01/47.21 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H15c | zenon_intro zenon_H17 ]. % 47.01/47.21 cut (((e11) = (e11)) = ((e10) = (e11))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H15b. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H15c. % 47.01/47.21 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 47.01/47.21 cut (((e11) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 47.01/47.21 congruence. % 47.01/47.21 cut (((op1 (e13) (e10)) = (e10)) = ((e11) = (e10))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H15d. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H71. % 47.01/47.21 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 47.01/47.21 cut (((op1 (e13) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H15e]. % 47.01/47.21 congruence. % 47.01/47.21 exact (zenon_H15e zenon_H15a). % 47.01/47.21 apply zenon_H32. apply refl_equal. % 47.01/47.21 apply zenon_H17. apply refl_equal. % 47.01/47.21 apply zenon_H17. apply refl_equal. % 47.01/47.21 (* end of lemma zenon_L119_ *) % 47.01/47.21 assert (zenon_L120_ : ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H141 zenon_H4f zenon_H24. % 47.01/47.21 elim (classic ((op1 (e10) (e12)) = (op1 (e10) (e12)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 47.01/47.21 cut (((op1 (e10) (e12)) = (op1 (e10) (e12))) = ((op1 (e10) (e10)) = (op1 (e10) (e12)))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H24. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H25. % 47.01/47.21 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 47.01/47.21 cut (((op1 (e10) (e12)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 47.01/47.21 congruence. % 47.01/47.21 cut (((op1 (e10) (e12)) = (e11)) = ((op1 (e10) (e12)) = (op1 (e10) (e10)))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H27. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H141. % 47.01/47.21 cut (((e11) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 47.01/47.21 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 47.01/47.21 congruence. % 47.01/47.21 apply zenon_H26. apply refl_equal. % 47.01/47.21 apply zenon_Hdd. apply sym_equal. exact zenon_H4f. % 47.01/47.21 apply zenon_H26. apply refl_equal. % 47.01/47.21 apply zenon_H26. apply refl_equal. % 47.01/47.21 (* end of lemma zenon_L120_ *) % 47.01/47.21 assert (zenon_L121_ : (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((e12) = (e13))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H133 zenon_H104 zenon_H129 zenon_H130 zenon_H51 zenon_Hf1 zenon_H12d zenon_H119 zenon_He6 zenon_Hb0 zenon_H115 zenon_H101 zenon_H10d zenon_H5c zenon_H116 zenon_H110 zenon_H63 zenon_Hed zenon_Hfd zenon_Hac zenon_H3b zenon_H2c zenon_Hf9 zenon_Hc5 zenon_H7d zenon_H56 zenon_H2b zenon_H71 zenon_H34 zenon_H19 zenon_Hb4 zenon_H1b zenon_H1c zenon_Hd4 zenon_Hd8. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H5f | zenon_intro zenon_H134 ]. % 47.01/47.21 apply (zenon_L106_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H128 | zenon_intro zenon_H135 ]. % 47.01/47.21 apply (zenon_L87_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H60 | zenon_intro zenon_Hb5 ]. % 47.01/47.21 apply (zenon_L41_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.01/47.21 apply (zenon_L50_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.01/47.21 apply (zenon_L51_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.01/47.21 apply (zenon_L88_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H5b | zenon_intro zenon_H12e ]. % 47.01/47.21 apply (zenon_L71_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_He5 | zenon_intro zenon_H12f ]. % 47.01/47.21 apply (zenon_L48_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.01/47.21 apply (zenon_L10_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.01/47.21 apply (zenon_L41_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.01/47.21 apply (zenon_L52_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.01/47.21 apply (zenon_L28_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.01/47.21 apply (zenon_L78_); trivial. % 47.01/47.21 apply (zenon_L68_); trivial. % 47.01/47.21 apply (zenon_L79_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.01/47.21 apply (zenon_L10_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.01/47.21 apply (zenon_L41_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.01/47.21 apply (zenon_L78_); trivial. % 47.01/47.21 apply (zenon_L84_); trivial. % 47.01/47.21 (* end of lemma zenon_L121_ *) % 47.01/47.21 assert (zenon_L122_ : ((op1 (e10) (e13)) = (e11)) -> ((op1 (e10) (e13)) = (e12)) -> (~((e11) = (e12))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H14f zenon_H8e zenon_H51. % 47.01/47.21 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 47.01/47.21 cut (((e12) = (e12)) = ((e11) = (e12))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H51. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H52. % 47.01/47.21 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.01/47.21 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 47.01/47.21 congruence. % 47.01/47.21 cut (((op1 (e10) (e13)) = (e11)) = ((e12) = (e11))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_H54. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H14f. % 47.01/47.21 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 47.01/47.21 cut (((op1 (e10) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H15f]. % 47.01/47.21 congruence. % 47.01/47.21 exact (zenon_H15f zenon_H8e). % 47.01/47.21 apply zenon_H17. apply refl_equal. % 47.01/47.21 apply zenon_H53. apply refl_equal. % 47.01/47.21 apply zenon_H53. apply refl_equal. % 47.01/47.21 (* end of lemma zenon_L122_ *) % 47.01/47.21 assert (zenon_L123_ : ((op1 (e10) (e13)) = (e11)) -> ((op1 (e10) (e13)) = (e13)) -> (~((e11) = (e13))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H14f zenon_Hd7 zenon_Ha9. % 47.01/47.21 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 47.01/47.21 cut (((e13) = (e13)) = ((e11) = (e13))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_Ha9. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H36. % 47.01/47.21 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 47.01/47.21 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 47.01/47.21 congruence. % 47.01/47.21 cut (((op1 (e10) (e13)) = (e11)) = ((e13) = (e11))). % 47.01/47.21 intro zenon_D_pnotp. % 47.01/47.21 apply zenon_Haa. % 47.01/47.21 rewrite <- zenon_D_pnotp. % 47.01/47.21 exact zenon_H14f. % 47.01/47.21 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 47.01/47.21 cut (((op1 (e10) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 47.01/47.21 congruence. % 47.01/47.21 exact (zenon_Hda zenon_Hd7). % 47.01/47.21 apply zenon_H17. apply refl_equal. % 47.01/47.21 apply zenon_H37. apply refl_equal. % 47.01/47.21 apply zenon_H37. apply refl_equal. % 47.01/47.21 (* end of lemma zenon_L123_ *) % 47.01/47.21 assert (zenon_L124_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((e10) = (e13))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e12)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((e10) = (e11))) -> False). % 47.01/47.21 do 0 intro. intros zenon_H160 zenon_H161 zenon_H35 zenon_Hcb zenon_Hb7 zenon_H13e zenon_H14c zenon_H154 zenon_H137 zenon_H157 zenon_H8f zenon_Hdb zenon_H142 zenon_H24 zenon_H162 zenon_H163 zenon_Hbe zenon_Hde zenon_H22 zenon_Hea zenon_Ha9 zenon_H48 zenon_Hd8 zenon_Hd4 zenon_H1b zenon_Hb4 zenon_H19 zenon_H2b zenon_H56 zenon_Hc5 zenon_Hf9 zenon_Hac zenon_Hfd zenon_H63 zenon_H110 zenon_H116 zenon_H5c zenon_H10d zenon_H101 zenon_H115 zenon_Hb0 zenon_He6 zenon_H119 zenon_H12d zenon_Hf1 zenon_H51 zenon_H130 zenon_H129 zenon_H104 zenon_H133 zenon_H4b zenon_Hd0 zenon_H6a zenon_H9c zenon_H11f zenon_H11b zenon_H125 zenon_H149 zenon_H3b zenon_H2c zenon_H1c zenon_H42 zenon_H150 zenon_H164 zenon_H15b. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H23 | zenon_intro zenon_H165 ]. % 47.01/47.21 apply (zenon_L5_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H33 | zenon_intro zenon_H166 ]. % 47.01/47.21 apply (zenon_L12_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H4c | zenon_intro zenon_H71 ]. % 47.01/47.21 apply (zenon_L13_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H4f | zenon_intro zenon_H167 ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H50 | zenon_intro zenon_H168 ]. % 47.01/47.21 apply (zenon_L14_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H57 | zenon_intro zenon_H169 ]. % 47.01/47.21 apply (zenon_L15_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H5b | zenon_intro zenon_H8e ]. % 47.01/47.21 apply (zenon_L16_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.01/47.21 apply (zenon_L7_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.01/47.21 apply (zenon_L7_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.01/47.21 apply (zenon_L10_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.01/47.21 apply (zenon_L17_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H62 | zenon_intro zenon_H111 ]. % 47.01/47.21 apply (zenon_L18_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H112 ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.01/47.21 apply (zenon_L19_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.01/47.21 apply (zenon_L27_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.01/47.21 apply (zenon_L28_); trivial. % 47.01/47.21 apply (zenon_L29_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Ha8 ]. % 47.01/47.21 apply (zenon_L30_); trivial. % 47.01/47.21 apply (zenon_L39_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hcc ]. % 47.01/47.21 apply (zenon_L31_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hcd ]. % 47.01/47.21 apply (zenon_L32_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hc4 ]. % 47.01/47.21 apply (zenon_L39_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.01/47.21 apply (zenon_L19_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.01/47.21 apply (zenon_L42_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.01/47.21 apply (zenon_L28_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.01/47.21 apply (zenon_L20_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.01/47.21 apply (zenon_L37_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.01/47.21 apply (zenon_L33_); trivial. % 47.01/47.21 apply (zenon_L24_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.01/47.21 apply (zenon_L10_); trivial. % 47.01/47.21 apply (zenon_L11_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.01/47.21 apply (zenon_L31_); trivial. % 47.01/47.21 apply (zenon_L44_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H16c ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.01/47.21 apply (zenon_L45_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.01/47.21 apply (zenon_L49_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.01/47.21 apply (zenon_L7_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.01/47.21 apply (zenon_L7_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.01/47.21 apply (zenon_L50_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.01/47.21 apply (zenon_L51_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.01/47.21 apply (zenon_L69_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.01/47.21 apply (zenon_L10_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.01/47.21 apply (zenon_L17_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.01/47.21 apply (zenon_L113_); trivial. % 47.01/47.21 apply (zenon_L84_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.01/47.21 apply (zenon_L10_); trivial. % 47.01/47.21 apply (zenon_L11_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.01/47.21 apply (zenon_L118_); trivial. % 47.01/47.21 apply (zenon_L91_); trivial. % 47.01/47.21 apply (zenon_L119_); trivial. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H141 | zenon_intro zenon_H14f ]. % 47.01/47.21 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.01/47.22 apply (zenon_L120_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.01/47.22 apply (zenon_L49_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.01/47.22 apply (zenon_L7_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H14a ]. % 47.01/47.22 apply (zenon_L94_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H145 | zenon_intro zenon_H14b ]. % 47.01/47.22 apply (zenon_L95_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H147 | zenon_intro zenon_H7d ]. % 47.01/47.22 apply (zenon_L96_); trivial. % 47.01/47.22 apply (zenon_L121_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.01/47.22 apply (zenon_L10_); trivial. % 47.01/47.22 apply (zenon_L11_); trivial. % 47.01/47.22 apply (zenon_L119_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H50 | zenon_intro zenon_H168 ]. % 47.01/47.22 apply (zenon_L14_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H57 | zenon_intro zenon_H169 ]. % 47.01/47.22 apply (zenon_L15_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H5b | zenon_intro zenon_H8e ]. % 47.01/47.22 apply (zenon_L16_); trivial. % 47.01/47.22 apply (zenon_L122_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.01/47.22 apply (zenon_L49_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.01/47.22 apply (zenon_L7_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.01/47.22 apply (zenon_L107_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.01/47.22 apply (zenon_L7_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H14a ]. % 47.01/47.22 apply (zenon_L117_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H145 | zenon_intro zenon_H14b ]. % 47.01/47.22 apply (zenon_L95_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H147 | zenon_intro zenon_H7d ]. % 47.01/47.22 apply (zenon_L96_); trivial. % 47.01/47.22 apply (zenon_L121_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.01/47.22 apply (zenon_L10_); trivial. % 47.01/47.22 apply (zenon_L11_); trivial. % 47.01/47.22 apply (zenon_L123_); trivial. % 47.01/47.22 apply (zenon_L119_); trivial. % 47.01/47.22 (* end of lemma zenon_L124_ *) % 47.01/47.22 assert (zenon_L125_ : ((op1 (e10) (e13)) = (e10)) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H13d zenon_H23 zenon_H16f. % 47.01/47.22 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_H13f | zenon_intro zenon_Hba ]. % 47.01/47.22 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((op1 (e10) (e10)) = (op1 (e10) (e13)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H16f. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H13f. % 47.01/47.22 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 47.01/47.22 cut (((op1 (e10) (e13)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H170]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op1 (e10) (e13)) = (e10)) = ((op1 (e10) (e13)) = (op1 (e10) (e10)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H170. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H13d. % 47.01/47.22 cut (((e10) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 47.01/47.22 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_Hba. apply refl_equal. % 47.01/47.22 apply zenon_H28. apply sym_equal. exact zenon_H23. % 47.01/47.22 apply zenon_Hba. apply refl_equal. % 47.01/47.22 apply zenon_Hba. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L125_ *) % 47.01/47.22 assert (zenon_L126_ : (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e13)) = (e10)) -> ((op1 (e11) (e13)) = (e10)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H171 zenon_H13d zenon_H172. % 47.01/47.22 cut (((op1 (e10) (e13)) = (e10)) = ((op1 (e10) (e13)) = (op1 (e11) (e13)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H171. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H13d. % 47.01/47.22 cut (((e10) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H173]. % 47.01/47.22 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_Hba. apply refl_equal. % 47.01/47.22 apply zenon_H173. apply sym_equal. exact zenon_H172. % 47.01/47.22 (* end of lemma zenon_L126_ *) % 47.01/47.22 assert (zenon_L127_ : (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e11)) -> ((op1 (e12) (e13)) = (e11)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H174 zenon_H175 zenon_Ha7. % 47.01/47.22 cut (((op1 (e11) (e13)) = (e11)) = ((op1 (e11) (e13)) = (op1 (e12) (e13)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H174. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H175. % 47.01/47.22 cut (((e11) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 47.01/47.22 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H139. apply refl_equal. % 47.01/47.22 apply zenon_Hfe. apply sym_equal. exact zenon_Ha7. % 47.01/47.22 (* end of lemma zenon_L127_ *) % 47.01/47.22 assert (zenon_L128_ : (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e13)) = (e12)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H10d zenon_H101 zenon_H104 zenon_H5b zenon_H119 zenon_H34 zenon_H71 zenon_H2b zenon_H56 zenon_H5f zenon_H7d zenon_Hc5 zenon_Ha8 zenon_Hf9 zenon_Hff. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H102 | zenon_intro zenon_H10e ]. % 47.01/47.22 apply (zenon_L56_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H105 | zenon_intro zenon_H10f ]. % 47.01/47.22 apply (zenon_L57_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hc4 ]. % 47.01/47.22 apply (zenon_L70_); trivial. % 47.01/47.22 apply (zenon_L60_); trivial. % 47.01/47.22 (* end of lemma zenon_L128_ *) % 47.01/47.22 assert (zenon_L129_ : (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e13)) -> False). % 47.01/47.22 do 0 intro. intros zenon_Hd0 zenon_H6a zenon_H1c zenon_H5f zenon_H56 zenon_H119 zenon_H5b zenon_H104 zenon_H101 zenon_H10d zenon_Hb0 zenon_H19 zenon_H34 zenon_H71 zenon_H2b zenon_Hc5 zenon_Ha8 zenon_Hf9 zenon_Hff zenon_Hc4. % 47.01/47.22 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.01/47.22 apply (zenon_L19_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.01/47.22 apply (zenon_L128_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.01/47.22 apply (zenon_L28_); trivial. % 47.01/47.22 apply (zenon_L66_); trivial. % 47.01/47.22 (* end of lemma zenon_L129_ *) % 47.01/47.22 assert (zenon_L130_ : (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e13)) = (e12)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H115 zenon_Hd0 zenon_H6a zenon_H1c zenon_H5f zenon_H56 zenon_H119 zenon_H5b zenon_H104 zenon_H101 zenon_H10d zenon_Hb0 zenon_H19 zenon_H34 zenon_H71 zenon_H2b zenon_Hc5 zenon_Ha8 zenon_Hf9 zenon_Hff. % 47.01/47.22 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.01/47.22 apply (zenon_L19_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.01/47.22 apply (zenon_L128_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.01/47.22 apply (zenon_L28_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H102 | zenon_intro zenon_H10e ]. % 47.01/47.22 apply (zenon_L56_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H105 | zenon_intro zenon_H10f ]. % 47.01/47.22 apply (zenon_L65_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hc4 ]. % 47.01/47.22 apply (zenon_L70_); trivial. % 47.01/47.22 apply (zenon_L129_); trivial. % 47.01/47.22 (* end of lemma zenon_L130_ *) % 47.01/47.22 assert (zenon_L131_ : (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e13)) = (e12)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H110 zenon_H63 zenon_H175 zenon_H174 zenon_H115 zenon_Hd0 zenon_H6a zenon_H1c zenon_H5f zenon_H56 zenon_H119 zenon_H5b zenon_H104 zenon_H101 zenon_H10d zenon_Hb0 zenon_H19 zenon_H34 zenon_H71 zenon_H2b zenon_Hc5 zenon_Hf9 zenon_Hff. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H62 | zenon_intro zenon_H111 ]. % 47.01/47.22 apply (zenon_L18_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H112 ]. % 47.01/47.22 apply (zenon_L127_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Ha8 ]. % 47.01/47.22 apply (zenon_L55_); trivial. % 47.01/47.22 apply (zenon_L130_); trivial. % 47.01/47.22 (* end of lemma zenon_L131_ *) % 47.01/47.22 assert (zenon_L132_ : ((e12) = (op1 (e11) (e11))) -> ((op1 (e11) (e13)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H19 zenon_H176 zenon_H177. % 47.01/47.22 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 47.01/47.22 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((op1 (e11) (e11)) = (op1 (e11) (e13)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H177. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H138. % 47.01/47.22 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 47.01/47.22 cut (((op1 (e11) (e13)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((e12) = (op1 (e11) (e11))) = ((op1 (e11) (e13)) = (op1 (e11) (e11)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H178. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H19. % 47.01/47.22 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 47.01/47.22 cut (((e12) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 47.01/47.22 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e12) = (op1 (e11) (e13)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H179. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H138. % 47.01/47.22 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 47.01/47.22 cut (((op1 (e11) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H17a]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H17a zenon_H176). % 47.01/47.22 apply zenon_H139. apply refl_equal. % 47.01/47.22 apply zenon_H139. apply refl_equal. % 47.01/47.22 apply zenon_H58. apply refl_equal. % 47.01/47.22 apply zenon_H139. apply refl_equal. % 47.01/47.22 apply zenon_H139. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L132_ *) % 47.01/47.22 assert (zenon_L133_ : ((op1 (e10) (e12)) = (e12)) -> ((op1 (e10) (e12)) = (e13)) -> (~((e12) = (e13))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H5b zenon_Hbb zenon_Hd8. % 47.01/47.22 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 47.01/47.22 cut (((e13) = (e13)) = ((e12) = (e13))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_Hd8. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H36. % 47.01/47.22 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 47.01/47.22 cut (((e13) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op1 (e10) (e12)) = (e12)) = ((e13) = (e12))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_Hd9. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H5b. % 47.01/47.22 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.01/47.22 cut (((op1 (e10) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hbc]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_Hbc zenon_Hbb). % 47.01/47.22 apply zenon_H53. apply refl_equal. % 47.01/47.22 apply zenon_H37. apply refl_equal. % 47.01/47.22 apply zenon_H37. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L133_ *) % 47.01/47.22 assert (zenon_L134_ : ((op1 (e10) (e13)) = (e10)) -> ((op1 (e10) (e13)) = (e13)) -> (~((e10) = (e13))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H13d zenon_Hd7 zenon_H35. % 47.01/47.22 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 47.01/47.22 cut (((e13) = (e13)) = ((e10) = (e13))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H35. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H36. % 47.01/47.22 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 47.01/47.22 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op1 (e10) (e13)) = (e10)) = ((e13) = (e10))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H38. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H13d. % 47.01/47.22 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 47.01/47.22 cut (((op1 (e10) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_Hda zenon_Hd7). % 47.01/47.22 apply zenon_H32. apply refl_equal. % 47.01/47.22 apply zenon_H37. apply refl_equal. % 47.01/47.22 apply zenon_H37. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L134_ *) % 47.01/47.22 assert (zenon_L135_ : ((op1 (e10) (e13)) = (e10)) -> ((op1 (e10) (e13)) = (e12)) -> (~((e10) = (e12))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H13d zenon_H8e zenon_H5c. % 47.01/47.22 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 47.01/47.22 cut (((e12) = (e12)) = ((e10) = (e12))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H5c. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H52. % 47.01/47.22 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.01/47.22 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op1 (e10) (e13)) = (e10)) = ((e12) = (e10))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H5d. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H13d. % 47.01/47.22 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 47.01/47.22 cut (((op1 (e10) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H15f]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H15f zenon_H8e). % 47.01/47.22 apply zenon_H32. apply refl_equal. % 47.01/47.22 apply zenon_H53. apply refl_equal. % 47.01/47.22 apply zenon_H53. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L135_ *) % 47.01/47.22 assert (zenon_L136_ : (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e10) (e13)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (e11) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H17b zenon_H13d zenon_H171 zenon_He1 zenon_H177 zenon_H19 zenon_H2c zenon_H1c zenon_H137. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H17b); [ zenon_intro zenon_H172 | zenon_intro zenon_H17c ]. % 47.01/47.22 apply (zenon_L126_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H17c); [ zenon_intro zenon_H175 | zenon_intro zenon_H17d ]. % 47.01/47.22 cut (((op1 (e11) (e10)) = (e11)) = ((op1 (e11) (e10)) = (op1 (e11) (e13)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H137. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_He1. % 47.01/47.22 cut (((e11) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 47.01/47.22 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_He4. apply refl_equal. % 47.01/47.22 apply zenon_H17e. apply sym_equal. exact zenon_H175. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H176 | zenon_intro zenon_H136 ]. % 47.01/47.22 apply (zenon_L132_); trivial. % 47.01/47.22 apply (zenon_L92_); trivial. % 47.01/47.22 (* end of lemma zenon_L136_ *) % 47.01/47.22 assert (zenon_L137_ : (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> ((op1 (e12) (e12)) = (e12)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H9c zenon_H5b zenon_Hfa. % 47.01/47.22 cut (((op1 (e10) (e12)) = (e12)) = ((op1 (e10) (e12)) = (op1 (e12) (e12)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H9c. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H5b. % 47.01/47.22 cut (((e12) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 47.01/47.22 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H26. apply refl_equal. % 47.01/47.22 apply zenon_H17f. apply sym_equal. exact zenon_Hfa. % 47.01/47.22 (* end of lemma zenon_L137_ *) % 47.01/47.22 assert (zenon_L138_ : (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H130 zenon_H51 zenon_Hed zenon_Hf1 zenon_H9c zenon_H116 zenon_H5c zenon_H71 zenon_Hb0 zenon_H19 zenon_H5b zenon_H119 zenon_Hc5. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.01/47.22 apply (zenon_L50_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.01/47.22 apply (zenon_L51_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.01/47.22 apply (zenon_L137_); trivial. % 47.01/47.22 apply (zenon_L71_); trivial. % 47.01/47.22 (* end of lemma zenon_L138_ *) % 47.01/47.22 assert (zenon_L139_ : (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e13)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e13) (e10)) = (e10)) -> (~((e10) = (e11))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H162 zenon_Hdb zenon_H137 zenon_H177 zenon_H171 zenon_H17b zenon_H42 zenon_H1c zenon_H2c zenon_H3b zenon_Hd0 zenon_H6a zenon_Hd3 zenon_Hb4 zenon_H130 zenon_H51 zenon_Hf1 zenon_H2b zenon_H115 zenon_H101 zenon_H10d zenon_Hfd zenon_H63 zenon_H110 zenon_H116 zenon_H5c zenon_Hb0 zenon_H9c zenon_Hf9 zenon_H11f zenon_H19 zenon_H11b zenon_H125 zenon_Hc5 zenon_H48 zenon_H119 zenon_H142 zenon_H13d zenon_H13e zenon_H14c zenon_H71 zenon_H15b. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.01/47.22 apply (zenon_L45_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.01/47.22 apply (zenon_L136_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H22 | zenon_intro zenon_H14d ]. % 47.01/47.22 apply (zenon_L93_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H141 | zenon_intro zenon_H14e ]. % 47.01/47.22 apply (zenon_L94_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbb ]. % 47.01/47.22 apply (zenon_L138_); trivial. % 47.01/47.22 apply (zenon_L118_); trivial. % 47.01/47.22 apply (zenon_L119_); trivial. % 47.01/47.22 (* end of lemma zenon_L139_ *) % 47.01/47.22 assert (zenon_L140_ : ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e12)) = (e13)) -> (~((e11) = (e13))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H141 zenon_Hbb zenon_Ha9. % 47.01/47.22 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 47.01/47.22 cut (((e13) = (e13)) = ((e11) = (e13))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_Ha9. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H36. % 47.01/47.22 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 47.01/47.22 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op1 (e10) (e12)) = (e11)) = ((e13) = (e11))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_Haa. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H141. % 47.01/47.22 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 47.01/47.22 cut (((op1 (e10) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hbc]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_Hbc zenon_Hbb). % 47.01/47.22 apply zenon_H17. apply refl_equal. % 47.01/47.22 apply zenon_H37. apply refl_equal. % 47.01/47.22 apply zenon_H37. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L140_ *) % 47.01/47.22 assert (zenon_L141_ : ((op1 (e10) (e13)) = (e10)) -> ((op1 (e10) (e13)) = (e11)) -> (~((e10) = (e11))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H13d zenon_H14f zenon_H15b. % 47.01/47.22 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H15c | zenon_intro zenon_H17 ]. % 47.01/47.22 cut (((e11) = (e11)) = ((e10) = (e11))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H15b. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H15c. % 47.01/47.22 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 47.01/47.22 cut (((e11) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op1 (e10) (e13)) = (e10)) = ((e11) = (e10))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H15d. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H13d. % 47.01/47.22 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 47.01/47.22 cut (((op1 (e10) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H180]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H180 zenon_H14f). % 47.01/47.22 apply zenon_H32. apply refl_equal. % 47.01/47.22 apply zenon_H17. apply refl_equal. % 47.01/47.22 apply zenon_H17. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L141_ *) % 47.01/47.22 assert (zenon_L142_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e11) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> ((op1 (e10) (e13)) = (e10)) -> (~((e10) = (e11))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H160 zenon_H16f zenon_H161 zenon_H104 zenon_H174 zenon_H163 zenon_H14c zenon_H13e zenon_H125 zenon_H11b zenon_H11f zenon_H9c zenon_H115 zenon_Hb4 zenon_H6a zenon_Hd0 zenon_Hdb zenon_H164 zenon_H42 zenon_H1c zenon_H2c zenon_H3b zenon_H149 zenon_H142 zenon_H4b zenon_H130 zenon_H51 zenon_Hf1 zenon_H119 zenon_H101 zenon_H10d zenon_Hfd zenon_H63 zenon_H110 zenon_Hac zenon_H1b zenon_Hc5 zenon_H2b zenon_H56 zenon_Hf9 zenon_H19 zenon_Hb0 zenon_H5c zenon_H116 zenon_Hd8 zenon_H48 zenon_Ha9 zenon_H35 zenon_H17b zenon_H171 zenon_H177 zenon_H137 zenon_H24 zenon_H162 zenon_H13d zenon_H15b. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H23 | zenon_intro zenon_H165 ]. % 47.01/47.22 apply (zenon_L125_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H33 | zenon_intro zenon_H166 ]. % 47.01/47.22 apply (zenon_L12_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H4c | zenon_intro zenon_H71 ]. % 47.01/47.22 apply (zenon_L13_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H4f | zenon_intro zenon_H167 ]. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H50 | zenon_intro zenon_H168 ]. % 47.01/47.22 apply (zenon_L14_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H57 | zenon_intro zenon_H169 ]. % 47.01/47.22 apply (zenon_L15_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H5b | zenon_intro zenon_H8e ]. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.01/47.22 apply (zenon_L7_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.01/47.22 apply (zenon_L7_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.01/47.22 apply (zenon_L52_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.01/47.22 apply (zenon_L28_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.01/47.22 apply (zenon_L70_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H17b); [ zenon_intro zenon_H172 | zenon_intro zenon_H17c ]. % 47.01/47.22 apply (zenon_L126_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H17c); [ zenon_intro zenon_H175 | zenon_intro zenon_H17d ]. % 47.01/47.22 apply (zenon_L131_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H176 | zenon_intro zenon_H136 ]. % 47.01/47.22 apply (zenon_L132_); trivial. % 47.01/47.22 apply (zenon_L92_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.01/47.22 apply (zenon_L10_); trivial. % 47.01/47.22 apply (zenon_L11_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.01/47.22 apply (zenon_L133_); trivial. % 47.01/47.22 apply (zenon_L134_); trivial. % 47.01/47.22 apply (zenon_L135_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H16c ]. % 47.01/47.22 apply (zenon_L139_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H141 | zenon_intro zenon_H14f ]. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.01/47.22 apply (zenon_L120_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.01/47.22 apply (zenon_L136_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.01/47.22 apply (zenon_L7_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.01/47.22 apply (zenon_L101_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.01/47.22 apply (zenon_L140_); trivial. % 47.01/47.22 apply (zenon_L134_); trivial. % 47.01/47.22 apply (zenon_L119_); trivial. % 47.01/47.22 apply (zenon_L141_); trivial. % 47.01/47.22 (* end of lemma zenon_L142_ *) % 47.01/47.22 assert (zenon_L143_ : (~((e21) = (e21))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H181. % 47.01/47.22 apply zenon_H181. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L143_ *) % 47.01/47.22 assert (zenon_L144_ : (~((op2 (op2 (e21) (e21)) (e21)) = (op2 (e22) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H182 zenon_H183. % 47.01/47.22 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.01/47.22 cut (((op2 (e21) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H184. apply sym_equal. exact zenon_H183. % 47.01/47.22 apply zenon_H181. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L144_ *) % 47.01/47.22 assert (zenon_L145_ : (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e20) (e21)) = (e20)) -> ((e22) = (op2 (e21) (e21))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H185 zenon_H14 zenon_H186 zenon_H183. % 47.01/47.22 cut (((e20) = (op2 (op2 (e21) (e21)) (e21))) = ((op2 (e20) (e21)) = (op2 (e22) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H185. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H14. % 47.01/47.22 cut (((op2 (op2 (e21) (e21)) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H182]. % 47.01/47.22 cut (((e20) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e20) (e21)) = (op2 (e20) (e21)))); [ zenon_intro zenon_H188 | zenon_intro zenon_H189 ]. % 47.01/47.22 cut (((op2 (e20) (e21)) = (op2 (e20) (e21))) = ((e20) = (op2 (e20) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H187. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H188. % 47.01/47.22 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 47.01/47.22 cut (((op2 (e20) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H18a]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H18a zenon_H186). % 47.01/47.22 apply zenon_H189. apply refl_equal. % 47.01/47.22 apply zenon_H189. apply refl_equal. % 47.01/47.22 apply (zenon_L144_); trivial. % 47.01/47.22 (* end of lemma zenon_L145_ *) % 47.01/47.22 assert (zenon_L146_ : ((op2 (e20) (e22)) = (e20)) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H18b zenon_H18c zenon_H18d. % 47.01/47.22 elim (classic ((op2 (e20) (e22)) = (op2 (e20) (e22)))); [ zenon_intro zenon_H18e | zenon_intro zenon_H18f ]. % 47.01/47.22 cut (((op2 (e20) (e22)) = (op2 (e20) (e22))) = ((op2 (e20) (e20)) = (op2 (e20) (e22)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H18d. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H18e. % 47.01/47.22 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 47.01/47.22 cut (((op2 (e20) (e22)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op2 (e20) (e22)) = (e20)) = ((op2 (e20) (e22)) = (op2 (e20) (e20)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H190. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H18b. % 47.01/47.22 cut (((e20) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 47.01/47.22 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H18f. apply refl_equal. % 47.01/47.22 apply zenon_H191. apply sym_equal. exact zenon_H18c. % 47.01/47.22 apply zenon_H18f. apply refl_equal. % 47.01/47.22 apply zenon_H18f. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L146_ *) % 47.01/47.22 assert (zenon_L147_ : (~((op2 (e21) (op2 (op2 (e21) (e21)) (e21))) = (op2 (e21) (e20)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H192 zenon_H14. % 47.01/47.22 cut (((op2 (op2 (e21) (e21)) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 47.01/47.22 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H181. apply refl_equal. % 47.01/47.22 apply zenon_H15. apply sym_equal. exact zenon_H14. % 47.01/47.22 (* end of lemma zenon_L147_ *) % 47.01/47.22 assert (zenon_L148_ : (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((op2 (e20) (e20)) = (e23)) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H193 zenon_H194 zenon_H195 zenon_H14. % 47.01/47.22 cut (((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) = ((op2 (e20) (e20)) = (op2 (e21) (e20)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H193. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H194. % 47.01/47.22 cut (((op2 (e21) (op2 (op2 (e21) (e21)) (e21))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 47.01/47.22 cut (((e23) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e20) (e20)) = (op2 (e20) (e20)))); [ zenon_intro zenon_H197 | zenon_intro zenon_H198 ]. % 47.01/47.22 cut (((op2 (e20) (e20)) = (op2 (e20) (e20))) = ((e23) = (op2 (e20) (e20)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H196. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H197. % 47.01/47.22 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 47.01/47.22 cut (((op2 (e20) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H199 zenon_H195). % 47.01/47.22 apply zenon_H198. apply refl_equal. % 47.01/47.22 apply zenon_H198. apply refl_equal. % 47.01/47.22 apply (zenon_L147_); trivial. % 47.01/47.22 (* end of lemma zenon_L148_ *) % 47.01/47.22 assert (zenon_L149_ : (~((e20) = (e20))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H19a. % 47.01/47.22 apply zenon_H19a. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L149_ *) % 47.01/47.22 assert (zenon_L150_ : ((op2 (e21) (e20)) = (e20)) -> ((op2 (e21) (e20)) = (e23)) -> (~((e20) = (e23))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H19b zenon_H19c zenon_H19d. % 47.01/47.22 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H19e | zenon_intro zenon_H19f ]. % 47.01/47.22 cut (((e23) = (e23)) = ((e20) = (e23))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H19d. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H19e. % 47.01/47.22 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 47.01/47.22 cut (((e23) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op2 (e21) (e20)) = (e20)) = ((e23) = (e20))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1a0. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H19b. % 47.01/47.22 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 47.01/47.22 cut (((op2 (e21) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H1a1 zenon_H19c). % 47.01/47.22 apply zenon_H19a. apply refl_equal. % 47.01/47.22 apply zenon_H19f. apply refl_equal. % 47.01/47.22 apply zenon_H19f. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L150_ *) % 47.01/47.22 assert (zenon_L151_ : ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((op2 (e22) (e20)) = (e23)) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H194 zenon_H1a2 zenon_H14 zenon_H1a3. % 47.01/47.22 elim (classic ((op2 (e22) (e20)) = (op2 (e22) (e20)))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 47.01/47.22 cut (((op2 (e22) (e20)) = (op2 (e22) (e20))) = ((op2 (e21) (e20)) = (op2 (e22) (e20)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1a3. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1a4. % 47.01/47.22 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 47.01/47.22 cut (((op2 (e22) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1a6]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) = ((op2 (e22) (e20)) = (op2 (e21) (e20)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1a6. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H194. % 47.01/47.22 cut (((op2 (e21) (op2 (op2 (e21) (e21)) (e21))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 47.01/47.22 cut (((e23) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e22) (e20)) = (op2 (e22) (e20)))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 47.01/47.22 cut (((op2 (e22) (e20)) = (op2 (e22) (e20))) = ((e23) = (op2 (e22) (e20)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1a7. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1a4. % 47.01/47.22 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 47.01/47.22 cut (((op2 (e22) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1a8]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H1a8 zenon_H1a2). % 47.01/47.22 apply zenon_H1a5. apply refl_equal. % 47.01/47.22 apply zenon_H1a5. apply refl_equal. % 47.01/47.22 apply (zenon_L147_); trivial. % 47.01/47.22 apply zenon_H1a5. apply refl_equal. % 47.01/47.22 apply zenon_H1a5. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L151_ *) % 47.01/47.22 assert (zenon_L152_ : ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((op2 (e23) (e20)) = (e23)) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H194 zenon_H1a9 zenon_H14 zenon_H1aa. % 47.01/47.22 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1ac ]. % 47.01/47.22 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((op2 (e21) (e20)) = (op2 (e23) (e20)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1aa. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1ab. % 47.01/47.22 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1ac]. % 47.01/47.22 cut (((op2 (e23) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1ad]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) = ((op2 (e23) (e20)) = (op2 (e21) (e20)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1ad. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H194. % 47.01/47.22 cut (((op2 (e21) (op2 (op2 (e21) (e21)) (e21))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 47.01/47.22 cut (((e23) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1ac ]. % 47.01/47.22 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((e23) = (op2 (e23) (e20)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1ae. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1ab. % 47.01/47.22 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1ac]. % 47.01/47.22 cut (((op2 (e23) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H1af zenon_H1a9). % 47.01/47.22 apply zenon_H1ac. apply refl_equal. % 47.01/47.22 apply zenon_H1ac. apply refl_equal. % 47.01/47.22 apply (zenon_L147_); trivial. % 47.01/47.22 apply zenon_H1ac. apply refl_equal. % 47.01/47.22 apply zenon_H1ac. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L152_ *) % 47.01/47.22 assert (zenon_L153_ : (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((e20) = (e23))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H1b0 zenon_H193 zenon_H19d zenon_H19b zenon_H1a3 zenon_H194 zenon_H14 zenon_H1aa. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.01/47.22 apply (zenon_L148_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.01/47.22 apply (zenon_L150_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.01/47.22 apply (zenon_L151_); trivial. % 47.01/47.22 apply (zenon_L152_); trivial. % 47.01/47.22 (* end of lemma zenon_L153_ *) % 47.01/47.22 assert (zenon_L154_ : (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e22) (e20)) = (e20)) -> ((e22) = (op2 (e21) (e21))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H1b3 zenon_H14 zenon_H1b4 zenon_H183. % 47.01/47.22 cut (((e20) = (op2 (op2 (e21) (e21)) (e21))) = ((op2 (e22) (e20)) = (op2 (e22) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1b3. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H14. % 47.01/47.22 cut (((op2 (op2 (e21) (e21)) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H182]. % 47.01/47.22 cut (((e20) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e22) (e20)) = (op2 (e22) (e20)))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 47.01/47.22 cut (((op2 (e22) (e20)) = (op2 (e22) (e20))) = ((e20) = (op2 (e22) (e20)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1b5. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1a4. % 47.01/47.22 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 47.01/47.22 cut (((op2 (e22) (e20)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H1b6 zenon_H1b4). % 47.01/47.22 apply zenon_H1a5. apply refl_equal. % 47.01/47.22 apply zenon_H1a5. apply refl_equal. % 47.01/47.22 apply (zenon_L144_); trivial. % 47.01/47.22 (* end of lemma zenon_L154_ *) % 47.01/47.22 assert (zenon_L155_ : ((op2 (e20) (e20)) = (e21)) -> ((op2 (e20) (e20)) = (e22)) -> (~((e21) = (e22))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H1b7 zenon_H1b8 zenon_H1b9. % 47.01/47.22 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 47.01/47.22 cut (((e22) = (e22)) = ((e21) = (e22))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1b9. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1ba. % 47.01/47.22 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.01/47.22 cut (((e22) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op2 (e20) (e20)) = (e21)) = ((e22) = (e21))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1bc. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1b7. % 47.01/47.22 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.01/47.22 cut (((op2 (e20) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bd]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H1bd zenon_H1b8). % 47.01/47.22 apply zenon_H181. apply refl_equal. % 47.01/47.22 apply zenon_H1bb. apply refl_equal. % 47.01/47.22 apply zenon_H1bb. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L155_ *) % 47.01/47.22 assert (zenon_L156_ : (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e20) (e21)) = (e22)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H1be zenon_H183 zenon_H1bf. % 47.01/47.22 cut (((e22) = (op2 (e21) (e21))) = ((op2 (e20) (e21)) = (op2 (e21) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1be. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H183. % 47.01/47.22 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 47.01/47.22 cut (((e22) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c1]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e20) (e21)) = (op2 (e20) (e21)))); [ zenon_intro zenon_H188 | zenon_intro zenon_H189 ]. % 47.01/47.22 cut (((op2 (e20) (e21)) = (op2 (e20) (e21))) = ((e22) = (op2 (e20) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1c1. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H188. % 47.01/47.22 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 47.01/47.22 cut (((op2 (e20) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H1c2 zenon_H1bf). % 47.01/47.22 apply zenon_H189. apply refl_equal. % 47.01/47.22 apply zenon_H189. apply refl_equal. % 47.01/47.22 apply zenon_H1c0. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L156_ *) % 47.01/47.22 assert (zenon_L157_ : ((op2 (e20) (e22)) = (e20)) -> ((op2 (e20) (e22)) = (e22)) -> (~((e20) = (e22))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H18b zenon_H1c3 zenon_H1c4. % 47.01/47.22 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 47.01/47.22 cut (((e22) = (e22)) = ((e20) = (e22))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1c4. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1ba. % 47.01/47.22 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.01/47.22 cut (((e22) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1c5]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op2 (e20) (e22)) = (e20)) = ((e22) = (e20))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1c5. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H18b. % 47.01/47.22 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 47.01/47.22 cut (((op2 (e20) (e22)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H1c6 zenon_H1c3). % 47.01/47.22 apply zenon_H19a. apply refl_equal. % 47.01/47.22 apply zenon_H1bb. apply refl_equal. % 47.01/47.22 apply zenon_H1bb. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L157_ *) % 47.01/47.22 assert (zenon_L158_ : (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e21) (e20)) = (e22)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H1c7 zenon_H183 zenon_H1c8. % 47.01/47.22 cut (((e22) = (op2 (e21) (e21))) = ((op2 (e21) (e20)) = (op2 (e21) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1c7. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H183. % 47.01/47.22 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 47.01/47.22 cut (((e22) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1c9]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1cb ]. % 47.01/47.22 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((e22) = (op2 (e21) (e20)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1c9. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1ca. % 47.01/47.22 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1cb]. % 47.01/47.22 cut (((op2 (e21) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1cc]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H1cc zenon_H1c8). % 47.01/47.22 apply zenon_H1cb. apply refl_equal. % 47.01/47.22 apply zenon_H1cb. apply refl_equal. % 47.01/47.22 apply zenon_H1c0. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L158_ *) % 47.01/47.22 assert (zenon_L159_ : (~((e22) = (e22))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H1bb. % 47.01/47.22 apply zenon_H1bb. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L159_ *) % 47.01/47.22 assert (zenon_L160_ : ((e22) = (op2 (e21) (e21))) -> ((op2 (e21) (e21)) = (e20)) -> (~((e20) = (e22))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H183 zenon_H1cd zenon_H1c4. % 47.01/47.22 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 47.01/47.22 cut (((e22) = (e22)) = ((e20) = (e22))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1c4. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1ba. % 47.01/47.22 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.01/47.22 cut (((e22) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1c5]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((e22) = (op2 (e21) (e21))) = ((e22) = (e20))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1c5. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H183. % 47.01/47.22 cut (((op2 (e21) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1ce]. % 47.01/47.22 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H1bb. apply refl_equal. % 47.01/47.22 exact (zenon_H1ce zenon_H1cd). % 47.01/47.22 apply zenon_H1bb. apply refl_equal. % 47.01/47.22 apply zenon_H1bb. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L160_ *) % 47.01/47.22 assert (zenon_L161_ : (~((op2 (e20) (e22)) = (op2 (e21) (e22)))) -> ((op2 (e20) (e22)) = (e20)) -> ((op2 (e21) (e22)) = (e20)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H1cf zenon_H18b zenon_H1d0. % 47.01/47.22 cut (((op2 (e20) (e22)) = (e20)) = ((op2 (e20) (e22)) = (op2 (e21) (e22)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1cf. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H18b. % 47.01/47.22 cut (((e20) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1d1]. % 47.01/47.22 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H18f. apply refl_equal. % 47.01/47.22 apply zenon_H1d1. apply sym_equal. exact zenon_H1d0. % 47.01/47.22 (* end of lemma zenon_L161_ *) % 47.01/47.22 assert (zenon_L162_ : ((op2 (e21) (e20)) = (e21)) -> ((op2 (e21) (e20)) = (e23)) -> (~((e21) = (e23))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H1d2 zenon_H19c zenon_H1d3. % 47.01/47.22 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H19e | zenon_intro zenon_H19f ]. % 47.01/47.22 cut (((e23) = (e23)) = ((e21) = (e23))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1d3. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H19e. % 47.01/47.22 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 47.01/47.22 cut (((e23) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1d4]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op2 (e21) (e20)) = (e21)) = ((e23) = (e21))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1d4. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1d2. % 47.01/47.22 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.01/47.22 cut (((op2 (e21) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H1a1 zenon_H19c). % 47.01/47.22 apply zenon_H181. apply refl_equal. % 47.01/47.22 apply zenon_H19f. apply refl_equal. % 47.01/47.22 apply zenon_H19f. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L162_ *) % 47.01/47.22 assert (zenon_L163_ : ((e22) = (op2 (e21) (e21))) -> ((op2 (e21) (e21)) = (e21)) -> (~((e21) = (e22))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H183 zenon_H1d5 zenon_H1b9. % 47.01/47.22 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 47.01/47.22 cut (((e22) = (e22)) = ((e21) = (e22))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1b9. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1ba. % 47.01/47.22 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.01/47.22 cut (((e22) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((e22) = (op2 (e21) (e21))) = ((e22) = (e21))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1bc. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H183. % 47.01/47.22 cut (((op2 (e21) (e21)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 47.01/47.22 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H1bb. apply refl_equal. % 47.01/47.22 exact (zenon_H1d6 zenon_H1d5). % 47.01/47.22 apply zenon_H1bb. apply refl_equal. % 47.01/47.22 apply zenon_H1bb. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L163_ *) % 47.01/47.22 assert (zenon_L164_ : (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e22) (e21)) = (e23)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H185 zenon_H1d7 zenon_H1d8. % 47.01/47.22 cut (((op2 (e20) (e21)) = (e23)) = ((op2 (e20) (e21)) = (op2 (e22) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H185. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1d7. % 47.01/47.22 cut (((e23) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1d9]. % 47.01/47.22 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H189. apply refl_equal. % 47.01/47.22 apply zenon_H1d9. apply sym_equal. exact zenon_H1d8. % 47.01/47.22 (* end of lemma zenon_L164_ *) % 47.01/47.22 assert (zenon_L165_ : ((op2 (e20) (e23)) = (e21)) -> ((op2 (e20) (e23)) = (e22)) -> (~((e21) = (e22))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H1da zenon_H1db zenon_H1b9. % 47.01/47.22 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 47.01/47.22 cut (((e22) = (e22)) = ((e21) = (e22))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1b9. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1ba. % 47.01/47.22 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.01/47.22 cut (((e22) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op2 (e20) (e23)) = (e21)) = ((e22) = (e21))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1bc. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1da. % 47.01/47.22 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.01/47.22 cut (((op2 (e20) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1dc]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H1dc zenon_H1db). % 47.01/47.22 apply zenon_H181. apply refl_equal. % 47.01/47.22 apply zenon_H1bb. apply refl_equal. % 47.01/47.22 apply zenon_H1bb. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L165_ *) % 47.01/47.22 assert (zenon_L166_ : ((op2 (e21) (e23)) = (e20)) -> ((op2 (e21) (e23)) = (e21)) -> (~((e20) = (e21))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H1dd zenon_H1de zenon_H1df. % 47.01/47.22 elim (classic ((e21) = (e21))); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H181 ]. % 47.01/47.22 cut (((e21) = (e21)) = ((e20) = (e21))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1df. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1e0. % 47.01/47.22 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.01/47.22 cut (((e21) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op2 (e21) (e23)) = (e20)) = ((e21) = (e20))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1e1. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1dd. % 47.01/47.22 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 47.01/47.22 cut (((op2 (e21) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H1e2 zenon_H1de). % 47.01/47.22 apply zenon_H19a. apply refl_equal. % 47.01/47.22 apply zenon_H181. apply refl_equal. % 47.01/47.22 apply zenon_H181. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L166_ *) % 47.01/47.22 assert (zenon_L167_ : ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e23) (e21)) = (e20)) -> ((e22) = (op2 (e21) (e21))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H14 zenon_H1e3 zenon_H183 zenon_H1e4. % 47.01/47.22 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e6 ]. % 47.01/47.22 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((op2 (e22) (e21)) = (op2 (e23) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1e4. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1e5. % 47.01/47.22 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 47.01/47.22 cut (((op2 (e23) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1e7]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((e20) = (op2 (op2 (e21) (e21)) (e21))) = ((op2 (e23) (e21)) = (op2 (e22) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1e7. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H14. % 47.01/47.22 cut (((op2 (op2 (e21) (e21)) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H182]. % 47.01/47.22 cut (((e20) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e6 ]. % 47.01/47.22 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((e20) = (op2 (e23) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1e8. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1e5. % 47.01/47.22 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 47.01/47.22 cut (((op2 (e23) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1e9]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H1e9 zenon_H1e3). % 47.01/47.22 apply zenon_H1e6. apply refl_equal. % 47.01/47.22 apply zenon_H1e6. apply refl_equal. % 47.01/47.22 apply (zenon_L144_); trivial. % 47.01/47.22 apply zenon_H1e6. apply refl_equal. % 47.01/47.22 apply zenon_H1e6. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L167_ *) % 47.01/47.22 assert (zenon_L168_ : ((op2 (e22) (e21)) = (e20)) -> ((op2 (e22) (e21)) = (e23)) -> (~((e20) = (e23))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H1ea zenon_H1d8 zenon_H19d. % 47.01/47.22 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H19e | zenon_intro zenon_H19f ]. % 47.01/47.22 cut (((e23) = (e23)) = ((e20) = (e23))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H19d. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H19e. % 47.01/47.22 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 47.01/47.22 cut (((e23) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op2 (e22) (e21)) = (e20)) = ((e23) = (e20))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1a0. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1ea. % 47.01/47.22 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 47.01/47.22 cut (((op2 (e22) (e21)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1eb]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H1eb zenon_H1d8). % 47.01/47.22 apply zenon_H19a. apply refl_equal. % 47.01/47.22 apply zenon_H19f. apply refl_equal. % 47.01/47.22 apply zenon_H19f. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L168_ *) % 47.01/47.22 assert (zenon_L169_ : (((op2 (op2 (e20) (e20)) (op2 (e20) (e20))) = (e20))/\(((op2 (op2 (e21) (e20)) (op2 (e21) (e20))) = (e21))/\(((op2 (op2 (e22) (e20)) (op2 (e22) (e20))) = (e22))/\((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e20)) = (e20)) -> ((op2 (e21) (e20)) = (e23)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H1ec zenon_H193 zenon_H1ed zenon_H19c. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_H1ef. zenon_intro zenon_H1ee. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H1ee). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_H1f3. zenon_intro zenon_H1f2. % 47.01/47.22 cut (((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (e23)) = ((op2 (e20) (e20)) = (op2 (e21) (e20)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H193. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1f2. % 47.01/47.22 cut (((e23) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 47.01/47.22 cut (((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e20) (e20)) = (op2 (e20) (e20)))); [ zenon_intro zenon_H197 | zenon_intro zenon_H198 ]. % 47.01/47.22 cut (((op2 (e20) (e20)) = (op2 (e20) (e20))) = ((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (op2 (e20) (e20)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1f5. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H197. % 47.01/47.22 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 47.01/47.22 cut (((op2 (e20) (e20)) = (op2 (op2 (e23) (e20)) (op2 (e23) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((e20) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1f7]. % 47.01/47.22 cut (((e20) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1f7]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H1f7. apply sym_equal. exact zenon_H1ed. % 47.01/47.22 apply zenon_H1f7. apply sym_equal. exact zenon_H1ed. % 47.01/47.22 apply zenon_H198. apply refl_equal. % 47.01/47.22 apply zenon_H198. apply refl_equal. % 47.01/47.22 apply zenon_H1f4. apply sym_equal. exact zenon_H19c. % 47.01/47.22 (* end of lemma zenon_L169_ *) % 47.01/47.22 assert (zenon_L170_ : (((op2 (op2 (e20) (e21)) (op2 (e20) (e21))) = (e20))/\(((op2 (op2 (e21) (e21)) (op2 (e21) (e21))) = (e21))/\(((op2 (op2 (e22) (e21)) (op2 (e22) (e21))) = (e22))/\((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (e23))))) -> ((op2 (e23) (e21)) = (e21)) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H1f8 zenon_H1f9 zenon_H1d7 zenon_H1be. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H1f8). zenon_intro zenon_H1fb. zenon_intro zenon_H1fa. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_H1fd. zenon_intro zenon_H1fc. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_H1ff. zenon_intro zenon_H1fe. % 47.01/47.22 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H200 | zenon_intro zenon_H1c0 ]. % 47.01/47.22 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((op2 (e20) (e21)) = (op2 (e21) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1be. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H200. % 47.01/47.22 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 47.01/47.22 cut (((op2 (e21) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H201]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (e23)) = ((op2 (e21) (e21)) = (op2 (e20) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H201. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1fe. % 47.01/47.22 cut (((e23) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H202]. % 47.01/47.22 cut (((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H203]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H200 | zenon_intro zenon_H1c0 ]. % 47.01/47.22 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (op2 (e21) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H203. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H200. % 47.01/47.22 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 47.01/47.22 cut (((op2 (e21) (e21)) = (op2 (op2 (e23) (e21)) (op2 (e23) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H204]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((e21) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H205]. % 47.01/47.22 cut (((e21) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H205]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H205. apply sym_equal. exact zenon_H1f9. % 47.01/47.22 apply zenon_H205. apply sym_equal. exact zenon_H1f9. % 47.01/47.22 apply zenon_H1c0. apply refl_equal. % 47.01/47.22 apply zenon_H1c0. apply refl_equal. % 47.01/47.22 apply zenon_H202. apply sym_equal. exact zenon_H1d7. % 47.01/47.22 apply zenon_H1c0. apply refl_equal. % 47.01/47.22 apply zenon_H1c0. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L170_ *) % 47.01/47.22 assert (zenon_L171_ : (~((op2 (e23) (e23)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))) -> ((op2 (e22) (e22)) = (e23)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H206 zenon_H207. % 47.01/47.22 cut (((e23) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H208]. % 47.01/47.22 cut (((e23) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H208]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H208. apply sym_equal. exact zenon_H207. % 47.01/47.22 apply zenon_H208. apply sym_equal. exact zenon_H207. % 47.01/47.22 (* end of lemma zenon_L171_ *) % 47.01/47.22 assert (zenon_L172_ : (((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (e20))/\(((op2 (op2 (e21) (e22)) (op2 (e21) (e22))) = (e21))/\(((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (e22))/\((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e23))))) -> ((op2 (e22) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H209 zenon_H207 zenon_H1db zenon_H20a. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H209). zenon_intro zenon_H20c. zenon_intro zenon_H20b. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_H20e. zenon_intro zenon_H20d. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H210. zenon_intro zenon_H20f. % 47.01/47.22 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 47.01/47.22 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e20) (e23)) = (op2 (e23) (e23)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H20a. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H211. % 47.01/47.22 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 47.01/47.22 cut (((op2 (e23) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H213]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (e22)) = ((op2 (e23) (e23)) = (op2 (e20) (e23)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H213. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H210. % 47.01/47.22 cut (((e22) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 47.01/47.22 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 47.01/47.22 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (e23) (e23)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H215. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H211. % 47.01/47.22 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 47.01/47.22 cut (((op2 (e23) (e23)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 47.01/47.22 congruence. % 47.01/47.22 apply (zenon_L171_); trivial. % 47.01/47.22 apply zenon_H212. apply refl_equal. % 47.01/47.22 apply zenon_H212. apply refl_equal. % 47.01/47.22 apply zenon_H214. apply sym_equal. exact zenon_H1db. % 47.01/47.22 apply zenon_H212. apply refl_equal. % 47.01/47.22 apply zenon_H212. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L172_ *) % 47.01/47.22 assert (zenon_L173_ : ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e20) (e22)) = (e20)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H19c zenon_H1ed zenon_H193 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H20a zenon_H207 zenon_H1db zenon_H18b zenon_H216. % 47.01/47.22 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.01/47.22 apply (zenon_L169_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.01/47.22 apply (zenon_L170_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.01/47.22 apply (zenon_L172_); trivial. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H21b. zenon_intro zenon_H21a. % 47.01/47.22 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H21c | zenon_intro zenon_H21d ]. % 47.01/47.22 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e20) (e22)) = (op2 (e22) (e22)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H216. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H21c. % 47.01/47.22 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 47.01/47.22 cut (((op2 (e22) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (e20)) = ((op2 (e22) (e22)) = (op2 (e20) (e22)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H21e. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H21b. % 47.01/47.22 cut (((e20) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 47.01/47.22 cut (((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H220]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H21c | zenon_intro zenon_H21d ]. % 47.01/47.22 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (op2 (e22) (e22)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H220. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H21c. % 47.01/47.22 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 47.01/47.22 cut (((op2 (e22) (e22)) = (op2 (op2 (e20) (e23)) (op2 (e20) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((e22) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 47.01/47.22 cut (((e22) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H214. apply sym_equal. exact zenon_H1db. % 47.01/47.22 apply zenon_H214. apply sym_equal. exact zenon_H1db. % 47.01/47.22 apply zenon_H21d. apply refl_equal. % 47.01/47.22 apply zenon_H21d. apply refl_equal. % 47.01/47.22 apply zenon_H21f. apply sym_equal. exact zenon_H18b. % 47.01/47.22 apply zenon_H21d. apply refl_equal. % 47.01/47.22 apply zenon_H21d. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L173_ *) % 47.01/47.22 assert (zenon_L174_ : ((op2 (e22) (e23)) = (e21)) -> ((op2 (e22) (e23)) = (e23)) -> (~((e21) = (e23))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H222 zenon_H223 zenon_H1d3. % 47.01/47.22 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H19e | zenon_intro zenon_H19f ]. % 47.01/47.22 cut (((e23) = (e23)) = ((e21) = (e23))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1d3. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H19e. % 47.01/47.22 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 47.01/47.22 cut (((e23) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1d4]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op2 (e22) (e23)) = (e21)) = ((e23) = (e21))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1d4. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H222. % 47.01/47.22 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.01/47.22 cut (((op2 (e22) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H224]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H224 zenon_H223). % 47.01/47.22 apply zenon_H181. apply refl_equal. % 47.01/47.22 apply zenon_H19f. apply refl_equal. % 47.01/47.22 apply zenon_H19f. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L174_ *) % 47.01/47.22 assert (zenon_L175_ : (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((e20) = (e23))) -> ((op2 (e22) (e21)) = (e20)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e20)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e21)) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e20)) = (e20)) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e21)) -> (~((e21) = (e23))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H225 zenon_H1a3 zenon_H14 zenon_H194 zenon_H19d zenon_H1ea zenon_H216 zenon_H18b zenon_H1db zenon_H20a zenon_H1f9 zenon_H1d7 zenon_H1be zenon_H193 zenon_H1ed zenon_H19c zenon_H222 zenon_H1d3. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.01/47.22 apply (zenon_L151_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.01/47.22 apply (zenon_L168_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.01/47.22 apply (zenon_L173_); trivial. % 47.01/47.22 apply (zenon_L174_); trivial. % 47.01/47.22 (* end of lemma zenon_L175_ *) % 47.01/47.22 assert (zenon_L176_ : ((e22) = (op2 (e21) (e21))) -> ((op2 (e23) (e21)) = (e22)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H183 zenon_H228 zenon_H229. % 47.01/47.22 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e6 ]. % 47.01/47.22 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((op2 (e21) (e21)) = (op2 (e23) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H229. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1e5. % 47.01/47.22 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 47.01/47.22 cut (((op2 (e23) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H22a]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((e22) = (op2 (e21) (e21))) = ((op2 (e23) (e21)) = (op2 (e21) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H22a. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H183. % 47.01/47.22 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 47.01/47.22 cut (((e22) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H22b]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e6 ]. % 47.01/47.22 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((e22) = (op2 (e23) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H22b. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1e5. % 47.01/47.22 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 47.01/47.22 cut (((op2 (e23) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H22c]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H22c zenon_H228). % 47.01/47.22 apply zenon_H1e6. apply refl_equal. % 47.01/47.22 apply zenon_H1e6. apply refl_equal. % 47.01/47.22 apply zenon_H1c0. apply refl_equal. % 47.01/47.22 apply zenon_H1e6. apply refl_equal. % 47.01/47.22 apply zenon_H1e6. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L176_ *) % 47.01/47.22 assert (zenon_L177_ : (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e23)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H22d zenon_H1d7 zenon_H22e. % 47.01/47.22 cut (((op2 (e20) (e21)) = (e23)) = ((op2 (e20) (e21)) = (op2 (e23) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H22d. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1d7. % 47.01/47.22 cut (((e23) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H22f]. % 47.01/47.22 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H189. apply refl_equal. % 47.01/47.22 apply zenon_H22f. apply sym_equal. exact zenon_H22e. % 47.01/47.22 (* end of lemma zenon_L177_ *) % 47.01/47.22 assert (zenon_L178_ : (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> (~((e21) = (e23))) -> ((op2 (e22) (e23)) = (e21)) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e20) (e22)) = (e20)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e21)) = (e20)) -> (~((e20) = (e23))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H230 zenon_H1e4 zenon_H1d3 zenon_H222 zenon_H19c zenon_H1ed zenon_H193 zenon_H1be zenon_H20a zenon_H1db zenon_H18b zenon_H216 zenon_H1ea zenon_H19d zenon_H194 zenon_H14 zenon_H1a3 zenon_H225 zenon_H229 zenon_H183 zenon_H22d zenon_H1d7. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H231 ]. % 47.01/47.22 apply (zenon_L167_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H232 ]. % 47.01/47.22 apply (zenon_L175_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H228 | zenon_intro zenon_H22e ]. % 47.01/47.22 apply (zenon_L176_); trivial. % 47.01/47.22 apply (zenon_L177_); trivial. % 47.01/47.22 (* end of lemma zenon_L178_ *) % 47.01/47.22 assert (zenon_L179_ : ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e22) (e23)) = (e20)) -> ((e22) = (op2 (e21) (e21))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H14 zenon_H233 zenon_H183 zenon_H234. % 47.01/47.22 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H235 | zenon_intro zenon_H236 ]. % 47.01/47.22 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((op2 (e22) (e21)) = (op2 (e22) (e23)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H234. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H235. % 47.01/47.22 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H236]. % 47.01/47.22 cut (((op2 (e22) (e23)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H237]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((e20) = (op2 (op2 (e21) (e21)) (e21))) = ((op2 (e22) (e23)) = (op2 (e22) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H237. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H14. % 47.01/47.22 cut (((op2 (op2 (e21) (e21)) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H182]. % 47.01/47.22 cut (((e20) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H238]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H235 | zenon_intro zenon_H236 ]. % 47.01/47.22 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e20) = (op2 (e22) (e23)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H238. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H235. % 47.01/47.22 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H236]. % 47.01/47.22 cut (((op2 (e22) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H239]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H239 zenon_H233). % 47.01/47.22 apply zenon_H236. apply refl_equal. % 47.01/47.22 apply zenon_H236. apply refl_equal. % 47.01/47.22 apply (zenon_L144_); trivial. % 47.01/47.22 apply zenon_H236. apply refl_equal. % 47.01/47.22 apply zenon_H236. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L179_ *) % 47.01/47.22 assert (zenon_L180_ : (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e22)) -> ((op2 (e22) (e23)) = (e22)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H23a zenon_H23b zenon_H23c. % 47.01/47.22 cut (((op2 (e22) (e20)) = (e22)) = ((op2 (e22) (e20)) = (op2 (e22) (e23)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H23a. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H23b. % 47.01/47.22 cut (((e22) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 47.01/47.22 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H1a5. apply refl_equal. % 47.01/47.22 apply zenon_H23d. apply sym_equal. exact zenon_H23c. % 47.01/47.22 (* end of lemma zenon_L180_ *) % 47.01/47.22 assert (zenon_L181_ : (~((op2 (e23) (e23)) = (op2 (op2 (e23) (e21)) (op2 (e23) (e21))))) -> ((op2 (e23) (e21)) = (e23)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H23e zenon_H22e. % 47.01/47.22 cut (((e23) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H22f]. % 47.01/47.22 cut (((e23) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H22f]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H22f. apply sym_equal. exact zenon_H22e. % 47.01/47.22 apply zenon_H22f. apply sym_equal. exact zenon_H22e. % 47.01/47.22 (* end of lemma zenon_L181_ *) % 47.01/47.22 assert (zenon_L182_ : (((op2 (op2 (e20) (e21)) (op2 (e20) (e21))) = (e20))/\(((op2 (op2 (e21) (e21)) (op2 (e21) (e21))) = (e21))/\(((op2 (op2 (e22) (e21)) (op2 (e22) (e21))) = (e22))/\((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (e23))))) -> ((op2 (e23) (e21)) = (e23)) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H1f8 zenon_H22e zenon_H223 zenon_H23f. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H1f8). zenon_intro zenon_H1fb. zenon_intro zenon_H1fa. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_H1fd. zenon_intro zenon_H1fc. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_H1ff. zenon_intro zenon_H1fe. % 47.01/47.22 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 47.01/47.22 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e22) (e23)) = (op2 (e23) (e23)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H23f. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H211. % 47.01/47.22 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 47.01/47.22 cut (((op2 (e23) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H240]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (e23)) = ((op2 (e23) (e23)) = (op2 (e22) (e23)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H240. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1fe. % 47.01/47.22 cut (((e23) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 47.01/47.22 cut (((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H242]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 47.01/47.22 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (op2 (e23) (e23)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H242. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H211. % 47.01/47.22 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 47.01/47.22 cut (((op2 (e23) (e23)) = (op2 (op2 (e23) (e21)) (op2 (e23) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H23e]. % 47.01/47.22 congruence. % 47.01/47.22 apply (zenon_L181_); trivial. % 47.01/47.22 apply zenon_H212. apply refl_equal. % 47.01/47.22 apply zenon_H212. apply refl_equal. % 47.01/47.22 apply zenon_H241. apply sym_equal. exact zenon_H223. % 47.01/47.22 apply zenon_H212. apply refl_equal. % 47.01/47.22 apply zenon_H212. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L182_ *) % 47.01/47.22 assert (zenon_L183_ : (((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (e20))/\(((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (e21))/\(((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (e22))/\((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e23)) = (e21)) -> ((op2 (e23) (e21)) = (e23)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H219 zenon_H229 zenon_H243 zenon_H22e. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H21b. zenon_intro zenon_H21a. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H21a). zenon_intro zenon_H245. zenon_intro zenon_H244. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H244). zenon_intro zenon_H247. zenon_intro zenon_H246. % 47.01/47.22 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23)) = ((op2 (e21) (e21)) = (op2 (e23) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H229. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H246. % 47.01/47.22 cut (((e23) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H22f]. % 47.01/47.22 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H248]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H200 | zenon_intro zenon_H1c0 ]. % 47.01/47.22 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H248. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H200. % 47.01/47.22 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 47.01/47.22 cut (((op2 (e21) (e21)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H249]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((e21) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H24a]. % 47.01/47.22 cut (((e21) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H24a]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H24a. apply sym_equal. exact zenon_H243. % 47.01/47.22 apply zenon_H24a. apply sym_equal. exact zenon_H243. % 47.01/47.22 apply zenon_H1c0. apply refl_equal. % 47.01/47.22 apply zenon_H1c0. apply refl_equal. % 47.01/47.22 apply zenon_H22f. apply sym_equal. exact zenon_H22e. % 47.01/47.22 (* end of lemma zenon_L183_ *) % 47.01/47.22 assert (zenon_L184_ : (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e20)) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e23)) = (e21)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H230 zenon_H1e4 zenon_H14 zenon_H216 zenon_H18b zenon_H1d7 zenon_H1be zenon_H183 zenon_H19c zenon_H1ed zenon_H193 zenon_H23f zenon_H223 zenon_H20a zenon_H1db zenon_H207 zenon_H229 zenon_H243. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H231 ]. % 47.01/47.22 apply (zenon_L167_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H232 ]. % 47.01/47.22 apply (zenon_L173_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H228 | zenon_intro zenon_H22e ]. % 47.01/47.22 apply (zenon_L176_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.01/47.22 apply (zenon_L169_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.01/47.22 apply (zenon_L182_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.01/47.22 apply (zenon_L172_); trivial. % 47.01/47.22 apply (zenon_L183_); trivial. % 47.01/47.22 (* end of lemma zenon_L184_ *) % 47.01/47.22 assert (zenon_L185_ : (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((e20) = (e23))) -> ((op2 (e22) (e21)) = (e20)) -> (~((e21) = (e23))) -> ((op2 (e22) (e20)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e20)) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e23)) = (e21)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H24b zenon_H234 zenon_H22d zenon_H225 zenon_H1a3 zenon_H194 zenon_H19d zenon_H1ea zenon_H1d3 zenon_H23b zenon_H23a zenon_H230 zenon_H1e4 zenon_H14 zenon_H216 zenon_H18b zenon_H1d7 zenon_H1be zenon_H183 zenon_H19c zenon_H1ed zenon_H193 zenon_H23f zenon_H20a zenon_H1db zenon_H207 zenon_H229 zenon_H243. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H233 | zenon_intro zenon_H24c ]. % 47.01/47.22 apply (zenon_L179_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H222 | zenon_intro zenon_H24d ]. % 47.01/47.22 apply (zenon_L178_); trivial. % 47.01/47.22 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H23c | zenon_intro zenon_H223 ]. % 47.01/47.22 apply (zenon_L180_); trivial. % 47.01/47.22 apply (zenon_L184_); trivial. % 47.01/47.22 (* end of lemma zenon_L185_ *) % 47.01/47.22 assert (zenon_L186_ : ((op2 (e20) (e22)) = (e20)) -> ((op2 (e20) (e22)) = (e23)) -> (~((e20) = (e23))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H18b zenon_H24e zenon_H19d. % 47.01/47.22 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H19e | zenon_intro zenon_H19f ]. % 47.01/47.22 cut (((e23) = (e23)) = ((e20) = (e23))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H19d. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H19e. % 47.01/47.22 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 47.01/47.22 cut (((e23) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op2 (e20) (e22)) = (e20)) = ((e23) = (e20))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1a0. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H18b. % 47.01/47.22 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 47.01/47.22 cut (((op2 (e20) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H24f]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H24f zenon_H24e). % 47.01/47.22 apply zenon_H19a. apply refl_equal. % 47.01/47.22 apply zenon_H19f. apply refl_equal. % 47.01/47.22 apply zenon_H19f. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L186_ *) % 47.01/47.22 assert (zenon_L187_ : ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((op2 (e21) (e22)) = (e23)) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H194 zenon_H250 zenon_H14 zenon_H251. % 47.01/47.22 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_H252 | zenon_intro zenon_H253 ]. % 47.01/47.22 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((op2 (e21) (e20)) = (op2 (e21) (e22)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H251. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H252. % 47.01/47.22 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H253]. % 47.01/47.22 cut (((op2 (e21) (e22)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H254]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) = ((op2 (e21) (e22)) = (op2 (e21) (e20)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H254. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H194. % 47.01/47.22 cut (((op2 (e21) (op2 (op2 (e21) (e21)) (e21))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 47.01/47.22 cut (((e23) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H255]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_H252 | zenon_intro zenon_H253 ]. % 47.01/47.22 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((e23) = (op2 (e21) (e22)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H255. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H252. % 47.01/47.22 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H253]. % 47.01/47.22 cut (((op2 (e21) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H256]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H256 zenon_H250). % 47.01/47.22 apply zenon_H253. apply refl_equal. % 47.01/47.22 apply zenon_H253. apply refl_equal. % 47.01/47.22 apply (zenon_L147_); trivial. % 47.01/47.22 apply zenon_H253. apply refl_equal. % 47.01/47.22 apply zenon_H253. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L187_ *) % 47.01/47.22 assert (zenon_L188_ : ((op2 (e23) (e20)) = (e20)) -> ((op2 (e23) (e20)) = (e22)) -> (~((e20) = (e22))) -> False). % 47.01/47.22 do 0 intro. intros zenon_H1ed zenon_H257 zenon_H1c4. % 47.01/47.22 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 47.01/47.22 cut (((e22) = (e22)) = ((e20) = (e22))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1c4. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1ba. % 47.01/47.22 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.01/47.22 cut (((e22) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1c5]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((op2 (e23) (e20)) = (e20)) = ((e22) = (e20))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H1c5. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1ed. % 47.01/47.22 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 47.01/47.22 cut (((op2 (e23) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H258]. % 47.01/47.22 congruence. % 47.01/47.22 exact (zenon_H258 zenon_H257). % 47.01/47.22 apply zenon_H19a. apply refl_equal. % 47.01/47.22 apply zenon_H1bb. apply refl_equal. % 47.01/47.22 apply zenon_H1bb. apply refl_equal. % 47.01/47.22 (* end of lemma zenon_L188_ *) % 47.01/47.22 assert (zenon_L189_ : (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e22)) = (e22)) -> ((op2 (e23) (e22)) = (e22)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H259 zenon_H1c3 zenon_H25a. % 47.01/47.22 cut (((op2 (e20) (e22)) = (e22)) = ((op2 (e20) (e22)) = (op2 (e23) (e22)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H259. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1c3. % 47.01/47.22 cut (((e22) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H25b]. % 47.01/47.22 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H18f. apply refl_equal. % 47.01/47.22 apply zenon_H25b. apply sym_equal. exact zenon_H25a. % 47.01/47.22 (* end of lemma zenon_L189_ *) % 47.01/47.22 assert (zenon_L190_ : (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e21)) -> ((op2 (e22) (e23)) = (e21)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H25c zenon_H1da zenon_H222. % 47.01/47.22 cut (((op2 (e20) (e23)) = (e21)) = ((op2 (e20) (e23)) = (op2 (e22) (e23)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H25c. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1da. % 47.01/47.22 cut (((e21) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H25d]. % 47.01/47.22 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H25e. apply refl_equal. % 47.01/47.22 apply zenon_H25d. apply sym_equal. exact zenon_H222. % 47.01/47.22 (* end of lemma zenon_L190_ *) % 47.01/47.22 assert (zenon_L191_ : (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e20)) -> ((op2 (e23) (e22)) = (e20)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H25f zenon_H1ed zenon_H260. % 47.01/47.22 cut (((op2 (e23) (e20)) = (e20)) = ((op2 (e23) (e20)) = (op2 (e23) (e22)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H25f. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1ed. % 47.01/47.22 cut (((e20) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H261]. % 47.01/47.22 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1ac]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H1ac. apply refl_equal. % 47.01/47.22 apply zenon_H261. apply sym_equal. exact zenon_H260. % 47.01/47.22 (* end of lemma zenon_L191_ *) % 47.01/47.22 assert (zenon_L192_ : (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e21)) = (e21)) -> ((op2 (e23) (e22)) = (e21)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H262 zenon_H1f9 zenon_H263. % 47.01/47.22 cut (((op2 (e23) (e21)) = (e21)) = ((op2 (e23) (e21)) = (op2 (e23) (e22)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H262. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H1f9. % 47.01/47.22 cut (((e21) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 47.01/47.22 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H1e6. apply refl_equal. % 47.01/47.22 apply zenon_H264. apply sym_equal. exact zenon_H263. % 47.01/47.22 (* end of lemma zenon_L192_ *) % 47.01/47.22 assert (zenon_L193_ : (((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (e20))/\(((op2 (op2 (e21) (e22)) (op2 (e21) (e22))) = (e21))/\(((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (e22))/\((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e23))))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e22)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H209 zenon_H265 zenon_H25a zenon_H223. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H209). zenon_intro zenon_H20c. zenon_intro zenon_H20b. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_H20e. zenon_intro zenon_H20d. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H210. zenon_intro zenon_H20f. % 47.01/47.22 cut (((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e23)) = ((op2 (e22) (e22)) = (op2 (e22) (e23)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H265. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H20f. % 47.01/47.22 cut (((e23) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 47.01/47.22 cut (((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H266]. % 47.01/47.22 congruence. % 47.01/47.22 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H21c | zenon_intro zenon_H21d ]. % 47.01/47.22 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (op2 (e22) (e22)))). % 47.01/47.22 intro zenon_D_pnotp. % 47.01/47.22 apply zenon_H266. % 47.01/47.22 rewrite <- zenon_D_pnotp. % 47.01/47.22 exact zenon_H21c. % 47.01/47.22 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 47.01/47.22 cut (((op2 (e22) (e22)) = (op2 (op2 (e23) (e22)) (op2 (e23) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H267]. % 47.01/47.22 congruence. % 47.01/47.22 cut (((e22) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H25b]. % 47.01/47.22 cut (((e22) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H25b]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H25b. apply sym_equal. exact zenon_H25a. % 47.01/47.22 apply zenon_H25b. apply sym_equal. exact zenon_H25a. % 47.01/47.22 apply zenon_H21d. apply refl_equal. % 47.01/47.22 apply zenon_H21d. apply refl_equal. % 47.01/47.22 apply zenon_H241. apply sym_equal. exact zenon_H223. % 47.01/47.22 (* end of lemma zenon_L193_ *) % 47.01/47.22 assert (zenon_L194_ : (~((op2 (e22) (e22)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op2 (e23) (e23)) = (e22)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H268 zenon_H269. % 47.01/47.22 cut (((e22) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H26a]. % 47.01/47.22 cut (((e22) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H26a]. % 47.01/47.22 congruence. % 47.01/47.22 apply zenon_H26a. apply sym_equal. exact zenon_H269. % 47.01/47.22 apply zenon_H26a. apply sym_equal. exact zenon_H269. % 47.01/47.22 (* end of lemma zenon_L194_ *) % 47.01/47.22 assert (zenon_L195_ : (((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (e20))/\(((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (e21))/\(((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (e22))/\((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23))))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> False). % 47.01/47.22 do 0 intro. intros zenon_H219 zenon_H265 zenon_H269 zenon_H223. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H21b. zenon_intro zenon_H21a. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H21a). zenon_intro zenon_H245. zenon_intro zenon_H244. % 47.01/47.22 apply (zenon_and_s _ _ zenon_H244). zenon_intro zenon_H247. zenon_intro zenon_H246. % 47.01/47.22 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23)) = ((op2 (e22) (e22)) = (op2 (e22) (e23)))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H265. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H246. % 47.05/47.22 cut (((e23) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 47.05/47.22 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H26b]. % 47.05/47.22 congruence. % 47.05/47.22 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H21c | zenon_intro zenon_H21d ]. % 47.05/47.22 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e22) (e22)))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H26b. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H21c. % 47.05/47.22 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 47.05/47.22 cut (((op2 (e22) (e22)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H268]. % 47.05/47.22 congruence. % 47.05/47.22 apply (zenon_L194_); trivial. % 47.05/47.22 apply zenon_H21d. apply refl_equal. % 47.05/47.22 apply zenon_H21d. apply refl_equal. % 47.05/47.22 apply zenon_H241. apply sym_equal. exact zenon_H223. % 47.05/47.22 (* end of lemma zenon_L195_ *) % 47.05/47.22 assert (zenon_L196_ : ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> False). % 47.05/47.22 do 0 intro. intros zenon_H19c zenon_H1ed zenon_H193 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H25a zenon_H265 zenon_H269 zenon_H223. % 47.05/47.22 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.05/47.22 apply (zenon_L169_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.05/47.22 apply (zenon_L170_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.05/47.22 apply (zenon_L193_); trivial. % 47.05/47.22 apply (zenon_L195_); trivial. % 47.05/47.22 (* end of lemma zenon_L196_ *) % 47.05/47.22 assert (zenon_L197_ : (((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (e20))/\(((op2 (op2 (e21) (e22)) (op2 (e21) (e22))) = (e21))/\(((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (e22))/\((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e23))))) -> ((op2 (e23) (e22)) = (e23)) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> False). % 47.05/47.22 do 0 intro. intros zenon_H209 zenon_H26c zenon_H223 zenon_H23f. % 47.05/47.22 apply (zenon_and_s _ _ zenon_H209). zenon_intro zenon_H20c. zenon_intro zenon_H20b. % 47.05/47.22 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_H20e. zenon_intro zenon_H20d. % 47.05/47.22 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H210. zenon_intro zenon_H20f. % 47.05/47.22 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 47.05/47.22 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e22) (e23)) = (op2 (e23) (e23)))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H23f. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H211. % 47.05/47.22 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 47.05/47.22 cut (((op2 (e23) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H240]. % 47.05/47.22 congruence. % 47.05/47.22 cut (((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e23)) = ((op2 (e23) (e23)) = (op2 (e22) (e23)))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H240. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H20f. % 47.05/47.22 cut (((e23) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 47.05/47.22 cut (((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H26d]. % 47.05/47.22 congruence. % 47.05/47.22 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 47.05/47.22 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (op2 (e23) (e23)))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H26d. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H211. % 47.05/47.22 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 47.05/47.22 cut (((op2 (e23) (e23)) = (op2 (op2 (e23) (e22)) (op2 (e23) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H26e]. % 47.05/47.22 congruence. % 47.05/47.22 cut (((e23) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 47.05/47.22 cut (((e23) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 47.05/47.22 congruence. % 47.05/47.22 apply zenon_H26f. apply sym_equal. exact zenon_H26c. % 47.05/47.22 apply zenon_H26f. apply sym_equal. exact zenon_H26c. % 47.05/47.22 apply zenon_H212. apply refl_equal. % 47.05/47.22 apply zenon_H212. apply refl_equal. % 47.05/47.22 apply zenon_H241. apply sym_equal. exact zenon_H223. % 47.05/47.22 apply zenon_H212. apply refl_equal. % 47.05/47.22 apply zenon_H212. apply refl_equal. % 47.05/47.22 (* end of lemma zenon_L197_ *) % 47.05/47.22 assert (zenon_L198_ : (((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (e20))/\(((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (e21))/\(((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (e22))/\((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> False). % 47.05/47.22 do 0 intro. intros zenon_H219 zenon_H270 zenon_H269 zenon_H26c. % 47.05/47.22 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H21b. zenon_intro zenon_H21a. % 47.05/47.22 apply (zenon_and_s _ _ zenon_H21a). zenon_intro zenon_H245. zenon_intro zenon_H244. % 47.05/47.22 apply (zenon_and_s _ _ zenon_H244). zenon_intro zenon_H247. zenon_intro zenon_H246. % 47.05/47.22 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23)) = ((op2 (e22) (e22)) = (op2 (e23) (e22)))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H270. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H246. % 47.05/47.22 cut (((e23) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 47.05/47.22 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H26b]. % 47.05/47.22 congruence. % 47.05/47.22 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H21c | zenon_intro zenon_H21d ]. % 47.05/47.22 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e22) (e22)))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H26b. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H21c. % 47.05/47.22 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 47.05/47.22 cut (((op2 (e22) (e22)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H268]. % 47.05/47.22 congruence. % 47.05/47.22 apply (zenon_L194_); trivial. % 47.05/47.22 apply zenon_H21d. apply refl_equal. % 47.05/47.22 apply zenon_H21d. apply refl_equal. % 47.05/47.22 apply zenon_H26f. apply sym_equal. exact zenon_H26c. % 47.05/47.22 (* end of lemma zenon_L198_ *) % 47.05/47.22 assert (zenon_L199_ : ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> False). % 47.05/47.22 do 0 intro. intros zenon_H19c zenon_H1ed zenon_H193 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H23f zenon_H223 zenon_H270 zenon_H269 zenon_H26c. % 47.05/47.22 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.05/47.22 apply (zenon_L169_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.05/47.22 apply (zenon_L170_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.05/47.22 apply (zenon_L197_); trivial. % 47.05/47.22 apply (zenon_L198_); trivial. % 47.05/47.22 (* end of lemma zenon_L199_ *) % 47.05/47.22 assert (zenon_L200_ : (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> False). % 47.05/47.22 do 0 intro. intros zenon_H271 zenon_H25f zenon_H262 zenon_H265 zenon_H19c zenon_H1ed zenon_H193 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H23f zenon_H223 zenon_H270 zenon_H269. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H260 | zenon_intro zenon_H272 ]. % 47.05/47.22 apply (zenon_L191_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H263 | zenon_intro zenon_H273 ]. % 47.05/47.22 apply (zenon_L192_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H25a | zenon_intro zenon_H26c ]. % 47.05/47.22 apply (zenon_L196_); trivial. % 47.05/47.22 apply (zenon_L199_); trivial. % 47.05/47.22 (* end of lemma zenon_L200_ *) % 47.05/47.22 assert (zenon_L201_ : (((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (e20))/\(((op2 (op2 (e21) (e22)) (op2 (e21) (e22))) = (e21))/\(((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (e22))/\((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e22)) = (e21)) -> ((op2 (e23) (e21)) = (e23)) -> False). % 47.05/47.22 do 0 intro. intros zenon_H209 zenon_H229 zenon_H263 zenon_H22e. % 47.05/47.22 apply (zenon_and_s _ _ zenon_H209). zenon_intro zenon_H20c. zenon_intro zenon_H20b. % 47.05/47.22 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_H20e. zenon_intro zenon_H20d. % 47.05/47.22 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H210. zenon_intro zenon_H20f. % 47.05/47.22 cut (((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e23)) = ((op2 (e21) (e21)) = (op2 (e23) (e21)))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H229. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H20f. % 47.05/47.22 cut (((e23) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H22f]. % 47.05/47.22 cut (((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H274]. % 47.05/47.22 congruence. % 47.05/47.22 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H200 | zenon_intro zenon_H1c0 ]. % 47.05/47.22 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (op2 (e21) (e21)))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H274. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H200. % 47.05/47.22 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 47.05/47.22 cut (((op2 (e21) (e21)) = (op2 (op2 (e23) (e22)) (op2 (e23) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H275]. % 47.05/47.22 congruence. % 47.05/47.22 cut (((e21) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 47.05/47.22 cut (((e21) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 47.05/47.22 congruence. % 47.05/47.22 apply zenon_H264. apply sym_equal. exact zenon_H263. % 47.05/47.22 apply zenon_H264. apply sym_equal. exact zenon_H263. % 47.05/47.22 apply zenon_H1c0. apply refl_equal. % 47.05/47.22 apply zenon_H1c0. apply refl_equal. % 47.05/47.22 apply zenon_H22f. apply sym_equal. exact zenon_H22e. % 47.05/47.22 (* end of lemma zenon_L201_ *) % 47.05/47.22 assert (zenon_L202_ : ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e23)) -> ((op2 (e23) (e22)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> False). % 47.05/47.22 do 0 intro. intros zenon_H19c zenon_H1ed zenon_H193 zenon_H23f zenon_H22e zenon_H263 zenon_H229 zenon_H265 zenon_H269 zenon_H223. % 47.05/47.22 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.05/47.22 apply (zenon_L169_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.05/47.22 apply (zenon_L182_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.05/47.22 apply (zenon_L201_); trivial. % 47.05/47.22 apply (zenon_L195_); trivial. % 47.05/47.22 (* end of lemma zenon_L202_ *) % 47.05/47.22 assert (zenon_L203_ : ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> False). % 47.05/47.22 do 0 intro. intros zenon_H19c zenon_H1ed zenon_H193 zenon_H22e zenon_H23f zenon_H223 zenon_H270 zenon_H269 zenon_H26c. % 47.05/47.22 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.05/47.22 apply (zenon_L169_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.05/47.22 apply (zenon_L182_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.05/47.22 apply (zenon_L197_); trivial. % 47.05/47.22 apply (zenon_L198_); trivial. % 47.05/47.22 (* end of lemma zenon_L203_ *) % 47.05/47.22 assert (zenon_L204_ : (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e20) (e22)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> False). % 47.05/47.22 do 0 intro. intros zenon_H271 zenon_H25f zenon_H265 zenon_H229 zenon_H1c3 zenon_H259 zenon_H19c zenon_H1ed zenon_H193 zenon_H22e zenon_H23f zenon_H223 zenon_H270 zenon_H269. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H260 | zenon_intro zenon_H272 ]. % 47.05/47.22 apply (zenon_L191_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H263 | zenon_intro zenon_H273 ]. % 47.05/47.22 apply (zenon_L202_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H25a | zenon_intro zenon_H26c ]. % 47.05/47.22 apply (zenon_L189_); trivial. % 47.05/47.22 apply (zenon_L203_); trivial. % 47.05/47.22 (* end of lemma zenon_L204_ *) % 47.05/47.22 assert (zenon_L205_ : (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e22) = (op2 (e21) (e21))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e20) (e22)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> False). % 47.05/47.22 do 0 intro. intros zenon_H230 zenon_H1e4 zenon_H14 zenon_H1d7 zenon_H1be zenon_H262 zenon_H183 zenon_H271 zenon_H25f zenon_H265 zenon_H229 zenon_H1c3 zenon_H259 zenon_H19c zenon_H1ed zenon_H193 zenon_H23f zenon_H223 zenon_H270 zenon_H269. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H231 ]. % 47.05/47.22 apply (zenon_L167_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H232 ]. % 47.05/47.22 apply (zenon_L200_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H228 | zenon_intro zenon_H22e ]. % 47.05/47.22 apply (zenon_L176_); trivial. % 47.05/47.22 apply (zenon_L204_); trivial. % 47.05/47.22 (* end of lemma zenon_L205_ *) % 47.05/47.22 assert (zenon_L206_ : ((op2 (e20) (e22)) = (e22)) -> ((op2 (e20) (e22)) = (e23)) -> (~((e22) = (e23))) -> False). % 47.05/47.22 do 0 intro. intros zenon_H1c3 zenon_H24e zenon_H276. % 47.05/47.22 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H19e | zenon_intro zenon_H19f ]. % 47.05/47.22 cut (((e23) = (e23)) = ((e22) = (e23))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H276. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H19e. % 47.05/47.22 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 47.05/47.22 cut (((e23) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H277]. % 47.05/47.22 congruence. % 47.05/47.22 cut (((op2 (e20) (e22)) = (e22)) = ((e23) = (e22))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H277. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H1c3. % 47.05/47.22 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.05/47.22 cut (((op2 (e20) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H24f]. % 47.05/47.22 congruence. % 47.05/47.22 exact (zenon_H24f zenon_H24e). % 47.05/47.22 apply zenon_H1bb. apply refl_equal. % 47.05/47.22 apply zenon_H19f. apply refl_equal. % 47.05/47.22 apply zenon_H19f. apply refl_equal. % 47.05/47.22 (* end of lemma zenon_L206_ *) % 47.05/47.22 assert (zenon_L207_ : ((op2 (e20) (e23)) = (e21)) -> ((op2 (e20) (e23)) = (e23)) -> (~((e21) = (e23))) -> False). % 47.05/47.22 do 0 intro. intros zenon_H1da zenon_H278 zenon_H1d3. % 47.05/47.22 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H19e | zenon_intro zenon_H19f ]. % 47.05/47.22 cut (((e23) = (e23)) = ((e21) = (e23))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H1d3. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H19e. % 47.05/47.22 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 47.05/47.22 cut (((e23) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1d4]. % 47.05/47.22 congruence. % 47.05/47.22 cut (((op2 (e20) (e23)) = (e21)) = ((e23) = (e21))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H1d4. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H1da. % 47.05/47.22 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.05/47.22 cut (((op2 (e20) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 47.05/47.22 congruence. % 47.05/47.22 exact (zenon_H279 zenon_H278). % 47.05/47.22 apply zenon_H181. apply refl_equal. % 47.05/47.22 apply zenon_H19f. apply refl_equal. % 47.05/47.22 apply zenon_H19f. apply refl_equal. % 47.05/47.22 (* end of lemma zenon_L207_ *) % 47.05/47.22 assert (zenon_L208_ : (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((e20) = (e22))) -> ((op2 (e23) (e20)) = (e20)) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e22) = (op2 (e21) (e21))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((e22) = (e23))) -> (~((e21) = (e23))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e20)) = (e21)) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> ((op2 (e20) (e23)) = (e21)) -> (~((e21) = (e22))) -> False). % 47.05/47.22 do 0 intro. intros zenon_H27a zenon_H1c4 zenon_H1ed zenon_H27b zenon_H1aa zenon_H14 zenon_H194 zenon_H1a3 zenon_H27c zenon_H24b zenon_H234 zenon_H25c zenon_H23a zenon_H230 zenon_H1e4 zenon_H1be zenon_H262 zenon_H183 zenon_H271 zenon_H25f zenon_H265 zenon_H229 zenon_H259 zenon_H193 zenon_H23f zenon_H270 zenon_H1b0 zenon_H276 zenon_H1d3 zenon_H1c7 zenon_H1b7 zenon_H27d zenon_H1da zenon_H1b9. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.05/47.22 apply (zenon_L155_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.05/47.22 apply (zenon_L156_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H27d); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H280 ]. % 47.05/47.22 apply (zenon_L155_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H281 ]. % 47.05/47.22 apply (zenon_L158_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H23b | zenon_intro zenon_H257 ]. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.05/47.22 apply (zenon_L148_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.05/47.22 apply (zenon_L148_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H257 | zenon_intro zenon_H284 ]. % 47.05/47.22 apply (zenon_L188_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H228 | zenon_intro zenon_H285 ]. % 47.05/47.22 apply (zenon_L176_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H25a | zenon_intro zenon_H269 ]. % 47.05/47.22 apply (zenon_L189_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H233 | zenon_intro zenon_H24c ]. % 47.05/47.22 apply (zenon_L179_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H222 | zenon_intro zenon_H24d ]. % 47.05/47.22 apply (zenon_L190_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H23c | zenon_intro zenon_H223 ]. % 47.05/47.22 apply (zenon_L180_); trivial. % 47.05/47.22 apply (zenon_L205_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.05/47.22 apply (zenon_L151_); trivial. % 47.05/47.22 apply (zenon_L152_); trivial. % 47.05/47.22 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.05/47.22 apply (zenon_L206_); trivial. % 47.05/47.22 apply (zenon_L207_); trivial. % 47.05/47.22 apply (zenon_L188_); trivial. % 47.05/47.22 apply (zenon_L165_); trivial. % 47.05/47.22 (* end of lemma zenon_L208_ *) % 47.05/47.22 assert (zenon_L209_ : ((e22) = (op2 (e21) (e21))) -> ((op2 (e21) (e23)) = (e22)) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> False). % 47.05/47.22 do 0 intro. intros zenon_H183 zenon_H286 zenon_H287. % 47.05/47.22 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H288 | zenon_intro zenon_H289 ]. % 47.05/47.22 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((op2 (e21) (e21)) = (op2 (e21) (e23)))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H287. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H288. % 47.05/47.22 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H289]. % 47.05/47.22 cut (((op2 (e21) (e23)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H28a]. % 47.05/47.22 congruence. % 47.05/47.22 cut (((e22) = (op2 (e21) (e21))) = ((op2 (e21) (e23)) = (op2 (e21) (e21)))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H28a. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H183. % 47.05/47.22 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 47.05/47.22 cut (((e22) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H28b]. % 47.05/47.22 congruence. % 47.05/47.22 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H288 | zenon_intro zenon_H289 ]. % 47.05/47.22 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e22) = (op2 (e21) (e23)))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H28b. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H288. % 47.05/47.22 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H289]. % 47.05/47.22 cut (((op2 (e21) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H28c]. % 47.05/47.22 congruence. % 47.05/47.22 exact (zenon_H28c zenon_H286). % 47.05/47.22 apply zenon_H289. apply refl_equal. % 47.05/47.22 apply zenon_H289. apply refl_equal. % 47.05/47.22 apply zenon_H1c0. apply refl_equal. % 47.05/47.22 apply zenon_H289. apply refl_equal. % 47.05/47.22 apply zenon_H289. apply refl_equal. % 47.05/47.22 (* end of lemma zenon_L209_ *) % 47.05/47.22 assert (zenon_L210_ : ((op2 (e22) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> (~((e22) = (e23))) -> False). % 47.05/47.22 do 0 intro. intros zenon_H23c zenon_H223 zenon_H276. % 47.05/47.22 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H19e | zenon_intro zenon_H19f ]. % 47.05/47.22 cut (((e23) = (e23)) = ((e22) = (e23))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H276. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H19e. % 47.05/47.22 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 47.05/47.22 cut (((e23) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H277]. % 47.05/47.22 congruence. % 47.05/47.22 cut (((op2 (e22) (e23)) = (e22)) = ((e23) = (e22))). % 47.05/47.22 intro zenon_D_pnotp. % 47.05/47.22 apply zenon_H277. % 47.05/47.22 rewrite <- zenon_D_pnotp. % 47.05/47.22 exact zenon_H23c. % 47.05/47.22 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.05/47.22 cut (((op2 (e22) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H224]. % 47.05/47.22 congruence. % 47.05/47.22 exact (zenon_H224 zenon_H223). % 47.05/47.22 apply zenon_H1bb. apply refl_equal. % 47.05/47.23 apply zenon_H19f. apply refl_equal. % 47.05/47.23 apply zenon_H19f. apply refl_equal. % 47.05/47.23 (* end of lemma zenon_L210_ *) % 47.05/47.23 assert (zenon_L211_ : (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H230 zenon_H1e4 zenon_H14 zenon_H1d7 zenon_H1be zenon_H229 zenon_H183 zenon_H19c zenon_H1ed zenon_H193 zenon_H23f zenon_H223 zenon_H270 zenon_H269 zenon_H26c. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H231 ]. % 47.05/47.23 apply (zenon_L167_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H232 ]. % 47.05/47.23 apply (zenon_L199_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H228 | zenon_intro zenon_H22e ]. % 47.05/47.23 apply (zenon_L176_); trivial. % 47.05/47.23 apply (zenon_L203_); trivial. % 47.05/47.23 (* end of lemma zenon_L211_ *) % 47.05/47.23 assert (zenon_L212_ : (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e21) = (e22))) -> ((op2 (e20) (e23)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((e22) = (e23))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e23)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H28d zenon_H1b9 zenon_H1da zenon_H287 zenon_H276 zenon_H230 zenon_H1e4 zenon_H14 zenon_H1d7 zenon_H1be zenon_H229 zenon_H183 zenon_H19c zenon_H1ed zenon_H193 zenon_H23f zenon_H223 zenon_H270 zenon_H26c. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H1db | zenon_intro zenon_H28e ]. % 47.05/47.23 apply (zenon_L165_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H286 | zenon_intro zenon_H28f ]. % 47.05/47.23 apply (zenon_L209_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H23c | zenon_intro zenon_H269 ]. % 47.05/47.23 apply (zenon_L210_); trivial. % 47.05/47.23 apply (zenon_L211_); trivial. % 47.05/47.23 (* end of lemma zenon_L212_ *) % 47.05/47.23 assert (zenon_L213_ : ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e22) (e22)) = (e20)) -> ((e22) = (op2 (e21) (e21))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H14 zenon_H290 zenon_H183 zenon_H291. % 47.05/47.23 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H21c | zenon_intro zenon_H21d ]. % 47.05/47.23 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e22) (e21)) = (op2 (e22) (e22)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H291. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H21c. % 47.05/47.23 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 47.05/47.23 cut (((op2 (e22) (e22)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H292]. % 47.05/47.23 congruence. % 47.05/47.23 cut (((e20) = (op2 (op2 (e21) (e21)) (e21))) = ((op2 (e22) (e22)) = (op2 (e22) (e21)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H292. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H14. % 47.05/47.23 cut (((op2 (op2 (e21) (e21)) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H182]. % 47.05/47.23 cut (((e20) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H293]. % 47.05/47.23 congruence. % 47.05/47.23 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H21c | zenon_intro zenon_H21d ]. % 47.05/47.23 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((e20) = (op2 (e22) (e22)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H293. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H21c. % 47.05/47.23 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 47.05/47.23 cut (((op2 (e22) (e22)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H294]. % 47.05/47.23 congruence. % 47.05/47.23 exact (zenon_H294 zenon_H290). % 47.05/47.23 apply zenon_H21d. apply refl_equal. % 47.05/47.23 apply zenon_H21d. apply refl_equal. % 47.05/47.23 apply (zenon_L144_); trivial. % 47.05/47.23 apply zenon_H21d. apply refl_equal. % 47.05/47.23 apply zenon_H21d. apply refl_equal. % 47.05/47.23 (* end of lemma zenon_L213_ *) % 47.05/47.23 assert (zenon_L214_ : (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e21) (e22)) = (e21)) -> ((op2 (e22) (e22)) = (e21)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H295 zenon_H296 zenon_H297. % 47.05/47.23 cut (((op2 (e21) (e22)) = (e21)) = ((op2 (e21) (e22)) = (op2 (e22) (e22)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H295. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H296. % 47.05/47.23 cut (((e21) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H298]. % 47.05/47.23 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H253]. % 47.05/47.23 congruence. % 47.05/47.23 apply zenon_H253. apply refl_equal. % 47.05/47.23 apply zenon_H298. apply sym_equal. exact zenon_H297. % 47.05/47.23 (* end of lemma zenon_L214_ *) % 47.05/47.23 assert (zenon_L215_ : (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e20)) = (e22)) -> ((op2 (e22) (e22)) = (e22)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H299 zenon_H23b zenon_H29a. % 47.05/47.23 cut (((op2 (e22) (e20)) = (e22)) = ((op2 (e22) (e20)) = (op2 (e22) (e22)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H299. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H23b. % 47.05/47.23 cut (((e22) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H29b]. % 47.05/47.23 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 47.05/47.23 congruence. % 47.05/47.23 apply zenon_H1a5. apply refl_equal. % 47.05/47.23 apply zenon_H29b. apply sym_equal. exact zenon_H29a. % 47.05/47.23 (* end of lemma zenon_L215_ *) % 47.05/47.23 assert (zenon_L216_ : (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((op2 (e21) (e22)) = (e21)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e20)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e20)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e23)) = (e21)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H29c zenon_H291 zenon_H296 zenon_H295 zenon_H23b zenon_H299 zenon_H230 zenon_H1e4 zenon_H14 zenon_H216 zenon_H18b zenon_H1db zenon_H20a zenon_H1d7 zenon_H1be zenon_H183 zenon_H19c zenon_H1ed zenon_H193 zenon_H23f zenon_H223 zenon_H26c zenon_H229 zenon_H243. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H29c); [ zenon_intro zenon_H290 | zenon_intro zenon_H29d ]. % 47.05/47.23 apply (zenon_L213_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H29d); [ zenon_intro zenon_H297 | zenon_intro zenon_H29e ]. % 47.05/47.23 apply (zenon_L214_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H29e); [ zenon_intro zenon_H29a | zenon_intro zenon_H207 ]. % 47.05/47.23 apply (zenon_L215_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H231 ]. % 47.05/47.23 apply (zenon_L167_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H232 ]. % 47.05/47.23 apply (zenon_L173_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H228 | zenon_intro zenon_H22e ]. % 47.05/47.23 apply (zenon_L176_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.05/47.23 apply (zenon_L169_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.05/47.23 apply (zenon_L182_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.05/47.23 apply (zenon_L197_); trivial. % 47.05/47.23 apply (zenon_L183_); trivial. % 47.05/47.23 (* end of lemma zenon_L216_ *) % 47.05/47.23 assert (zenon_L217_ : ((op2 (e20) (e23)) = (e22)) -> ((op2 (e20) (e23)) = (e23)) -> (~((e22) = (e23))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H1db zenon_H278 zenon_H276. % 47.05/47.23 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H19e | zenon_intro zenon_H19f ]. % 47.05/47.23 cut (((e23) = (e23)) = ((e22) = (e23))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H276. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H19e. % 47.05/47.23 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 47.05/47.23 cut (((e23) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H277]. % 47.05/47.23 congruence. % 47.05/47.23 cut (((op2 (e20) (e23)) = (e22)) = ((e23) = (e22))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H277. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H1db. % 47.05/47.23 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.05/47.23 cut (((op2 (e20) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 47.05/47.23 congruence. % 47.05/47.23 exact (zenon_H279 zenon_H278). % 47.05/47.23 apply zenon_H1bb. apply refl_equal. % 47.05/47.23 apply zenon_H19f. apply refl_equal. % 47.05/47.23 apply zenon_H19f. apply refl_equal. % 47.05/47.23 (* end of lemma zenon_L217_ *) % 47.05/47.23 assert (zenon_L218_ : ((op2 (e20) (e21)) = (e21)) -> ((op2 (e20) (e20)) = (e21)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H29f zenon_H1b7 zenon_H2a0. % 47.05/47.23 elim (classic ((op2 (e20) (e21)) = (op2 (e20) (e21)))); [ zenon_intro zenon_H188 | zenon_intro zenon_H189 ]. % 47.05/47.23 cut (((op2 (e20) (e21)) = (op2 (e20) (e21))) = ((op2 (e20) (e20)) = (op2 (e20) (e21)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H2a0. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H188. % 47.05/47.23 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 47.05/47.23 cut (((op2 (e20) (e21)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2a1]. % 47.05/47.23 congruence. % 47.05/47.23 cut (((op2 (e20) (e21)) = (e21)) = ((op2 (e20) (e21)) = (op2 (e20) (e20)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H2a1. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H29f. % 47.05/47.23 cut (((e21) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2a2]. % 47.05/47.23 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 47.05/47.23 congruence. % 47.05/47.23 apply zenon_H189. apply refl_equal. % 47.05/47.23 apply zenon_H2a2. apply sym_equal. exact zenon_H1b7. % 47.05/47.23 apply zenon_H189. apply refl_equal. % 47.05/47.23 apply zenon_H189. apply refl_equal. % 47.05/47.23 (* end of lemma zenon_L218_ *) % 47.05/47.23 assert (zenon_L219_ : (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((e21) = (e23))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H1b0 zenon_H193 zenon_H1d3 zenon_H1d2 zenon_H1a3 zenon_H194 zenon_H14 zenon_H1aa. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.05/47.23 apply (zenon_L148_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.05/47.23 apply (zenon_L162_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.05/47.23 apply (zenon_L151_); trivial. % 47.05/47.23 apply (zenon_L152_); trivial. % 47.05/47.23 (* end of lemma zenon_L219_ *) % 47.05/47.23 assert (zenon_L220_ : ((op2 (e20) (e21)) = (e21)) -> ((op2 (e20) (e21)) = (e23)) -> (~((e21) = (e23))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H29f zenon_H1d7 zenon_H1d3. % 47.05/47.23 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H19e | zenon_intro zenon_H19f ]. % 47.05/47.23 cut (((e23) = (e23)) = ((e21) = (e23))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H1d3. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H19e. % 47.05/47.23 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 47.05/47.23 cut (((e23) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1d4]. % 47.05/47.23 congruence. % 47.05/47.23 cut (((op2 (e20) (e21)) = (e21)) = ((e23) = (e21))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H1d4. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H29f. % 47.05/47.23 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.05/47.23 cut (((op2 (e20) (e21)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H2a3]. % 47.05/47.23 congruence. % 47.05/47.23 exact (zenon_H2a3 zenon_H1d7). % 47.05/47.23 apply zenon_H181. apply refl_equal. % 47.05/47.23 apply zenon_H19f. apply refl_equal. % 47.05/47.23 apply zenon_H19f. apply refl_equal. % 47.05/47.23 (* end of lemma zenon_L220_ *) % 47.05/47.23 assert (zenon_L221_ : ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((op2 (e21) (e21)) = (e23)) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H194 zenon_H2a4 zenon_H14 zenon_H1c7. % 47.05/47.23 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H200 | zenon_intro zenon_H1c0 ]. % 47.05/47.23 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((op2 (e21) (e20)) = (op2 (e21) (e21)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H1c7. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H200. % 47.05/47.23 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 47.05/47.23 cut (((op2 (e21) (e21)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2a5]. % 47.05/47.23 congruence. % 47.05/47.23 cut (((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) = ((op2 (e21) (e21)) = (op2 (e21) (e20)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H2a5. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H194. % 47.05/47.23 cut (((op2 (e21) (op2 (op2 (e21) (e21)) (e21))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 47.05/47.23 cut (((e23) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2a6]. % 47.05/47.23 congruence. % 47.05/47.23 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H200 | zenon_intro zenon_H1c0 ]. % 47.05/47.23 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((e23) = (op2 (e21) (e21)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H2a6. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H200. % 47.05/47.23 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 47.05/47.23 cut (((op2 (e21) (e21)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H2a7]. % 47.05/47.23 congruence. % 47.05/47.23 exact (zenon_H2a7 zenon_H2a4). % 47.05/47.23 apply zenon_H1c0. apply refl_equal. % 47.05/47.23 apply zenon_H1c0. apply refl_equal. % 47.05/47.23 apply (zenon_L147_); trivial. % 47.05/47.23 apply zenon_H1c0. apply refl_equal. % 47.05/47.23 apply zenon_H1c0. apply refl_equal. % 47.05/47.23 (* end of lemma zenon_L221_ *) % 47.05/47.23 assert (zenon_L222_ : ((op2 (e22) (e20)) = (e21)) -> ((op2 (e22) (e20)) = (e22)) -> (~((e21) = (e22))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H2a8 zenon_H23b zenon_H1b9. % 47.05/47.23 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 47.05/47.23 cut (((e22) = (e22)) = ((e21) = (e22))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H1b9. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H1ba. % 47.05/47.23 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.05/47.23 cut (((e22) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 47.05/47.23 congruence. % 47.05/47.23 cut (((op2 (e22) (e20)) = (e21)) = ((e22) = (e21))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H1bc. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H2a8. % 47.05/47.23 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.05/47.23 cut (((op2 (e22) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H2a9]. % 47.05/47.23 congruence. % 47.05/47.23 exact (zenon_H2a9 zenon_H23b). % 47.05/47.23 apply zenon_H181. apply refl_equal. % 47.05/47.23 apply zenon_H1bb. apply refl_equal. % 47.05/47.23 apply zenon_H1bb. apply refl_equal. % 47.05/47.23 (* end of lemma zenon_L222_ *) % 47.05/47.23 assert (zenon_L223_ : ((e22) = (op2 (e21) (e21))) -> ((op2 (e22) (e21)) = (e22)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H183 zenon_H2aa zenon_H2ab. % 47.05/47.23 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_H2ac | zenon_intro zenon_H2ad ]. % 47.05/47.23 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((op2 (e21) (e21)) = (op2 (e22) (e21)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H2ab. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H2ac. % 47.05/47.23 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2ad]. % 47.05/47.23 cut (((op2 (e22) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2ae]. % 47.05/47.23 congruence. % 47.05/47.23 cut (((e22) = (op2 (e21) (e21))) = ((op2 (e22) (e21)) = (op2 (e21) (e21)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H2ae. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H183. % 47.05/47.23 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 47.05/47.23 cut (((e22) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2af]. % 47.05/47.23 congruence. % 47.05/47.23 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_H2ac | zenon_intro zenon_H2ad ]. % 47.05/47.23 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((e22) = (op2 (e22) (e21)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H2af. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H2ac. % 47.05/47.23 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2ad]. % 47.05/47.23 cut (((op2 (e22) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H2b0]. % 47.05/47.23 congruence. % 47.05/47.23 exact (zenon_H2b0 zenon_H2aa). % 47.05/47.23 apply zenon_H2ad. apply refl_equal. % 47.05/47.23 apply zenon_H2ad. apply refl_equal. % 47.05/47.23 apply zenon_H1c0. apply refl_equal. % 47.05/47.23 apply zenon_H2ad. apply refl_equal. % 47.05/47.23 apply zenon_H2ad. apply refl_equal. % 47.05/47.23 (* end of lemma zenon_L223_ *) % 47.05/47.23 assert (zenon_L224_ : (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e20)) = (e21)) -> ((op2 (e22) (e21)) = (e21)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H1b3 zenon_H2a8 zenon_H2b1. % 47.05/47.23 cut (((op2 (e22) (e20)) = (e21)) = ((op2 (e22) (e20)) = (op2 (e22) (e21)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H1b3. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H2a8. % 47.05/47.23 cut (((e21) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2b2]. % 47.05/47.23 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 47.05/47.23 congruence. % 47.05/47.23 apply zenon_H1a5. apply refl_equal. % 47.05/47.23 apply zenon_H2b2. apply sym_equal. exact zenon_H2b1. % 47.05/47.23 (* end of lemma zenon_L224_ *) % 47.05/47.23 assert (zenon_L225_ : (((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (e20))/\(((op2 (op2 (e21) (e22)) (op2 (e21) (e22))) = (e21))/\(((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (e22))/\((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e23))))) -> ((op2 (e22) (e22)) = (e23)) -> ((op2 (e22) (e23)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H209 zenon_H207 zenon_H23c zenon_H23f. % 47.05/47.23 apply (zenon_and_s _ _ zenon_H209). zenon_intro zenon_H20c. zenon_intro zenon_H20b. % 47.05/47.23 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_H20e. zenon_intro zenon_H20d. % 47.05/47.23 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H210. zenon_intro zenon_H20f. % 47.05/47.23 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 47.05/47.23 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e22) (e23)) = (op2 (e23) (e23)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H23f. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H211. % 47.05/47.23 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 47.05/47.23 cut (((op2 (e23) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H240]. % 47.05/47.23 congruence. % 47.05/47.23 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (e22)) = ((op2 (e23) (e23)) = (op2 (e22) (e23)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H240. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H210. % 47.05/47.23 cut (((e22) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 47.05/47.23 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 47.05/47.23 congruence. % 47.05/47.23 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 47.05/47.23 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (e23) (e23)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H215. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H211. % 47.05/47.23 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 47.05/47.23 cut (((op2 (e23) (e23)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 47.05/47.23 congruence. % 47.05/47.23 apply (zenon_L171_); trivial. % 47.05/47.23 apply zenon_H212. apply refl_equal. % 47.05/47.23 apply zenon_H212. apply refl_equal. % 47.05/47.23 apply zenon_H23d. apply sym_equal. exact zenon_H23c. % 47.05/47.23 apply zenon_H212. apply refl_equal. % 47.05/47.23 apply zenon_H212. apply refl_equal. % 47.05/47.23 (* end of lemma zenon_L225_ *) % 47.05/47.23 assert (zenon_L226_ : (~((op2 (e22) (e22)) = (op2 (op2 (e22) (e23)) (op2 (e22) (e23))))) -> ((op2 (e22) (e23)) = (e22)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H2b3 zenon_H23c. % 47.05/47.23 cut (((e22) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 47.05/47.23 cut (((e22) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 47.05/47.23 congruence. % 47.05/47.23 apply zenon_H23d. apply sym_equal. exact zenon_H23c. % 47.05/47.23 apply zenon_H23d. apply sym_equal. exact zenon_H23c. % 47.05/47.23 (* end of lemma zenon_L226_ *) % 47.05/47.23 assert (zenon_L227_ : (((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (e20))/\(((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (e21))/\(((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (e22))/\((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e22) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e22)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H219 zenon_H270 zenon_H23c zenon_H25a. % 47.05/47.23 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H21b. zenon_intro zenon_H21a. % 47.05/47.23 apply (zenon_and_s _ _ zenon_H21a). zenon_intro zenon_H245. zenon_intro zenon_H244. % 47.05/47.23 apply (zenon_and_s _ _ zenon_H244). zenon_intro zenon_H247. zenon_intro zenon_H246. % 47.05/47.23 cut (((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (e22)) = ((op2 (e22) (e22)) = (op2 (e23) (e22)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H270. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H247. % 47.05/47.23 cut (((e22) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H25b]. % 47.05/47.23 cut (((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H2b4]. % 47.05/47.23 congruence. % 47.05/47.23 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H21c | zenon_intro zenon_H21d ]. % 47.05/47.23 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (op2 (e22) (e22)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H2b4. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H21c. % 47.05/47.23 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 47.05/47.23 cut (((op2 (e22) (e22)) = (op2 (op2 (e22) (e23)) (op2 (e22) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H2b3]. % 47.05/47.23 congruence. % 47.05/47.23 apply (zenon_L226_); trivial. % 47.05/47.23 apply zenon_H21d. apply refl_equal. % 47.05/47.23 apply zenon_H21d. apply refl_equal. % 47.05/47.23 apply zenon_H25b. apply sym_equal. exact zenon_H25a. % 47.05/47.23 (* end of lemma zenon_L227_ *) % 47.05/47.23 assert (zenon_L228_ : ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e22) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e22)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H19c zenon_H1ed zenon_H193 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H23f zenon_H207 zenon_H270 zenon_H23c zenon_H25a. % 47.05/47.23 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.05/47.23 apply (zenon_L169_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.05/47.23 apply (zenon_L170_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.05/47.23 apply (zenon_L225_); trivial. % 47.05/47.23 apply (zenon_L227_); trivial. % 47.05/47.23 (* end of lemma zenon_L228_ *) % 47.05/47.23 assert (zenon_L229_ : (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((e20) = (e23))) -> ((op2 (e22) (e21)) = (e20)) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e21)) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e20)) = (e20)) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e22)) -> (~((e22) = (e23))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H225 zenon_H1a3 zenon_H14 zenon_H194 zenon_H19d zenon_H1ea zenon_H25a zenon_H270 zenon_H23f zenon_H1f9 zenon_H1d7 zenon_H1be zenon_H193 zenon_H1ed zenon_H19c zenon_H23c zenon_H276. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.05/47.23 apply (zenon_L151_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.05/47.23 apply (zenon_L168_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.05/47.23 apply (zenon_L228_); trivial. % 47.05/47.23 apply (zenon_L210_); trivial. % 47.05/47.23 (* end of lemma zenon_L229_ *) % 47.05/47.23 assert (zenon_L230_ : ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e22)) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H19c zenon_H1ed zenon_H193 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H23f zenon_H23c zenon_H207 zenon_H270 zenon_H269 zenon_H26c. % 47.05/47.23 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.05/47.23 apply (zenon_L169_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.05/47.23 apply (zenon_L170_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.05/47.23 apply (zenon_L225_); trivial. % 47.05/47.23 apply (zenon_L198_); trivial. % 47.05/47.23 (* end of lemma zenon_L230_ *) % 47.05/47.23 assert (zenon_L231_ : (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e22) = (e23))) -> ((op2 (e22) (e21)) = (e20)) -> (~((e20) = (e23))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e22)) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H271 zenon_H25f zenon_H262 zenon_H276 zenon_H1ea zenon_H19d zenon_H194 zenon_H14 zenon_H1a3 zenon_H225 zenon_H19c zenon_H1ed zenon_H193 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H23f zenon_H23c zenon_H207 zenon_H270 zenon_H269. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H260 | zenon_intro zenon_H272 ]. % 47.05/47.23 apply (zenon_L191_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H263 | zenon_intro zenon_H273 ]. % 47.05/47.23 apply (zenon_L192_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H25a | zenon_intro zenon_H26c ]. % 47.05/47.23 apply (zenon_L229_); trivial. % 47.05/47.23 apply (zenon_L230_); trivial. % 47.05/47.23 (* end of lemma zenon_L231_ *) % 47.05/47.23 assert (zenon_L232_ : (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e22) = (e23))) -> ((op2 (e22) (e21)) = (e20)) -> (~((e20) = (e23))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e22)) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H27c zenon_H1c4 zenon_H229 zenon_H183 zenon_H271 zenon_H25f zenon_H262 zenon_H276 zenon_H1ea zenon_H19d zenon_H194 zenon_H14 zenon_H1a3 zenon_H225 zenon_H19c zenon_H1ed zenon_H193 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H23f zenon_H23c zenon_H207 zenon_H270. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H257 | zenon_intro zenon_H284 ]. % 47.05/47.23 apply (zenon_L188_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H228 | zenon_intro zenon_H285 ]. % 47.05/47.23 apply (zenon_L176_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H25a | zenon_intro zenon_H269 ]. % 47.05/47.23 apply (zenon_L229_); trivial. % 47.05/47.23 apply (zenon_L231_); trivial. % 47.05/47.23 (* end of lemma zenon_L232_ *) % 47.05/47.23 assert (zenon_L233_ : (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e21)) -> ((op2 (e22) (e23)) = (e21)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H23a zenon_H2a8 zenon_H222. % 47.05/47.23 cut (((op2 (e22) (e20)) = (e21)) = ((op2 (e22) (e20)) = (op2 (e22) (e23)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H23a. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H2a8. % 47.05/47.23 cut (((e21) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H25d]. % 47.05/47.23 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 47.05/47.23 congruence. % 47.05/47.23 apply zenon_H1a5. apply refl_equal. % 47.05/47.23 apply zenon_H25d. apply sym_equal. exact zenon_H222. % 47.05/47.23 (* end of lemma zenon_L233_ *) % 47.05/47.23 assert (zenon_L234_ : (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> ((e22) = (op2 (e21) (e21))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e23)) = (e21)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H2b5 zenon_H183 zenon_H1b3 zenon_H222 zenon_H23a zenon_H29a zenon_H299 zenon_H194 zenon_H14 zenon_H1a3. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H2b6 ]. % 47.05/47.23 apply (zenon_L154_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b7 ]. % 47.05/47.23 apply (zenon_L233_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H23b | zenon_intro zenon_H1a2 ]. % 47.05/47.23 apply (zenon_L215_); trivial. % 47.05/47.23 apply (zenon_L151_); trivial. % 47.05/47.23 (* end of lemma zenon_L234_ *) % 47.05/47.23 assert (zenon_L235_ : (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> ((op2 (e22) (e22)) = (e23)) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((e20) = (e23))) -> ((op2 (e22) (e21)) = (e20)) -> (~((e22) = (e23))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H24b zenon_H234 zenon_H299 zenon_H29a zenon_H23a zenon_H1b3 zenon_H183 zenon_H2b5 zenon_H207 zenon_H225 zenon_H1a3 zenon_H14 zenon_H194 zenon_H19d zenon_H1ea zenon_H276 zenon_H271 zenon_H25f zenon_H262 zenon_H265 zenon_H19c zenon_H1ed zenon_H193 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H23f zenon_H270 zenon_H269. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H233 | zenon_intro zenon_H24c ]. % 47.05/47.23 apply (zenon_L179_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H222 | zenon_intro zenon_H24d ]. % 47.05/47.23 apply (zenon_L234_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H23c | zenon_intro zenon_H223 ]. % 47.05/47.23 apply (zenon_L231_); trivial. % 47.05/47.23 apply (zenon_L200_); trivial. % 47.05/47.23 (* end of lemma zenon_L235_ *) % 47.05/47.23 assert (zenon_L236_ : ((op2 (e23) (e20)) = (e20)) -> ((op2 (e23) (e20)) = (e21)) -> (~((e20) = (e21))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H1ed zenon_H2b8 zenon_H1df. % 47.05/47.23 elim (classic ((e21) = (e21))); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H181 ]. % 47.05/47.23 cut (((e21) = (e21)) = ((e20) = (e21))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H1df. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H1e0. % 47.05/47.23 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.05/47.23 cut (((e21) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 47.05/47.23 congruence. % 47.05/47.23 cut (((op2 (e23) (e20)) = (e20)) = ((e21) = (e20))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H1e1. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H1ed. % 47.05/47.23 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 47.05/47.23 cut (((op2 (e23) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2b9]. % 47.05/47.23 congruence. % 47.05/47.23 exact (zenon_H2b9 zenon_H2b8). % 47.05/47.23 apply zenon_H19a. apply refl_equal. % 47.05/47.23 apply zenon_H181. apply refl_equal. % 47.05/47.23 apply zenon_H181. apply refl_equal. % 47.05/47.23 (* end of lemma zenon_L236_ *) % 47.05/47.23 assert (zenon_L237_ : (((op2 (e20) (e20)) = (e21))\/(((op2 (e21) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e21))\/((op2 (e23) (e20)) = (e21))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((e21) = (e23))) -> ((op2 (e20) (e23)) = (e21)) -> ((op2 (e20) (e22)) = (e20)) -> (~((e20) = (e23))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e21) = (e22))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> ((op2 (e23) (e20)) = (e20)) -> (~((e20) = (e21))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H2ba zenon_H27d zenon_H1c7 zenon_H259 zenon_H230 zenon_H25c zenon_H27a zenon_H1d3 zenon_H1da zenon_H18b zenon_H19d zenon_H1b0 zenon_H1e4 zenon_H183 zenon_H2bb zenon_H2bc zenon_H2ab zenon_H265 zenon_H28d zenon_H1b9 zenon_H287 zenon_H24b zenon_H234 zenon_H299 zenon_H23a zenon_H1b3 zenon_H2b5 zenon_H185 zenon_H270 zenon_H23f zenon_H1be zenon_H193 zenon_H225 zenon_H262 zenon_H25f zenon_H271 zenon_H229 zenon_H1c4 zenon_H27c zenon_H276 zenon_H2bd zenon_H1a3 zenon_H194 zenon_H14 zenon_H1aa zenon_H27b zenon_H1ed zenon_H1df. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.05/47.23 apply (zenon_L208_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.05/47.23 apply (zenon_L219_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.05/47.23 apply (zenon_L148_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.05/47.23 apply (zenon_L148_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.05/47.23 apply (zenon_L145_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.05/47.23 apply (zenon_L160_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_H29f | zenon_intro zenon_H2c2 ]. % 47.05/47.23 apply (zenon_L220_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2c3 ]. % 47.05/47.23 apply (zenon_L163_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2c3); [ zenon_intro zenon_H2b1 | zenon_intro zenon_H1f9 ]. % 47.05/47.23 apply (zenon_L224_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2bc); [ zenon_intro zenon_H23b | zenon_intro zenon_H2c4 ]. % 47.05/47.23 apply (zenon_L222_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_H2aa | zenon_intro zenon_H2c5 ]. % 47.05/47.23 apply (zenon_L223_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H29a | zenon_intro zenon_H23c ]. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.05/47.23 apply (zenon_L151_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.05/47.23 apply (zenon_L164_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H1db | zenon_intro zenon_H28e ]. % 47.05/47.23 apply (zenon_L165_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H286 | zenon_intro zenon_H28f ]. % 47.05/47.23 apply (zenon_L209_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H23c | zenon_intro zenon_H269 ]. % 47.05/47.23 apply (zenon_L232_); trivial. % 47.05/47.23 apply (zenon_L235_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H257 | zenon_intro zenon_H284 ]. % 47.05/47.23 apply (zenon_L188_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H228 | zenon_intro zenon_H285 ]. % 47.05/47.23 apply (zenon_L176_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H25a | zenon_intro zenon_H269 ]. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H1db | zenon_intro zenon_H28e ]. % 47.05/47.23 apply (zenon_L165_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H286 | zenon_intro zenon_H28f ]. % 47.05/47.23 apply (zenon_L209_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H23c | zenon_intro zenon_H269 ]. % 47.05/47.23 apply (zenon_L229_); trivial. % 47.05/47.23 apply (zenon_L196_); trivial. % 47.05/47.23 apply (zenon_L200_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.05/47.23 apply (zenon_L151_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.05/47.23 apply (zenon_L168_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.05/47.23 apply (zenon_L232_); trivial. % 47.05/47.23 apply (zenon_L210_); trivial. % 47.05/47.23 apply (zenon_L167_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.05/47.23 apply (zenon_L151_); trivial. % 47.05/47.23 apply (zenon_L152_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.05/47.23 apply (zenon_L186_); trivial. % 47.05/47.23 apply (zenon_L207_); trivial. % 47.05/47.23 apply (zenon_L236_); trivial. % 47.05/47.23 (* end of lemma zenon_L237_ *) % 47.05/47.23 assert (zenon_L238_ : (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((e21) = (e23))) -> ((op2 (e20) (e21)) = (e21)) -> (~((e20) = (e23))) -> ((op2 (e20) (e22)) = (e20)) -> ((op2 (e20) (e23)) = (e22)) -> (~((e22) = (e23))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H27b zenon_H14 zenon_H194 zenon_H193 zenon_H1d3 zenon_H29f zenon_H19d zenon_H18b zenon_H1db zenon_H276. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.05/47.23 apply (zenon_L148_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.05/47.23 apply (zenon_L220_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.05/47.23 apply (zenon_L186_); trivial. % 47.05/47.23 apply (zenon_L217_); trivial. % 47.05/47.23 (* end of lemma zenon_L238_ *) % 47.05/47.23 assert (zenon_L239_ : (((op2 (op2 (e20) (e21)) (op2 (e20) (e21))) = (e20))/\(((op2 (op2 (e21) (e21)) (op2 (e21) (e21))) = (e21))/\(((op2 (op2 (e22) (e21)) (op2 (e22) (e21))) = (e22))/\((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (e23))))) -> ((op2 (e23) (e21)) = (e23)) -> ((op2 (e20) (e23)) = (e23)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H1f8 zenon_H22e zenon_H278 zenon_H20a. % 47.05/47.23 apply (zenon_and_s _ _ zenon_H1f8). zenon_intro zenon_H1fb. zenon_intro zenon_H1fa. % 47.05/47.23 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_H1fd. zenon_intro zenon_H1fc. % 47.05/47.23 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_H1ff. zenon_intro zenon_H1fe. % 47.05/47.23 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 47.05/47.23 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e20) (e23)) = (op2 (e23) (e23)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H20a. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H211. % 47.05/47.23 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 47.05/47.23 cut (((op2 (e23) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H213]. % 47.05/47.23 congruence. % 47.05/47.23 cut (((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (e23)) = ((op2 (e23) (e23)) = (op2 (e20) (e23)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H213. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H1fe. % 47.05/47.23 cut (((e23) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2c6]. % 47.05/47.23 cut (((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H242]. % 47.05/47.23 congruence. % 47.05/47.23 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 47.05/47.23 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (op2 (e23) (e23)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H242. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H211. % 47.05/47.23 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 47.05/47.23 cut (((op2 (e23) (e23)) = (op2 (op2 (e23) (e21)) (op2 (e23) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H23e]. % 47.05/47.23 congruence. % 47.05/47.23 apply (zenon_L181_); trivial. % 47.05/47.23 apply zenon_H212. apply refl_equal. % 47.05/47.23 apply zenon_H212. apply refl_equal. % 47.05/47.23 apply zenon_H2c6. apply sym_equal. exact zenon_H278. % 47.05/47.23 apply zenon_H212. apply refl_equal. % 47.05/47.23 apply zenon_H212. apply refl_equal. % 47.05/47.23 (* end of lemma zenon_L239_ *) % 47.05/47.23 assert (zenon_L240_ : ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e22)) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e23)) = (e21)) -> ((op2 (e23) (e21)) = (e23)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H19c zenon_H1ed zenon_H193 zenon_H20a zenon_H278 zenon_H23f zenon_H23c zenon_H207 zenon_H229 zenon_H243 zenon_H22e. % 47.05/47.23 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.05/47.23 apply (zenon_L169_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.05/47.23 apply (zenon_L239_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.05/47.23 apply (zenon_L225_); trivial. % 47.05/47.23 apply (zenon_L183_); trivial. % 47.05/47.23 (* end of lemma zenon_L240_ *) % 47.05/47.23 assert (zenon_L241_ : (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((e21) = (e23))) -> (~((e20) = (e21))) -> ((op2 (e21) (e23)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e22)) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e23)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H2c7 zenon_H1d3 zenon_H1df zenon_H1dd zenon_H1a3 zenon_H14 zenon_H194 zenon_H299 zenon_H29a zenon_H23a zenon_H1b3 zenon_H183 zenon_H2b5 zenon_H19c zenon_H1ed zenon_H193 zenon_H20a zenon_H278 zenon_H23f zenon_H23c zenon_H207 zenon_H229 zenon_H22e. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_H1da | zenon_intro zenon_H2c8 ]. % 47.05/47.23 apply (zenon_L207_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2c8); [ zenon_intro zenon_H1de | zenon_intro zenon_H2c9 ]. % 47.05/47.23 apply (zenon_L166_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2c9); [ zenon_intro zenon_H222 | zenon_intro zenon_H243 ]. % 47.05/47.23 apply (zenon_L234_); trivial. % 47.05/47.23 apply (zenon_L240_); trivial. % 47.05/47.23 (* end of lemma zenon_L241_ *) % 47.05/47.23 assert (zenon_L242_ : ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H19c zenon_H1ed zenon_H193 zenon_H23f zenon_H22e zenon_H25a zenon_H265 zenon_H269 zenon_H223. % 47.05/47.23 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.05/47.23 apply (zenon_L169_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.05/47.23 apply (zenon_L182_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.05/47.23 apply (zenon_L193_); trivial. % 47.05/47.23 apply (zenon_L195_); trivial. % 47.05/47.23 (* end of lemma zenon_L242_ *) % 47.05/47.23 assert (zenon_L243_ : (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H271 zenon_H25f zenon_H229 zenon_H265 zenon_H19c zenon_H1ed zenon_H193 zenon_H22e zenon_H23f zenon_H223 zenon_H270 zenon_H269. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H260 | zenon_intro zenon_H272 ]. % 47.05/47.23 apply (zenon_L191_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H263 | zenon_intro zenon_H273 ]. % 47.05/47.23 apply (zenon_L202_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H25a | zenon_intro zenon_H26c ]. % 47.05/47.23 apply (zenon_L242_); trivial. % 47.05/47.23 apply (zenon_L203_); trivial. % 47.05/47.23 (* end of lemma zenon_L243_ *) % 47.05/47.23 assert (zenon_L244_ : (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (e21) (e21))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e22) (e20)) = (e21)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e23)) = (e21)) -> ((op2 (e22) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e23)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H24b zenon_H234 zenon_H183 zenon_H14 zenon_H2a8 zenon_H23a zenon_H243 zenon_H207 zenon_H278 zenon_H20a zenon_H271 zenon_H25f zenon_H229 zenon_H265 zenon_H19c zenon_H1ed zenon_H193 zenon_H22e zenon_H23f zenon_H270 zenon_H269. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H233 | zenon_intro zenon_H24c ]. % 47.05/47.23 apply (zenon_L179_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H222 | zenon_intro zenon_H24d ]. % 47.05/47.23 apply (zenon_L233_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H23c | zenon_intro zenon_H223 ]. % 47.05/47.23 apply (zenon_L240_); trivial. % 47.05/47.23 apply (zenon_L243_); trivial. % 47.05/47.23 (* end of lemma zenon_L244_ *) % 47.05/47.23 assert (zenon_L245_ : (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> ((op2 (e20) (e22)) = (e20)) -> (~((e20) = (e23))) -> ((op2 (e20) (e21)) = (e21)) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e23)) = (e20)) -> (~((e20) = (e21))) -> (~((e21) = (e23))) -> (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (e21) (e21))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e22) (e20)) = (e21)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e23)) = (e21)) -> ((op2 (e22) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e23)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H28d zenon_H276 zenon_H18b zenon_H19d zenon_H29f zenon_H27b zenon_H287 zenon_H2b5 zenon_H1b3 zenon_H29a zenon_H299 zenon_H194 zenon_H1a3 zenon_H1dd zenon_H1df zenon_H1d3 zenon_H2c7 zenon_H24b zenon_H234 zenon_H183 zenon_H14 zenon_H2a8 zenon_H23a zenon_H243 zenon_H207 zenon_H278 zenon_H20a zenon_H271 zenon_H25f zenon_H229 zenon_H265 zenon_H19c zenon_H1ed zenon_H193 zenon_H22e zenon_H23f zenon_H270. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H1db | zenon_intro zenon_H28e ]. % 47.05/47.23 apply (zenon_L238_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H286 | zenon_intro zenon_H28f ]. % 47.05/47.23 apply (zenon_L209_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H23c | zenon_intro zenon_H269 ]. % 47.05/47.23 apply (zenon_L241_); trivial. % 47.05/47.23 apply (zenon_L244_); trivial. % 47.05/47.23 (* end of lemma zenon_L245_ *) % 47.05/47.23 assert (zenon_L246_ : ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e23)) -> ((op2 (e23) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e22) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e22)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H19c zenon_H1ed zenon_H193 zenon_H20a zenon_H278 zenon_H22e zenon_H23f zenon_H207 zenon_H270 zenon_H23c zenon_H25a. % 47.05/47.23 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.05/47.23 apply (zenon_L169_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.05/47.23 apply (zenon_L239_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.05/47.23 apply (zenon_L225_); trivial. % 47.05/47.23 apply (zenon_L227_); trivial. % 47.05/47.23 (* end of lemma zenon_L246_ *) % 47.05/47.23 assert (zenon_L247_ : (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((e22) = (op2 (e21) (e21))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H27c zenon_H1c4 zenon_H20a zenon_H278 zenon_H207 zenon_H183 zenon_H287 zenon_H276 zenon_H28d zenon_H271 zenon_H25f zenon_H229 zenon_H265 zenon_H19c zenon_H1ed zenon_H193 zenon_H22e zenon_H23f zenon_H223 zenon_H270. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H257 | zenon_intro zenon_H284 ]. % 47.05/47.23 apply (zenon_L188_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H228 | zenon_intro zenon_H285 ]. % 47.05/47.23 apply (zenon_L176_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H25a | zenon_intro zenon_H269 ]. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H1db | zenon_intro zenon_H28e ]. % 47.05/47.23 apply (zenon_L217_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H286 | zenon_intro zenon_H28f ]. % 47.05/47.23 apply (zenon_L209_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H23c | zenon_intro zenon_H269 ]. % 47.05/47.23 apply (zenon_L246_); trivial. % 47.05/47.23 apply (zenon_L242_); trivial. % 47.05/47.23 apply (zenon_L243_); trivial. % 47.05/47.23 (* end of lemma zenon_L247_ *) % 47.05/47.23 assert (zenon_L248_ : (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e20) (e22)) = (e20)) -> (~((e20) = (e23))) -> ((op2 (e20) (e21)) = (e21)) -> (~((e21) = (e23))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (e21) (e21))) -> (~((e22) = (e23))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e23)) -> False). % 47.05/47.23 do 0 intro. intros zenon_H28d zenon_H18b zenon_H19d zenon_H29f zenon_H1d3 zenon_H194 zenon_H14 zenon_H27b zenon_H287 zenon_H183 zenon_H276 zenon_H19c zenon_H1ed zenon_H193 zenon_H22e zenon_H23f zenon_H223 zenon_H270 zenon_H26c. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H1db | zenon_intro zenon_H28e ]. % 47.05/47.23 apply (zenon_L238_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H286 | zenon_intro zenon_H28f ]. % 47.05/47.23 apply (zenon_L209_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H23c | zenon_intro zenon_H269 ]. % 47.05/47.23 apply (zenon_L210_); trivial. % 47.05/47.23 apply (zenon_L203_); trivial. % 47.05/47.23 (* end of lemma zenon_L248_ *) % 47.05/47.23 assert (zenon_L249_ : ((e22) = (op2 (e21) (e21))) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H183 zenon_H2ca zenon_H2cb. % 47.05/47.23 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_H252 | zenon_intro zenon_H253 ]. % 47.05/47.23 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((op2 (e21) (e21)) = (op2 (e21) (e22)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H2cb. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H252. % 47.05/47.23 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H253]. % 47.05/47.23 cut (((op2 (e21) (e22)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 47.05/47.23 congruence. % 47.05/47.23 cut (((e22) = (op2 (e21) (e21))) = ((op2 (e21) (e22)) = (op2 (e21) (e21)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H2cc. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H183. % 47.05/47.23 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 47.05/47.23 cut (((e22) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H2cd]. % 47.05/47.23 congruence. % 47.05/47.23 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_H252 | zenon_intro zenon_H253 ]. % 47.05/47.23 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((e22) = (op2 (e21) (e22)))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H2cd. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H252. % 47.05/47.23 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H253]. % 47.05/47.23 cut (((op2 (e21) (e22)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H2ce]. % 47.05/47.23 congruence. % 47.05/47.23 exact (zenon_H2ce zenon_H2ca). % 47.05/47.23 apply zenon_H253. apply refl_equal. % 47.05/47.23 apply zenon_H253. apply refl_equal. % 47.05/47.23 apply zenon_H1c0. apply refl_equal. % 47.05/47.23 apply zenon_H253. apply refl_equal. % 47.05/47.23 apply zenon_H253. apply refl_equal. % 47.05/47.23 (* end of lemma zenon_L249_ *) % 47.05/47.23 assert (zenon_L250_ : ((op2 (e20) (e22)) = (e20)) -> ((op2 (e20) (e22)) = (e21)) -> (~((e20) = (e21))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H18b zenon_H2cf zenon_H1df. % 47.05/47.23 elim (classic ((e21) = (e21))); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H181 ]. % 47.05/47.23 cut (((e21) = (e21)) = ((e20) = (e21))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H1df. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H1e0. % 47.05/47.23 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.05/47.23 cut (((e21) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 47.05/47.23 congruence. % 47.05/47.23 cut (((op2 (e20) (e22)) = (e20)) = ((e21) = (e20))). % 47.05/47.23 intro zenon_D_pnotp. % 47.05/47.23 apply zenon_H1e1. % 47.05/47.23 rewrite <- zenon_D_pnotp. % 47.05/47.23 exact zenon_H18b. % 47.05/47.23 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 47.05/47.23 cut (((op2 (e20) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2d0]. % 47.05/47.23 congruence. % 47.05/47.23 exact (zenon_H2d0 zenon_H2cf). % 47.05/47.23 apply zenon_H19a. apply refl_equal. % 47.05/47.23 apply zenon_H181. apply refl_equal. % 47.05/47.23 apply zenon_H181. apply refl_equal. % 47.05/47.23 (* end of lemma zenon_L250_ *) % 47.05/47.23 assert (zenon_L251_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (((op2 (e20) (e21)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (((op2 (e20) (e22)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e23) (e22)) = (e23))))) -> (((op2 (e20) (e22)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e22)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e21) (e22)))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/((op2 (e21) (e23)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e21) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e21))\/((op2 (e23) (e20)) = (e21))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((e21) = (e23))) -> ((op2 (e20) (e22)) = (e20)) -> (~((e20) = (e23))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e21) = (e22))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> (~((e20) = (e21))) -> False). % 47.05/47.23 do 0 intro. intros zenon_H2d1 zenon_H18d zenon_H2d2 zenon_H22d zenon_H29c zenon_H291 zenon_H295 zenon_H216 zenon_H2d3 zenon_H2d4 zenon_H251 zenon_H2d5 zenon_H2d6 zenon_H2cb zenon_H2c7 zenon_H20a zenon_H1cf zenon_H2d7 zenon_H2a0 zenon_H2ba zenon_H27d zenon_H1c7 zenon_H259 zenon_H230 zenon_H25c zenon_H27a zenon_H1d3 zenon_H18b zenon_H19d zenon_H1b0 zenon_H1e4 zenon_H183 zenon_H2bb zenon_H2bc zenon_H2ab zenon_H265 zenon_H28d zenon_H1b9 zenon_H287 zenon_H24b zenon_H234 zenon_H299 zenon_H23a zenon_H1b3 zenon_H2b5 zenon_H185 zenon_H270 zenon_H23f zenon_H1be zenon_H193 zenon_H225 zenon_H262 zenon_H25f zenon_H271 zenon_H229 zenon_H1c4 zenon_H27c zenon_H276 zenon_H2bd zenon_H1a3 zenon_H194 zenon_H14 zenon_H1aa zenon_H27b zenon_H1df. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_H18c | zenon_intro zenon_H2d8 ]. % 47.05/47.23 apply (zenon_L146_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2d8); [ zenon_intro zenon_H19b | zenon_intro zenon_H2d9 ]. % 47.05/47.23 apply (zenon_L153_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2d9); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1ed ]. % 47.05/47.23 apply (zenon_L154_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2da ]. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.05/47.23 apply (zenon_L155_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.05/47.23 apply (zenon_L156_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.05/47.23 apply (zenon_L157_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H27d); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H280 ]. % 47.05/47.23 apply (zenon_L155_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H281 ]. % 47.05/47.23 apply (zenon_L158_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H23b | zenon_intro zenon_H257 ]. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.05/47.23 apply (zenon_L148_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.05/47.23 apply (zenon_L148_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H19b | zenon_intro zenon_H2db ]. % 47.05/47.23 apply (zenon_L150_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2dc ]. % 47.05/47.23 apply (zenon_L160_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H1dd ]. % 47.05/47.23 apply (zenon_L161_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.05/47.23 apply (zenon_L145_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.05/47.23 apply (zenon_L160_); trivial. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.05/47.23 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2dd ]. % 47.07/47.23 apply (zenon_L162_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2de ]. % 47.07/47.23 apply (zenon_L163_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2de); [ zenon_intro zenon_H296 | zenon_intro zenon_H1de ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.07/47.23 apply (zenon_L151_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.07/47.23 apply (zenon_L164_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_H1da | zenon_intro zenon_H2c8 ]. % 47.07/47.23 apply (zenon_L165_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c8); [ zenon_intro zenon_H1de | zenon_intro zenon_H2c9 ]. % 47.07/47.23 apply (zenon_L166_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c9); [ zenon_intro zenon_H222 | zenon_intro zenon_H243 ]. % 47.07/47.23 apply (zenon_L178_); trivial. % 47.07/47.23 apply (zenon_L185_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_H24e | zenon_intro zenon_H2df ]. % 47.07/47.23 apply (zenon_L186_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H250 | zenon_intro zenon_H2e0 ]. % 47.07/47.23 apply (zenon_L187_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_H1da | zenon_intro zenon_H2c8 ]. % 47.07/47.23 apply (zenon_L208_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c8); [ zenon_intro zenon_H1de | zenon_intro zenon_H2c9 ]. % 47.07/47.23 apply (zenon_L166_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c9); [ zenon_intro zenon_H222 | zenon_intro zenon_H243 ]. % 47.07/47.23 apply (zenon_L174_); trivial. % 47.07/47.23 apply (zenon_L184_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_H1da | zenon_intro zenon_H2c8 ]. % 47.07/47.23 apply (zenon_L212_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c8); [ zenon_intro zenon_H1de | zenon_intro zenon_H2c9 ]. % 47.07/47.23 apply (zenon_L166_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c9); [ zenon_intro zenon_H222 | zenon_intro zenon_H243 ]. % 47.07/47.23 apply (zenon_L174_); trivial. % 47.07/47.23 apply (zenon_L216_); trivial. % 47.07/47.23 apply (zenon_L166_); trivial. % 47.07/47.23 apply (zenon_L167_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.07/47.23 apply (zenon_L151_); trivial. % 47.07/47.23 apply (zenon_L152_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.23 apply (zenon_L186_); trivial. % 47.07/47.23 apply (zenon_L217_); trivial. % 47.07/47.23 apply (zenon_L188_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H29f | zenon_intro zenon_H2e1 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.07/47.23 apply (zenon_L218_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.07/47.23 apply (zenon_L219_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.23 apply (zenon_L148_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.23 apply (zenon_L220_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.23 apply (zenon_L186_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.07/47.23 apply (zenon_L148_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H19b | zenon_intro zenon_H2db ]. % 47.07/47.23 apply (zenon_L150_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2dc ]. % 47.07/47.23 apply (zenon_L160_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H1dd ]. % 47.07/47.23 apply (zenon_L161_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.07/47.23 apply (zenon_L145_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.07/47.23 apply (zenon_L160_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H2e2 ]. % 47.07/47.23 apply (zenon_L220_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2a4 | zenon_intro zenon_H2e3 ]. % 47.07/47.23 apply (zenon_L221_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H22e ]. % 47.07/47.23 apply (zenon_L168_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2bc); [ zenon_intro zenon_H23b | zenon_intro zenon_H2c4 ]. % 47.07/47.23 apply (zenon_L222_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_H2aa | zenon_intro zenon_H2c5 ]. % 47.07/47.23 apply (zenon_L223_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H29a | zenon_intro zenon_H23c ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.07/47.23 apply (zenon_L151_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.07/47.23 apply (zenon_L168_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_H1da | zenon_intro zenon_H2c8 ]. % 47.07/47.23 apply (zenon_L237_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c8); [ zenon_intro zenon_H1de | zenon_intro zenon_H2c9 ]. % 47.07/47.23 apply (zenon_L166_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c9); [ zenon_intro zenon_H222 | zenon_intro zenon_H243 ]. % 47.07/47.23 apply (zenon_L234_); trivial. % 47.07/47.23 apply (zenon_L245_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_H24e | zenon_intro zenon_H2df ]. % 47.07/47.23 apply (zenon_L186_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H250 | zenon_intro zenon_H2e0 ]. % 47.07/47.23 apply (zenon_L187_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 47.07/47.23 apply (zenon_L247_); trivial. % 47.07/47.23 apply (zenon_L248_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H2e4 ]. % 47.07/47.23 apply (zenon_L157_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2ca | zenon_intro zenon_H2e5 ]. % 47.07/47.23 apply (zenon_L249_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H29a | zenon_intro zenon_H25a ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.07/47.23 apply (zenon_L151_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.07/47.23 apply (zenon_L168_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.07/47.23 apply (zenon_L241_); trivial. % 47.07/47.23 apply (zenon_L210_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.07/47.23 apply (zenon_L151_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.07/47.23 apply (zenon_L168_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.07/47.23 apply (zenon_L246_); trivial. % 47.07/47.23 apply (zenon_L210_); trivial. % 47.07/47.23 apply (zenon_L167_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.07/47.23 apply (zenon_L151_); trivial. % 47.07/47.23 apply (zenon_L152_); trivial. % 47.07/47.23 apply (zenon_L236_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2cf | zenon_intro zenon_H1da ]. % 47.07/47.23 apply (zenon_L250_); trivial. % 47.07/47.23 apply (zenon_L237_); trivial. % 47.07/47.23 (* end of lemma zenon_L251_ *) % 47.07/47.23 assert (zenon_L252_ : ((op2 (e20) (e23)) = (e20)) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> False). % 47.07/47.23 do 0 intro. intros zenon_H2e6 zenon_H18c zenon_H2e7. % 47.07/47.23 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_H2e8 | zenon_intro zenon_H25e ]. % 47.07/47.23 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((op2 (e20) (e20)) = (op2 (e20) (e23)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H2e7. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H2e8. % 47.07/47.23 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 47.07/47.23 cut (((op2 (e20) (e23)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2e9]. % 47.07/47.23 congruence. % 47.07/47.23 cut (((op2 (e20) (e23)) = (e20)) = ((op2 (e20) (e23)) = (op2 (e20) (e20)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H2e9. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H2e6. % 47.07/47.23 cut (((e20) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 47.07/47.23 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 47.07/47.23 congruence. % 47.07/47.23 apply zenon_H25e. apply refl_equal. % 47.07/47.23 apply zenon_H191. apply sym_equal. exact zenon_H18c. % 47.07/47.23 apply zenon_H25e. apply refl_equal. % 47.07/47.23 apply zenon_H25e. apply refl_equal. % 47.07/47.23 (* end of lemma zenon_L252_ *) % 47.07/47.23 assert (zenon_L253_ : ((op2 (e21) (e22)) = (e20)) -> ((op2 (e21) (e22)) = (e21)) -> (~((e20) = (e21))) -> False). % 47.07/47.23 do 0 intro. intros zenon_H1d0 zenon_H296 zenon_H1df. % 47.07/47.23 elim (classic ((e21) = (e21))); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H181 ]. % 47.07/47.23 cut (((e21) = (e21)) = ((e20) = (e21))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H1df. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H1e0. % 47.07/47.23 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.07/47.23 cut (((e21) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 47.07/47.23 congruence. % 47.07/47.23 cut (((op2 (e21) (e22)) = (e20)) = ((e21) = (e20))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H1e1. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H1d0. % 47.07/47.23 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 47.07/47.23 cut (((op2 (e21) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2ea]. % 47.07/47.23 congruence. % 47.07/47.23 exact (zenon_H2ea zenon_H296). % 47.07/47.23 apply zenon_H19a. apply refl_equal. % 47.07/47.23 apply zenon_H181. apply refl_equal. % 47.07/47.23 apply zenon_H181. apply refl_equal. % 47.07/47.23 (* end of lemma zenon_L253_ *) % 47.07/47.23 assert (zenon_L254_ : (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e21) (e23)) = (e21)) -> ((op2 (e22) (e23)) = (e21)) -> False). % 47.07/47.23 do 0 intro. intros zenon_H2eb zenon_H1de zenon_H222. % 47.07/47.23 cut (((op2 (e21) (e23)) = (e21)) = ((op2 (e21) (e23)) = (op2 (e22) (e23)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H2eb. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H1de. % 47.07/47.23 cut (((e21) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H25d]. % 47.07/47.23 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H289]. % 47.07/47.23 congruence. % 47.07/47.23 apply zenon_H289. apply refl_equal. % 47.07/47.23 apply zenon_H25d. apply sym_equal. exact zenon_H222. % 47.07/47.23 (* end of lemma zenon_L254_ *) % 47.07/47.23 assert (zenon_L255_ : (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e21) (e23)) = (e21)) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e22)) = (e23)) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((e20) = (e23))) -> ((op2 (e22) (e21)) = (e20)) -> (~((e22) = (e23))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> False). % 47.07/47.23 do 0 intro. intros zenon_H24b zenon_H234 zenon_H183 zenon_H1de zenon_H2eb zenon_H207 zenon_H225 zenon_H1a3 zenon_H14 zenon_H194 zenon_H19d zenon_H1ea zenon_H276 zenon_H271 zenon_H25f zenon_H262 zenon_H265 zenon_H19c zenon_H1ed zenon_H193 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H23f zenon_H270 zenon_H269. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H233 | zenon_intro zenon_H24c ]. % 47.07/47.23 apply (zenon_L179_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H222 | zenon_intro zenon_H24d ]. % 47.07/47.23 apply (zenon_L254_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H23c | zenon_intro zenon_H223 ]. % 47.07/47.23 apply (zenon_L231_); trivial. % 47.07/47.23 apply (zenon_L200_); trivial. % 47.07/47.23 (* end of lemma zenon_L255_ *) % 47.07/47.23 assert (zenon_L256_ : (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e22) = (e23))) -> ((op2 (e22) (e21)) = (e20)) -> (~((e20) = (e23))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e21) (e23)) = (e21)) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> ((e22) = (op2 (e21) (e21))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e20) (e22)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> False). % 47.07/47.23 do 0 intro. intros zenon_H230 zenon_H1e4 zenon_H1d7 zenon_H1be zenon_H262 zenon_H276 zenon_H1ea zenon_H19d zenon_H194 zenon_H14 zenon_H1a3 zenon_H225 zenon_H207 zenon_H2eb zenon_H1de zenon_H234 zenon_H24b zenon_H183 zenon_H271 zenon_H25f zenon_H265 zenon_H229 zenon_H1c3 zenon_H259 zenon_H19c zenon_H1ed zenon_H193 zenon_H23f zenon_H223 zenon_H270 zenon_H269. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H231 ]. % 47.07/47.23 apply (zenon_L167_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H232 ]. % 47.07/47.23 apply (zenon_L255_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H228 | zenon_intro zenon_H22e ]. % 47.07/47.23 apply (zenon_L176_); trivial. % 47.07/47.23 apply (zenon_L204_); trivial. % 47.07/47.23 (* end of lemma zenon_L256_ *) % 47.07/47.23 assert (zenon_L257_ : (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e22)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e23)) -> False). % 47.07/47.23 do 0 intro. intros zenon_H27c zenon_H1c4 zenon_H1c3 zenon_H259 zenon_H230 zenon_H1e4 zenon_H14 zenon_H1d7 zenon_H1be zenon_H229 zenon_H183 zenon_H19c zenon_H1ed zenon_H193 zenon_H23f zenon_H223 zenon_H270 zenon_H26c. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H257 | zenon_intro zenon_H284 ]. % 47.07/47.23 apply (zenon_L188_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H228 | zenon_intro zenon_H285 ]. % 47.07/47.23 apply (zenon_L176_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H25a | zenon_intro zenon_H269 ]. % 47.07/47.23 apply (zenon_L189_); trivial. % 47.07/47.23 apply (zenon_L211_); trivial. % 47.07/47.23 (* end of lemma zenon_L257_ *) % 47.07/47.23 assert (zenon_L258_ : (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e22)) -> (((op2 (e20) (e22)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((op2 (e21) (e23)) = (e21)) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((e20) = (e23))) -> ((op2 (e22) (e21)) = (e20)) -> (~((e22) = (e23))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e22)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> False). % 47.07/47.23 do 0 intro. intros zenon_H23a zenon_H23b zenon_H2d5 zenon_H251 zenon_H265 zenon_H25f zenon_H271 zenon_H24b zenon_H234 zenon_H1de zenon_H2eb zenon_H225 zenon_H1a3 zenon_H194 zenon_H19d zenon_H1ea zenon_H276 zenon_H262 zenon_H27c zenon_H1c4 zenon_H1c3 zenon_H259 zenon_H230 zenon_H1e4 zenon_H14 zenon_H1d7 zenon_H1be zenon_H229 zenon_H183 zenon_H19c zenon_H1ed zenon_H193 zenon_H23f zenon_H270. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.07/47.23 apply (zenon_L151_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.07/47.23 apply (zenon_L168_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H257 | zenon_intro zenon_H284 ]. % 47.07/47.23 apply (zenon_L188_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H228 | zenon_intro zenon_H285 ]. % 47.07/47.23 apply (zenon_L176_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H25a | zenon_intro zenon_H269 ]. % 47.07/47.23 apply (zenon_L189_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H233 | zenon_intro zenon_H24c ]. % 47.07/47.23 apply (zenon_L179_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H222 | zenon_intro zenon_H24d ]. % 47.07/47.23 apply (zenon_L254_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H23c | zenon_intro zenon_H223 ]. % 47.07/47.23 apply (zenon_L180_); trivial. % 47.07/47.23 apply (zenon_L256_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_H24e | zenon_intro zenon_H2df ]. % 47.07/47.23 apply (zenon_L206_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H250 | zenon_intro zenon_H2e0 ]. % 47.07/47.23 apply (zenon_L187_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H257 | zenon_intro zenon_H284 ]. % 47.07/47.23 apply (zenon_L188_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H228 | zenon_intro zenon_H285 ]. % 47.07/47.23 apply (zenon_L176_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H25a | zenon_intro zenon_H269 ]. % 47.07/47.23 apply (zenon_L189_); trivial. % 47.07/47.23 apply (zenon_L256_); trivial. % 47.07/47.23 apply (zenon_L257_); trivial. % 47.07/47.23 (* end of lemma zenon_L258_ *) % 47.07/47.23 assert (zenon_L259_ : (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e20) (e23)) = (e20)) -> ((op2 (e21) (e23)) = (e20)) -> False). % 47.07/47.23 do 0 intro. intros zenon_H2ec zenon_H2e6 zenon_H1dd. % 47.07/47.23 cut (((op2 (e20) (e23)) = (e20)) = ((op2 (e20) (e23)) = (op2 (e21) (e23)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H2ec. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H2e6. % 47.07/47.23 cut (((e20) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2ed]. % 47.07/47.23 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 47.07/47.23 congruence. % 47.07/47.23 apply zenon_H25e. apply refl_equal. % 47.07/47.23 apply zenon_H2ed. apply sym_equal. exact zenon_H1dd. % 47.07/47.23 (* end of lemma zenon_L259_ *) % 47.07/47.23 assert (zenon_L260_ : ((op2 (e20) (e23)) = (e20)) -> ((op2 (e20) (e23)) = (e23)) -> (~((e20) = (e23))) -> False). % 47.07/47.23 do 0 intro. intros zenon_H2e6 zenon_H278 zenon_H19d. % 47.07/47.23 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H19e | zenon_intro zenon_H19f ]. % 47.07/47.23 cut (((e23) = (e23)) = ((e20) = (e23))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H19d. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H19e. % 47.07/47.23 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 47.07/47.23 cut (((e23) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 47.07/47.23 congruence. % 47.07/47.23 cut (((op2 (e20) (e23)) = (e20)) = ((e23) = (e20))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H1a0. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H2e6. % 47.07/47.23 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 47.07/47.23 cut (((op2 (e20) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 47.07/47.23 congruence. % 47.07/47.23 exact (zenon_H279 zenon_H278). % 47.07/47.23 apply zenon_H19a. apply refl_equal. % 47.07/47.23 apply zenon_H19f. apply refl_equal. % 47.07/47.23 apply zenon_H19f. apply refl_equal. % 47.07/47.23 (* end of lemma zenon_L260_ *) % 47.07/47.23 assert (zenon_L261_ : ((op2 (e20) (e23)) = (e20)) -> ((op2 (e20) (e23)) = (e22)) -> (~((e20) = (e22))) -> False). % 47.07/47.23 do 0 intro. intros zenon_H2e6 zenon_H1db zenon_H1c4. % 47.07/47.23 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 47.07/47.23 cut (((e22) = (e22)) = ((e20) = (e22))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H1c4. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H1ba. % 47.07/47.23 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.07/47.23 cut (((e22) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1c5]. % 47.07/47.23 congruence. % 47.07/47.23 cut (((op2 (e20) (e23)) = (e20)) = ((e22) = (e20))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H1c5. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H2e6. % 47.07/47.23 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 47.07/47.23 cut (((op2 (e20) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1dc]. % 47.07/47.23 congruence. % 47.07/47.23 exact (zenon_H1dc zenon_H1db). % 47.07/47.23 apply zenon_H19a. apply refl_equal. % 47.07/47.23 apply zenon_H1bb. apply refl_equal. % 47.07/47.23 apply zenon_H1bb. apply refl_equal. % 47.07/47.23 (* end of lemma zenon_L261_ *) % 47.07/47.23 assert (zenon_L262_ : ((op2 (e20) (e22)) = (e21)) -> ((op2 (e20) (e22)) = (e23)) -> (~((e21) = (e23))) -> False). % 47.07/47.23 do 0 intro. intros zenon_H2cf zenon_H24e zenon_H1d3. % 47.07/47.23 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H19e | zenon_intro zenon_H19f ]. % 47.07/47.23 cut (((e23) = (e23)) = ((e21) = (e23))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H1d3. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H19e. % 47.07/47.23 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 47.07/47.23 cut (((e23) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1d4]. % 47.07/47.23 congruence. % 47.07/47.23 cut (((op2 (e20) (e22)) = (e21)) = ((e23) = (e21))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H1d4. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H2cf. % 47.07/47.23 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.07/47.23 cut (((op2 (e20) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H24f]. % 47.07/47.23 congruence. % 47.07/47.23 exact (zenon_H24f zenon_H24e). % 47.07/47.23 apply zenon_H181. apply refl_equal. % 47.07/47.23 apply zenon_H19f. apply refl_equal. % 47.07/47.23 apply zenon_H19f. apply refl_equal. % 47.07/47.23 (* end of lemma zenon_L262_ *) % 47.07/47.23 assert (zenon_L263_ : (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e20)) = (e21)) -> ((op2 (e22) (e22)) = (e21)) -> False). % 47.07/47.23 do 0 intro. intros zenon_H299 zenon_H2a8 zenon_H297. % 47.07/47.23 cut (((op2 (e22) (e20)) = (e21)) = ((op2 (e22) (e20)) = (op2 (e22) (e22)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H299. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H2a8. % 47.07/47.23 cut (((e21) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H298]. % 47.07/47.23 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 47.07/47.23 congruence. % 47.07/47.23 apply zenon_H1a5. apply refl_equal. % 47.07/47.23 apply zenon_H298. apply sym_equal. exact zenon_H297. % 47.07/47.23 (* end of lemma zenon_L263_ *) % 47.07/47.23 assert (zenon_L264_ : (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> False). % 47.07/47.23 do 0 intro. intros zenon_H216 zenon_H24e zenon_H207. % 47.07/47.23 cut (((op2 (e20) (e22)) = (e23)) = ((op2 (e20) (e22)) = (op2 (e22) (e22)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H216. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H24e. % 47.07/47.23 cut (((e23) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H208]. % 47.07/47.23 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 47.07/47.23 congruence. % 47.07/47.23 apply zenon_H18f. apply refl_equal. % 47.07/47.23 apply zenon_H208. apply sym_equal. exact zenon_H207. % 47.07/47.23 (* end of lemma zenon_L264_ *) % 47.07/47.23 assert (zenon_L265_ : (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e23)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (e21) (e21))) -> (~((e22) = (e23))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e23)) -> ((op2 (e23) (e22)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> False). % 47.07/47.23 do 0 intro. intros zenon_H28d zenon_H1c4 zenon_H2e6 zenon_H287 zenon_H183 zenon_H276 zenon_H19c zenon_H1ed zenon_H193 zenon_H23f zenon_H22e zenon_H263 zenon_H229 zenon_H265 zenon_H223. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H1db | zenon_intro zenon_H28e ]. % 47.07/47.23 apply (zenon_L261_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H286 | zenon_intro zenon_H28f ]. % 47.07/47.23 apply (zenon_L209_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H23c | zenon_intro zenon_H269 ]. % 47.07/47.23 apply (zenon_L210_); trivial. % 47.07/47.23 apply (zenon_L202_); trivial. % 47.07/47.23 (* end of lemma zenon_L265_ *) % 47.07/47.23 assert (zenon_L266_ : ((op2 (e20) (e22)) = (e21)) -> ((op2 (e20) (e20)) = (e21)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> False). % 47.07/47.23 do 0 intro. intros zenon_H2cf zenon_H1b7 zenon_H18d. % 47.07/47.23 elim (classic ((op2 (e20) (e22)) = (op2 (e20) (e22)))); [ zenon_intro zenon_H18e | zenon_intro zenon_H18f ]. % 47.07/47.23 cut (((op2 (e20) (e22)) = (op2 (e20) (e22))) = ((op2 (e20) (e20)) = (op2 (e20) (e22)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H18d. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H18e. % 47.07/47.23 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 47.07/47.23 cut (((op2 (e20) (e22)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 47.07/47.23 congruence. % 47.07/47.23 cut (((op2 (e20) (e22)) = (e21)) = ((op2 (e20) (e22)) = (op2 (e20) (e20)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H190. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H2cf. % 47.07/47.23 cut (((e21) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2a2]. % 47.07/47.23 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 47.07/47.23 congruence. % 47.07/47.23 apply zenon_H18f. apply refl_equal. % 47.07/47.23 apply zenon_H2a2. apply sym_equal. exact zenon_H1b7. % 47.07/47.23 apply zenon_H18f. apply refl_equal. % 47.07/47.23 apply zenon_H18f. apply refl_equal. % 47.07/47.23 (* end of lemma zenon_L266_ *) % 47.07/47.23 assert (zenon_L267_ : (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((op2 (e20) (e23)) = (e20)) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (e21) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> False). % 47.07/47.23 do 0 intro. intros zenon_H2ee zenon_H2e6 zenon_H2ec zenon_H1d2 zenon_H287 zenon_H183 zenon_H194 zenon_H14 zenon_H2ef. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2ee); [ zenon_intro zenon_H1dd | zenon_intro zenon_H2f0 ]. % 47.07/47.23 apply (zenon_L259_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H1de | zenon_intro zenon_H2f1 ]. % 47.07/47.23 cut (((op2 (e21) (e20)) = (e21)) = ((op2 (e21) (e20)) = (op2 (e21) (e23)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H2ef. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H1d2. % 47.07/47.23 cut (((e21) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2f2]. % 47.07/47.23 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1cb]. % 47.07/47.23 congruence. % 47.07/47.23 apply zenon_H1cb. apply refl_equal. % 47.07/47.23 apply zenon_H2f2. apply sym_equal. exact zenon_H1de. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2f1); [ zenon_intro zenon_H286 | zenon_intro zenon_H2f3 ]. % 47.07/47.23 apply (zenon_L209_); trivial. % 47.07/47.23 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H288 | zenon_intro zenon_H289 ]. % 47.07/47.23 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((op2 (e21) (e20)) = (op2 (e21) (e23)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H2ef. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H288. % 47.07/47.23 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H289]. % 47.07/47.23 cut (((op2 (e21) (e23)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2f4]. % 47.07/47.23 congruence. % 47.07/47.23 cut (((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) = ((op2 (e21) (e23)) = (op2 (e21) (e20)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H2f4. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H194. % 47.07/47.23 cut (((op2 (e21) (op2 (op2 (e21) (e21)) (e21))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 47.07/47.23 cut (((e23) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2f5]. % 47.07/47.23 congruence. % 47.07/47.23 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H288 | zenon_intro zenon_H289 ]. % 47.07/47.23 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e23) = (op2 (e21) (e23)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H2f5. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H288. % 47.07/47.23 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H289]. % 47.07/47.23 cut (((op2 (e21) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H2f6]. % 47.07/47.23 congruence. % 47.07/47.23 exact (zenon_H2f6 zenon_H2f3). % 47.07/47.23 apply zenon_H289. apply refl_equal. % 47.07/47.23 apply zenon_H289. apply refl_equal. % 47.07/47.23 apply (zenon_L147_); trivial. % 47.07/47.23 apply zenon_H289. apply refl_equal. % 47.07/47.23 apply zenon_H289. apply refl_equal. % 47.07/47.23 (* end of lemma zenon_L267_ *) % 47.07/47.23 assert (zenon_L268_ : ((op2 (e20) (e22)) = (e21)) -> ((op2 (e20) (e21)) = (e21)) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> False). % 47.07/47.23 do 0 intro. intros zenon_H2cf zenon_H29f zenon_H2f7. % 47.07/47.23 elim (classic ((op2 (e20) (e22)) = (op2 (e20) (e22)))); [ zenon_intro zenon_H18e | zenon_intro zenon_H18f ]. % 47.07/47.23 cut (((op2 (e20) (e22)) = (op2 (e20) (e22))) = ((op2 (e20) (e21)) = (op2 (e20) (e22)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H2f7. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H18e. % 47.07/47.23 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 47.07/47.23 cut (((op2 (e20) (e22)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2f8]. % 47.07/47.23 congruence. % 47.07/47.23 cut (((op2 (e20) (e22)) = (e21)) = ((op2 (e20) (e22)) = (op2 (e20) (e21)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H2f8. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H2cf. % 47.07/47.23 cut (((e21) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2f9]. % 47.07/47.23 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 47.07/47.23 congruence. % 47.07/47.23 apply zenon_H18f. apply refl_equal. % 47.07/47.23 apply zenon_H2f9. apply sym_equal. exact zenon_H29f. % 47.07/47.23 apply zenon_H18f. apply refl_equal. % 47.07/47.23 apply zenon_H18f. apply refl_equal. % 47.07/47.23 (* end of lemma zenon_L268_ *) % 47.07/47.23 assert (zenon_L269_ : (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e22)) = (e21)) -> ((op2 (e23) (e22)) = (e21)) -> False). % 47.07/47.23 do 0 intro. intros zenon_H259 zenon_H2cf zenon_H263. % 47.07/47.23 cut (((op2 (e20) (e22)) = (e21)) = ((op2 (e20) (e22)) = (op2 (e23) (e22)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H259. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H2cf. % 47.07/47.23 cut (((e21) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 47.07/47.23 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 47.07/47.23 congruence. % 47.07/47.23 apply zenon_H18f. apply refl_equal. % 47.07/47.23 apply zenon_H264. apply sym_equal. exact zenon_H263. % 47.07/47.23 (* end of lemma zenon_L269_ *) % 47.07/47.23 assert (zenon_L270_ : (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e22)) = (e21)) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e22)) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> False). % 47.07/47.23 do 0 intro. intros zenon_H271 zenon_H25f zenon_H2cf zenon_H259 zenon_H19c zenon_H1ed zenon_H193 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H23f zenon_H23c zenon_H207 zenon_H270 zenon_H269. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H260 | zenon_intro zenon_H272 ]. % 47.07/47.23 apply (zenon_L191_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H263 | zenon_intro zenon_H273 ]. % 47.07/47.23 apply (zenon_L269_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H25a | zenon_intro zenon_H26c ]. % 47.07/47.23 apply (zenon_L228_); trivial. % 47.07/47.23 apply (zenon_L230_); trivial. % 47.07/47.23 (* end of lemma zenon_L270_ *) % 47.07/47.23 assert (zenon_L271_ : (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> (~((e22) = (e23))) -> ((op2 (e22) (e21)) = (e20)) -> (~((e20) = (e23))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e22)) = (e21)) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e22)) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> False). % 47.07/47.23 do 0 intro. intros zenon_H27c zenon_H1c4 zenon_H229 zenon_H183 zenon_H276 zenon_H1ea zenon_H19d zenon_H194 zenon_H14 zenon_H1a3 zenon_H225 zenon_H271 zenon_H25f zenon_H2cf zenon_H259 zenon_H19c zenon_H1ed zenon_H193 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H23f zenon_H23c zenon_H207 zenon_H270. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H257 | zenon_intro zenon_H284 ]. % 47.07/47.23 apply (zenon_L188_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H228 | zenon_intro zenon_H285 ]. % 47.07/47.23 apply (zenon_L176_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H25a | zenon_intro zenon_H269 ]. % 47.07/47.23 apply (zenon_L229_); trivial. % 47.07/47.23 apply (zenon_L270_); trivial. % 47.07/47.23 (* end of lemma zenon_L271_ *) % 47.07/47.23 assert (zenon_L272_ : (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e22)) = (e21)) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e21)) = (e21)) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> False). % 47.07/47.23 do 0 intro. intros zenon_H271 zenon_H25f zenon_H2cf zenon_H259 zenon_H265 zenon_H1f9 zenon_H230 zenon_H1e4 zenon_H14 zenon_H1d7 zenon_H1be zenon_H229 zenon_H183 zenon_H19c zenon_H1ed zenon_H193 zenon_H23f zenon_H223 zenon_H270 zenon_H269. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H260 | zenon_intro zenon_H272 ]. % 47.07/47.23 apply (zenon_L191_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H263 | zenon_intro zenon_H273 ]. % 47.07/47.23 apply (zenon_L269_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H25a | zenon_intro zenon_H26c ]. % 47.07/47.23 apply (zenon_L196_); trivial. % 47.07/47.23 apply (zenon_L211_); trivial. % 47.07/47.23 (* end of lemma zenon_L272_ *) % 47.07/47.23 assert (zenon_L273_ : (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((op2 (e21) (e23)) = (e21)) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e22)) = (e23)) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e22)) = (e21)) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e21)) = (e21)) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e23)) = (e22)) -> False). % 47.07/47.23 do 0 intro. intros zenon_H24b zenon_H234 zenon_H1de zenon_H2eb zenon_H207 zenon_H271 zenon_H25f zenon_H2cf zenon_H259 zenon_H265 zenon_H1f9 zenon_H230 zenon_H1e4 zenon_H14 zenon_H1d7 zenon_H1be zenon_H229 zenon_H183 zenon_H19c zenon_H1ed zenon_H193 zenon_H23f zenon_H270 zenon_H269. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H233 | zenon_intro zenon_H24c ]. % 47.07/47.23 apply (zenon_L179_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H222 | zenon_intro zenon_H24d ]. % 47.07/47.23 apply (zenon_L254_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H23c | zenon_intro zenon_H223 ]. % 47.07/47.23 apply (zenon_L270_); trivial. % 47.07/47.23 apply (zenon_L272_); trivial. % 47.07/47.23 (* end of lemma zenon_L273_ *) % 47.07/47.23 assert (zenon_L274_ : (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e23)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (e21) (e21))) -> (~((e22) = (e23))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e23)) -> False). % 47.07/47.23 do 0 intro. intros zenon_H28d zenon_H1c4 zenon_H2e6 zenon_H287 zenon_H183 zenon_H276 zenon_H19c zenon_H1ed zenon_H193 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H23f zenon_H223 zenon_H270 zenon_H26c. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H1db | zenon_intro zenon_H28e ]. % 47.07/47.23 apply (zenon_L261_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H286 | zenon_intro zenon_H28f ]. % 47.07/47.23 apply (zenon_L209_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H23c | zenon_intro zenon_H269 ]. % 47.07/47.23 apply (zenon_L210_); trivial. % 47.07/47.23 apply (zenon_L199_); trivial. % 47.07/47.23 (* end of lemma zenon_L274_ *) % 47.07/47.23 assert (zenon_L275_ : (~((op2 (e20) (e22)) = (op2 (e21) (e22)))) -> ((op2 (e20) (e22)) = (e21)) -> ((op2 (e21) (e22)) = (e21)) -> False). % 47.07/47.23 do 0 intro. intros zenon_H1cf zenon_H2cf zenon_H296. % 47.07/47.23 cut (((op2 (e20) (e22)) = (e21)) = ((op2 (e20) (e22)) = (op2 (e21) (e22)))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H1cf. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H2cf. % 47.07/47.23 cut (((e21) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H2fa]. % 47.07/47.23 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 47.07/47.23 congruence. % 47.07/47.23 apply zenon_H18f. apply refl_equal. % 47.07/47.23 apply zenon_H2fa. apply sym_equal. exact zenon_H296. % 47.07/47.23 (* end of lemma zenon_L275_ *) % 47.07/47.23 assert (zenon_L276_ : (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((e21) = (e23))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e22))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e20) (e22)) = (e21)) -> (~((op2 (e20) (e22)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e23)) = (e20)) -> (~((e20) = (e21))) -> False). % 47.07/47.23 do 0 intro. intros zenon_H2d3 zenon_H1aa zenon_H14 zenon_H194 zenon_H1a3 zenon_H1d3 zenon_H193 zenon_H1b0 zenon_H1b9 zenon_H183 zenon_H2cf zenon_H1cf zenon_H1dd zenon_H1df. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2dd ]. % 47.07/47.23 apply (zenon_L219_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2de ]. % 47.07/47.23 apply (zenon_L163_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2de); [ zenon_intro zenon_H296 | zenon_intro zenon_H1de ]. % 47.07/47.23 apply (zenon_L275_); trivial. % 47.07/47.23 apply (zenon_L166_); trivial. % 47.07/47.23 (* end of lemma zenon_L276_ *) % 47.07/47.23 assert (zenon_L277_ : ((op2 (e20) (e23)) = (e20)) -> ((op2 (e20) (e23)) = (e21)) -> (~((e20) = (e21))) -> False). % 47.07/47.23 do 0 intro. intros zenon_H2e6 zenon_H1da zenon_H1df. % 47.07/47.23 elim (classic ((e21) = (e21))); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H181 ]. % 47.07/47.23 cut (((e21) = (e21)) = ((e20) = (e21))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H1df. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H1e0. % 47.07/47.23 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.07/47.23 cut (((e21) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 47.07/47.23 congruence. % 47.07/47.23 cut (((op2 (e20) (e23)) = (e20)) = ((e21) = (e20))). % 47.07/47.23 intro zenon_D_pnotp. % 47.07/47.23 apply zenon_H1e1. % 47.07/47.23 rewrite <- zenon_D_pnotp. % 47.07/47.23 exact zenon_H2e6. % 47.07/47.23 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 47.07/47.23 cut (((op2 (e20) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2fb]. % 47.07/47.23 congruence. % 47.07/47.23 exact (zenon_H2fb zenon_H1da). % 47.07/47.23 apply zenon_H19a. apply refl_equal. % 47.07/47.23 apply zenon_H181. apply refl_equal. % 47.07/47.23 apply zenon_H181. apply refl_equal. % 47.07/47.23 (* end of lemma zenon_L277_ *) % 47.07/47.23 assert (zenon_L278_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (((op2 (e20) (e21)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e23) (e22)) = (e21))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/((op2 (e21) (e23)) = (e20))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (((op2 (e20) (e22)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((e22) = (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e22))) -> ((e22) = (op2 (e21) (e21))) -> (~((op2 (e20) (e22)) = (op2 (e21) (e22)))) -> (~((e21) = (e23))) -> (~((e20) = (e23))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e21) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e21))\/((op2 (e23) (e20)) = (e21))))) -> ((op2 (e20) (e23)) = (e20)) -> (~((e20) = (e21))) -> False). % 47.07/47.23 do 0 intro. intros zenon_H2d1 zenon_H2e7 zenon_H2d2 zenon_H27d zenon_H262 zenon_H23a zenon_H27a zenon_H2d4 zenon_H1c7 zenon_H2fc zenon_H299 zenon_H216 zenon_H2a0 zenon_H27b zenon_H1aa zenon_H14 zenon_H194 zenon_H1a3 zenon_H2d7 zenon_H1e4 zenon_H2bb zenon_H2f7 zenon_H1b3 zenon_H2eb zenon_H234 zenon_H24b zenon_H2d5 zenon_H251 zenon_H229 zenon_H230 zenon_H265 zenon_H259 zenon_H25f zenon_H271 zenon_H225 zenon_H27c zenon_H28d zenon_H1c4 zenon_H287 zenon_H276 zenon_H1be zenon_H23f zenon_H270 zenon_H185 zenon_H2bd zenon_H2d3 zenon_H193 zenon_H1b0 zenon_H1b9 zenon_H183 zenon_H1cf zenon_H1d3 zenon_H19d zenon_H2ee zenon_H2ec zenon_H2ef zenon_H18d zenon_H2ba zenon_H2e6 zenon_H1df. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_H18c | zenon_intro zenon_H2d8 ]. % 47.07/47.23 apply (zenon_L252_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d8); [ zenon_intro zenon_H19b | zenon_intro zenon_H2d9 ]. % 47.07/47.23 apply (zenon_L153_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d9); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1ed ]. % 47.07/47.23 apply (zenon_L154_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2da ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.07/47.23 apply (zenon_L155_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.07/47.23 apply (zenon_L156_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H27d); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H280 ]. % 47.07/47.23 apply (zenon_L155_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H281 ]. % 47.07/47.23 apply (zenon_L158_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H23b | zenon_intro zenon_H257 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.23 apply (zenon_L148_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.07/47.23 apply (zenon_L148_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H19b | zenon_intro zenon_H2db ]. % 47.07/47.23 apply (zenon_L150_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2dc ]. % 47.07/47.23 apply (zenon_L160_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H1dd ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.07/47.23 apply (zenon_L145_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.07/47.23 apply (zenon_L160_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2dd ]. % 47.07/47.23 apply (zenon_L162_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2de ]. % 47.07/47.23 apply (zenon_L163_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2de); [ zenon_intro zenon_H296 | zenon_intro zenon_H1de ]. % 47.07/47.23 apply (zenon_L253_); trivial. % 47.07/47.23 apply (zenon_L258_); trivial. % 47.07/47.23 apply (zenon_L167_); trivial. % 47.07/47.23 apply (zenon_L259_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.07/47.23 apply (zenon_L151_); trivial. % 47.07/47.23 apply (zenon_L152_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.23 apply (zenon_L206_); trivial. % 47.07/47.23 apply (zenon_L260_); trivial. % 47.07/47.23 apply (zenon_L188_); trivial. % 47.07/47.23 apply (zenon_L261_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H29f | zenon_intro zenon_H2e1 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.07/47.23 apply (zenon_L218_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.07/47.23 apply (zenon_L219_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.23 apply (zenon_L148_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.23 apply (zenon_L220_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.07/47.23 apply (zenon_L148_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H19b | zenon_intro zenon_H2db ]. % 47.07/47.23 apply (zenon_L150_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2dc ]. % 47.07/47.23 apply (zenon_L160_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H1dd ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.07/47.23 apply (zenon_L145_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.07/47.23 apply (zenon_L160_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H2e2 ]. % 47.07/47.23 apply (zenon_L220_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2a4 | zenon_intro zenon_H2e3 ]. % 47.07/47.23 apply (zenon_L221_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H22e ]. % 47.07/47.23 apply (zenon_L168_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H2cf | zenon_intro zenon_H2fd ]. % 47.07/47.23 apply (zenon_L262_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2fd); [ zenon_intro zenon_H296 | zenon_intro zenon_H2fe ]. % 47.07/47.23 apply (zenon_L253_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H297 | zenon_intro zenon_H263 ]. % 47.07/47.23 apply (zenon_L263_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.07/47.23 apply (zenon_L151_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.07/47.23 apply (zenon_L168_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.07/47.23 apply (zenon_L264_); trivial. % 47.07/47.23 apply (zenon_L265_); trivial. % 47.07/47.23 apply (zenon_L167_); trivial. % 47.07/47.23 apply (zenon_L259_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.07/47.23 apply (zenon_L151_); trivial. % 47.07/47.23 apply (zenon_L152_); trivial. % 47.07/47.23 apply (zenon_L260_); trivial. % 47.07/47.23 apply (zenon_L236_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2cf | zenon_intro zenon_H1da ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.07/47.23 apply (zenon_L266_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.07/47.23 apply (zenon_L267_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.23 apply (zenon_L148_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.07/47.23 apply (zenon_L148_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H19b | zenon_intro zenon_H2db ]. % 47.07/47.23 apply (zenon_L150_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2dc ]. % 47.07/47.23 apply (zenon_L160_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H1dd ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.07/47.23 apply (zenon_L145_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.07/47.23 apply (zenon_L160_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2dd ]. % 47.07/47.23 apply (zenon_L162_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2de ]. % 47.07/47.23 apply (zenon_L163_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2de); [ zenon_intro zenon_H296 | zenon_intro zenon_H1de ]. % 47.07/47.23 apply (zenon_L253_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_H29f | zenon_intro zenon_H2c2 ]. % 47.07/47.23 apply (zenon_L268_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2c3 ]. % 47.07/47.23 apply (zenon_L163_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2c3); [ zenon_intro zenon_H2b1 | zenon_intro zenon_H1f9 ]. % 47.07/47.23 apply (zenon_L224_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.07/47.23 apply (zenon_L151_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.07/47.23 apply (zenon_L168_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H1db | zenon_intro zenon_H28e ]. % 47.07/47.23 apply (zenon_L261_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H286 | zenon_intro zenon_H28f ]. % 47.07/47.23 apply (zenon_L209_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H23c | zenon_intro zenon_H269 ]. % 47.07/47.23 apply (zenon_L271_); trivial. % 47.07/47.23 apply (zenon_L273_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_H24e | zenon_intro zenon_H2df ]. % 47.07/47.23 apply (zenon_L262_); trivial. % 47.07/47.23 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H250 | zenon_intro zenon_H2e0 ]. % 47.07/47.23 apply (zenon_L187_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H257 | zenon_intro zenon_H284 ]. % 47.07/47.24 apply (zenon_L188_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H228 | zenon_intro zenon_H285 ]. % 47.07/47.24 apply (zenon_L176_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H25a | zenon_intro zenon_H269 ]. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H1db | zenon_intro zenon_H28e ]. % 47.07/47.24 apply (zenon_L261_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H286 | zenon_intro zenon_H28f ]. % 47.07/47.24 apply (zenon_L209_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H23c | zenon_intro zenon_H269 ]. % 47.07/47.24 apply (zenon_L271_); trivial. % 47.07/47.24 apply (zenon_L196_); trivial. % 47.07/47.24 apply (zenon_L272_); trivial. % 47.07/47.24 apply (zenon_L274_); trivial. % 47.07/47.24 apply (zenon_L167_); trivial. % 47.07/47.24 apply (zenon_L276_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.07/47.24 apply (zenon_L151_); trivial. % 47.07/47.24 apply (zenon_L152_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.24 apply (zenon_L262_); trivial. % 47.07/47.24 apply (zenon_L260_); trivial. % 47.07/47.24 apply (zenon_L236_); trivial. % 47.07/47.24 apply (zenon_L277_); trivial. % 47.07/47.24 (* end of lemma zenon_L278_ *) % 47.07/47.24 assert (zenon_L279_ : ((op2 (e20) (e20)) = (e20)) -> ((op2 (e20) (e20)) = (e21)) -> (~((e20) = (e21))) -> False). % 47.07/47.24 do 0 intro. intros zenon_H18c zenon_H1b7 zenon_H1df. % 47.07/47.24 elim (classic ((e21) = (e21))); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H181 ]. % 47.07/47.24 cut (((e21) = (e21)) = ((e20) = (e21))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H1df. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H1e0. % 47.07/47.24 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.07/47.24 cut (((e21) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 47.07/47.24 congruence. % 47.07/47.24 cut (((op2 (e20) (e20)) = (e20)) = ((e21) = (e20))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H1e1. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H18c. % 47.07/47.24 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 47.07/47.24 cut (((op2 (e20) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2ff]. % 47.07/47.24 congruence. % 47.07/47.24 exact (zenon_H2ff zenon_H1b7). % 47.07/47.24 apply zenon_H19a. apply refl_equal. % 47.07/47.24 apply zenon_H181. apply refl_equal. % 47.07/47.24 apply zenon_H181. apply refl_equal. % 47.07/47.24 (* end of lemma zenon_L279_ *) % 47.07/47.24 assert (zenon_L280_ : ((op1 (e10) (e10)) = (e10)) -> ((op1 (e10) (e10)) = (e11)) -> (~((e10) = (e11))) -> False). % 47.07/47.24 do 0 intro. intros zenon_H23 zenon_H4f zenon_H15b. % 47.07/47.24 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H15c | zenon_intro zenon_H17 ]. % 47.07/47.24 cut (((e11) = (e11)) = ((e10) = (e11))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H15b. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H15c. % 47.07/47.24 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 47.07/47.24 cut (((e11) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 47.07/47.24 congruence. % 47.07/47.24 cut (((op1 (e10) (e10)) = (e10)) = ((e11) = (e10))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H15d. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H23. % 47.07/47.24 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 47.07/47.24 cut (((op1 (e10) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H300]. % 47.07/47.24 congruence. % 47.07/47.24 exact (zenon_H300 zenon_H4f). % 47.07/47.24 apply zenon_H32. apply refl_equal. % 47.07/47.24 apply zenon_H17. apply refl_equal. % 47.07/47.24 apply zenon_H17. apply refl_equal. % 47.07/47.24 (* end of lemma zenon_L280_ *) % 47.07/47.24 assert (zenon_L281_ : ((op1 (e11) (e10)) = (e11)) -> ((op1 (e11) (e10)) = (e13)) -> (~((e11) = (e13))) -> False). % 47.07/47.24 do 0 intro. intros zenon_He1 zenon_H34 zenon_Ha9. % 47.07/47.24 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 47.07/47.24 cut (((e13) = (e13)) = ((e11) = (e13))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_Ha9. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H36. % 47.07/47.24 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 47.07/47.24 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 47.07/47.24 congruence. % 47.07/47.24 cut (((op1 (e11) (e10)) = (e11)) = ((e13) = (e11))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_Haa. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_He1. % 47.07/47.24 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 47.07/47.24 cut (((op1 (e11) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 47.07/47.24 congruence. % 47.07/47.24 exact (zenon_H39 zenon_H34). % 47.07/47.24 apply zenon_H17. apply refl_equal. % 47.07/47.24 apply zenon_H37. apply refl_equal. % 47.07/47.24 apply zenon_H37. apply refl_equal. % 47.07/47.24 (* end of lemma zenon_L281_ *) % 47.07/47.24 assert (zenon_L282_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((e11) = (e13))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> False). % 47.07/47.24 do 0 intro. intros zenon_H48 zenon_H2b zenon_Ha9 zenon_He1 zenon_H3b zenon_H2c zenon_H1c zenon_H42. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.24 apply (zenon_L7_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.24 apply (zenon_L281_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.24 apply (zenon_L10_); trivial. % 47.07/47.24 apply (zenon_L11_); trivial. % 47.07/47.24 (* end of lemma zenon_L282_ *) % 47.07/47.24 assert (zenon_L283_ : ((op1 (e10) (e10)) = (e10)) -> ((op1 (e10) (e10)) = (e12)) -> (~((e10) = (e12))) -> False). % 47.07/47.24 do 0 intro. intros zenon_H23 zenon_H50 zenon_H5c. % 47.07/47.24 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 47.07/47.24 cut (((e12) = (e12)) = ((e10) = (e12))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H5c. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H52. % 47.07/47.24 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.07/47.24 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 47.07/47.24 congruence. % 47.07/47.24 cut (((op1 (e10) (e10)) = (e10)) = ((e12) = (e10))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H5d. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H23. % 47.07/47.24 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 47.07/47.24 cut (((op1 (e10) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 47.07/47.24 congruence. % 47.07/47.24 exact (zenon_H55 zenon_H50). % 47.07/47.24 apply zenon_H32. apply refl_equal. % 47.07/47.24 apply zenon_H53. apply refl_equal. % 47.07/47.24 apply zenon_H53. apply refl_equal. % 47.07/47.24 (* end of lemma zenon_L283_ *) % 47.07/47.24 assert (zenon_L284_ : ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e12)) = (e12)) -> (~((e11) = (e12))) -> False). % 47.07/47.24 do 0 intro. intros zenon_H141 zenon_H5b zenon_H51. % 47.07/47.24 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 47.07/47.24 cut (((e12) = (e12)) = ((e11) = (e12))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H51. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H52. % 47.07/47.24 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.07/47.24 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 47.07/47.24 congruence. % 47.07/47.24 cut (((op1 (e10) (e12)) = (e11)) = ((e12) = (e11))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H54. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H141. % 47.07/47.24 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 47.07/47.24 cut (((op1 (e10) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 47.07/47.24 congruence. % 47.07/47.24 exact (zenon_H5e zenon_H5b). % 47.07/47.24 apply zenon_H17. apply refl_equal. % 47.07/47.24 apply zenon_H53. apply refl_equal. % 47.07/47.24 apply zenon_H53. apply refl_equal. % 47.07/47.24 (* end of lemma zenon_L284_ *) % 47.07/47.24 assert (zenon_L285_ : (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e11) (e10)) = (e12)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H129 zenon_H19 zenon_H301. % 47.07/47.24 cut (((e12) = (op1 (e11) (e11))) = ((op1 (e11) (e10)) = (op1 (e11) (e11)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H129. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H19. % 47.07/47.24 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 47.07/47.24 cut (((e12) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H302]. % 47.07/47.24 congruence. % 47.07/47.24 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_H303 | zenon_intro zenon_He4 ]. % 47.07/47.24 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((e12) = (op1 (e11) (e10)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H302. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H303. % 47.07/47.24 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 47.07/47.24 cut (((op1 (e11) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H304]. % 47.07/47.24 congruence. % 47.07/47.24 exact (zenon_H304 zenon_H301). % 47.07/47.24 apply zenon_He4. apply refl_equal. % 47.07/47.24 apply zenon_He4. apply refl_equal. % 47.07/47.24 apply zenon_H58. apply refl_equal. % 47.07/47.24 (* end of lemma zenon_L285_ *) % 47.07/47.24 assert (zenon_L286_ : (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e11) (e12)) = (e11)) -> False). % 47.07/47.24 do 0 intro. intros zenon_Hde zenon_H141 zenon_He2. % 47.07/47.24 cut (((op1 (e10) (e12)) = (e11)) = ((op1 (e10) (e12)) = (op1 (e11) (e12)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_Hde. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H141. % 47.07/47.24 cut (((e11) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_He3]. % 47.07/47.24 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 47.07/47.24 congruence. % 47.07/47.24 apply zenon_H26. apply refl_equal. % 47.07/47.24 apply zenon_He3. apply sym_equal. exact zenon_He2. % 47.07/47.24 (* end of lemma zenon_L286_ *) % 47.07/47.24 assert (zenon_L287_ : ((op1 (e11) (e13)) = (e10)) -> ((op1 (e11) (e13)) = (e11)) -> (~((e10) = (e11))) -> False). % 47.07/47.24 do 0 intro. intros zenon_H172 zenon_H175 zenon_H15b. % 47.07/47.24 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H15c | zenon_intro zenon_H17 ]. % 47.07/47.24 cut (((e11) = (e11)) = ((e10) = (e11))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H15b. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H15c. % 47.07/47.24 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 47.07/47.24 cut (((e11) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 47.07/47.24 congruence. % 47.07/47.24 cut (((op1 (e11) (e13)) = (e10)) = ((e11) = (e10))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H15d. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H172. % 47.07/47.24 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 47.07/47.24 cut (((op1 (e11) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H305]. % 47.07/47.24 congruence. % 47.07/47.24 exact (zenon_H305 zenon_H175). % 47.07/47.24 apply zenon_H32. apply refl_equal. % 47.07/47.24 apply zenon_H17. apply refl_equal. % 47.07/47.24 apply zenon_H17. apply refl_equal. % 47.07/47.24 (* end of lemma zenon_L287_ *) % 47.07/47.24 assert (zenon_L288_ : (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e13) (e12)) = (e10)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H306 zenon_Hdf zenon_H102. % 47.07/47.24 cut (((op1 (e11) (e12)) = (e10)) = ((op1 (e11) (e12)) = (op1 (e13) (e12)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H306. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_Hdf. % 47.07/47.24 cut (((e10) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 47.07/47.24 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 47.07/47.24 congruence. % 47.07/47.24 apply zenon_Hc0. apply refl_equal. % 47.07/47.24 apply zenon_H103. apply sym_equal. exact zenon_H102. % 47.07/47.24 (* end of lemma zenon_L288_ *) % 47.07/47.24 assert (zenon_L289_ : (~((op1 (e12) (e12)) = (op1 (op1 (e13) (e10)) (op1 (e13) (e10))))) -> ((op1 (e13) (e10)) = (e12)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H307 zenon_Hf7. % 47.07/47.24 cut (((e12) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H308]. % 47.07/47.24 cut (((e12) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H308]. % 47.07/47.24 congruence. % 47.07/47.24 apply zenon_H308. apply sym_equal. exact zenon_Hf7. % 47.07/47.24 apply zenon_H308. apply sym_equal. exact zenon_Hf7. % 47.07/47.24 (* end of lemma zenon_L289_ *) % 47.07/47.24 assert (zenon_L290_ : (((op1 (op1 (e10) (e10)) (op1 (e10) (e10))) = (e10))/\(((op1 (op1 (e11) (e10)) (op1 (e11) (e10))) = (e11))/\(((op1 (op1 (e12) (e10)) (op1 (e12) (e10))) = (e12))/\((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> ((op1 (e13) (e12)) = (e13)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H70 zenon_Hf9 zenon_Hf7 zenon_Hc4. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H73. zenon_intro zenon_H72. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H75. zenon_intro zenon_H74. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H74). zenon_intro zenon_H77. zenon_intro zenon_H76. % 47.07/47.24 cut (((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (e13)) = ((op1 (e12) (e12)) = (op1 (e13) (e12)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_Hf9. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H76. % 47.07/47.24 cut (((e13) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 47.07/47.24 cut (((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H309]. % 47.07/47.24 congruence. % 47.07/47.24 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 47.07/47.24 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (op1 (e12) (e12)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H309. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H9f. % 47.07/47.24 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 47.07/47.24 cut (((op1 (e12) (e12)) = (op1 (op1 (e13) (e10)) (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H307]. % 47.07/47.24 congruence. % 47.07/47.24 apply (zenon_L289_); trivial. % 47.07/47.24 apply zenon_Ha0. apply refl_equal. % 47.07/47.24 apply zenon_Ha0. apply refl_equal. % 47.07/47.24 apply zenon_Hca. apply sym_equal. exact zenon_Hc4. % 47.07/47.24 (* end of lemma zenon_L290_ *) % 47.07/47.24 assert (zenon_L291_ : (((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (e10))/\(((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (e11))/\(((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e12))/\((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H9b zenon_H2b zenon_H30a zenon_H34. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9e. zenon_intro zenon_H9d. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H9d). zenon_intro zenon_H109. zenon_intro zenon_H108. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H10b. zenon_intro zenon_H10a. % 47.07/47.24 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13)) = ((op1 (e10) (e10)) = (op1 (e11) (e10)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H2b. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H10a. % 47.07/47.24 cut (((e13) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 47.07/47.24 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H30b]. % 47.07/47.24 congruence. % 47.07/47.24 elim (classic ((op1 (e10) (e10)) = (op1 (e10) (e10)))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 47.07/47.24 cut (((op1 (e10) (e10)) = (op1 (e10) (e10))) = ((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e10) (e10)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H30b. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H2f. % 47.07/47.24 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 47.07/47.24 cut (((op1 (e10) (e10)) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H30c]. % 47.07/47.24 congruence. % 47.07/47.24 cut (((e10) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H30d]. % 47.07/47.24 cut (((e10) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H30d]. % 47.07/47.24 congruence. % 47.07/47.24 apply zenon_H30d. apply sym_equal. exact zenon_H30a. % 47.07/47.24 apply zenon_H30d. apply sym_equal. exact zenon_H30a. % 47.07/47.24 apply zenon_H30. apply refl_equal. % 47.07/47.24 apply zenon_H30. apply refl_equal. % 47.07/47.24 apply zenon_H78. apply sym_equal. exact zenon_H34. % 47.07/47.24 (* end of lemma zenon_L291_ *) % 47.07/47.24 assert (zenon_L292_ : ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e13) (e12)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.07/47.24 do 0 intro. intros zenon_Hf7 zenon_Hf9 zenon_H56 zenon_H5f zenon_H7d zenon_Hc5 zenon_Ha8 zenon_Hc4 zenon_H2b zenon_H30a zenon_H34. % 47.07/47.24 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.07/47.24 apply (zenon_L290_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.07/47.24 apply (zenon_L21_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.07/47.24 apply (zenon_L33_); trivial. % 47.07/47.24 apply (zenon_L291_); trivial. % 47.07/47.24 (* end of lemma zenon_L292_ *) % 47.07/47.24 assert (zenon_L293_ : (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H10d zenon_Hdf zenon_H306 zenon_H141 zenon_H119 zenon_Hfa zenon_Hf7 zenon_Hf9 zenon_H56 zenon_H5f zenon_H7d zenon_Hc5 zenon_Ha8 zenon_H2b zenon_H30a zenon_H34. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H102 | zenon_intro zenon_H10e ]. % 47.07/47.24 apply (zenon_L288_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H105 | zenon_intro zenon_H10f ]. % 47.07/47.24 apply (zenon_L97_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hc4 ]. % 47.07/47.24 apply (zenon_L53_); trivial. % 47.07/47.24 apply (zenon_L292_); trivial. % 47.07/47.24 (* end of lemma zenon_L293_ *) % 47.07/47.24 assert (zenon_L294_ : (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (e11) (e11))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e11) (e13)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H110 zenon_H63 zenon_H19 zenon_H1c zenon_H175 zenon_H174 zenon_H8e zenon_Hb7 zenon_H10d zenon_Hdf zenon_H306 zenon_H141 zenon_H119 zenon_Hfa zenon_Hf7 zenon_Hf9 zenon_H56 zenon_H5f zenon_H7d zenon_Hc5 zenon_H2b zenon_H30a zenon_H34. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H62 | zenon_intro zenon_H111 ]. % 47.07/47.24 apply (zenon_L18_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H112 ]. % 47.07/47.24 apply (zenon_L127_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Ha8 ]. % 47.07/47.24 apply (zenon_L30_); trivial. % 47.07/47.24 apply (zenon_L293_); trivial. % 47.07/47.24 (* end of lemma zenon_L294_ *) % 47.07/47.24 assert (zenon_L295_ : (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((e11) = (e13))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((e10) = (e11))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H30e zenon_Ha9 zenon_H149 zenon_H142 zenon_H4b zenon_H130 zenon_H51 zenon_Hed zenon_Hf1 zenon_Hbe zenon_H1c zenon_H2c zenon_H19 zenon_He6 zenon_Hde zenon_H141 zenon_H110 zenon_H63 zenon_H174 zenon_H10d zenon_H306 zenon_H119 zenon_Hf7 zenon_Hf9 zenon_H56 zenon_H5f zenon_Hc5 zenon_H2b zenon_H34 zenon_Hea zenon_H15b zenon_H23 zenon_H16f zenon_H30f zenon_Hb7 zenon_H8e. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H30e); [ zenon_intro zenon_He1 | zenon_intro zenon_H310 ]. % 47.07/47.24 apply (zenon_L281_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H310); [ zenon_intro zenon_H145 | zenon_intro zenon_H311 ]. % 47.07/47.24 apply (zenon_L95_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H311); [ zenon_intro zenon_He2 | zenon_intro zenon_H175 ]. % 47.07/47.24 apply (zenon_L286_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H14a ]. % 47.07/47.24 apply (zenon_L94_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H145 | zenon_intro zenon_H14b ]. % 47.07/47.24 apply (zenon_L95_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H147 | zenon_intro zenon_H7d ]. % 47.07/47.24 apply (zenon_L96_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.24 apply (zenon_L50_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.24 apply (zenon_L51_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H13d | zenon_intro zenon_H312 ]. % 47.07/47.24 apply (zenon_L125_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H172 | zenon_intro zenon_H313 ]. % 47.07/47.24 apply (zenon_L287_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H62 | zenon_intro zenon_H30a ]. % 47.07/47.24 apply (zenon_L18_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hdf | zenon_intro zenon_Heb ]. % 47.07/47.24 apply (zenon_L294_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_He2 | zenon_intro zenon_Hec ]. % 47.07/47.24 apply (zenon_L286_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_He5 | zenon_intro zenon_Hbd ]. % 47.07/47.24 apply (zenon_L48_); trivial. % 47.07/47.24 apply (zenon_L32_); trivial. % 47.07/47.24 apply (zenon_L30_); trivial. % 47.07/47.24 (* end of lemma zenon_L295_ *) % 47.07/47.24 assert (zenon_L296_ : (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e11)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H314 zenon_H15a zenon_H7d. % 47.07/47.24 cut (((op1 (e13) (e10)) = (e11)) = ((op1 (e13) (e10)) = (op1 (e13) (e11)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H314. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H15a. % 47.07/47.24 cut (((e11) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 47.07/47.24 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 47.07/47.24 congruence. % 47.07/47.24 apply zenon_H44. apply refl_equal. % 47.07/47.24 apply zenon_H89. apply sym_equal. exact zenon_H7d. % 47.07/47.24 (* end of lemma zenon_L296_ *) % 47.07/47.24 assert (zenon_L297_ : (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e13) (e10)) = (e11)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> False). % 47.07/47.24 do 0 intro. intros zenon_Hd0 zenon_H6a zenon_H1c zenon_H15a zenon_H314 zenon_Hb0 zenon_H19 zenon_Hb4 zenon_H5f. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.07/47.24 apply (zenon_L19_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.07/47.24 apply (zenon_L296_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.07/47.24 apply (zenon_L28_); trivial. % 47.07/47.24 apply (zenon_L29_); trivial. % 47.07/47.24 (* end of lemma zenon_L297_ *) % 47.07/47.24 assert (zenon_L298_ : (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e10) (e12)) = (e11)) -> (~((e12) = (e13))) -> False). % 47.07/47.24 do 0 intro. intros zenon_H162 zenon_H48 zenon_Hb7 zenon_H30f zenon_H16f zenon_H15b zenon_Hea zenon_Hc5 zenon_Hf9 zenon_H119 zenon_H306 zenon_H10d zenon_H174 zenon_H63 zenon_H110 zenon_Hde zenon_He6 zenon_Hbe zenon_Hf1 zenon_H130 zenon_H4b zenon_H142 zenon_H149 zenon_H30e zenon_H3b zenon_H42 zenon_H129 zenon_H315 zenon_H163 zenon_H5c zenon_H23 zenon_H56 zenon_H51 zenon_H164 zenon_H2c zenon_H2b zenon_Hb4 zenon_H19 zenon_Hb0 zenon_H314 zenon_H1c zenon_H6a zenon_Hd0 zenon_Ha9 zenon_H141 zenon_Hd8. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.07/47.24 apply (zenon_L280_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.07/47.24 apply (zenon_L282_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H50 | zenon_intro zenon_H168 ]. % 47.07/47.24 apply (zenon_L283_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H57 | zenon_intro zenon_H169 ]. % 47.07/47.24 apply (zenon_L15_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H5b | zenon_intro zenon_H8e ]. % 47.07/47.24 apply (zenon_L284_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H50 | zenon_intro zenon_H316 ]. % 47.07/47.24 apply (zenon_L283_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H316); [ zenon_intro zenon_H301 | zenon_intro zenon_H317 ]. % 47.07/47.24 apply (zenon_L285_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H317); [ zenon_intro zenon_Hee | zenon_intro zenon_Hf7 ]. % 47.07/47.24 apply (zenon_L50_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.07/47.24 apply (zenon_L7_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.24 apply (zenon_L7_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.24 apply (zenon_L295_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.24 apply (zenon_L10_); trivial. % 47.07/47.24 apply (zenon_L11_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.07/47.24 apply (zenon_L140_); trivial. % 47.07/47.24 apply (zenon_L44_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H50 | zenon_intro zenon_H168 ]. % 47.07/47.24 apply (zenon_L283_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H57 | zenon_intro zenon_H169 ]. % 47.07/47.24 apply (zenon_L15_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H5b | zenon_intro zenon_H8e ]. % 47.07/47.24 apply (zenon_L284_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.07/47.24 apply (zenon_L7_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.07/47.24 apply (zenon_L297_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.07/47.24 apply (zenon_L140_); trivial. % 47.07/47.24 apply (zenon_L44_); trivial. % 47.07/47.24 (* end of lemma zenon_L298_ *) % 47.07/47.24 assert (zenon_L299_ : (~((op1 (e13) (e13)) = (op1 (op1 (e11) (e10)) (op1 (e11) (e10))))) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H318 zenon_H34. % 47.07/47.24 cut (((e13) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 47.07/47.24 cut (((e13) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 47.07/47.24 congruence. % 47.07/47.24 apply zenon_H78. apply sym_equal. exact zenon_H34. % 47.07/47.24 apply zenon_H78. apply sym_equal. exact zenon_H34. % 47.07/47.24 (* end of lemma zenon_L299_ *) % 47.07/47.24 assert (zenon_L300_ : (((op1 (op1 (e10) (e10)) (op1 (e10) (e10))) = (e10))/\(((op1 (op1 (e11) (e10)) (op1 (e11) (e10))) = (e11))/\(((op1 (op1 (e12) (e10)) (op1 (e12) (e10))) = (e12))/\((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (e13))))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e10) (e13)) = (e11)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 47.07/47.24 do 0 intro. intros zenon_H70 zenon_H34 zenon_H14f zenon_H8f. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H73. zenon_intro zenon_H72. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H75. zenon_intro zenon_H74. % 47.07/47.24 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 47.07/47.24 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e10) (e13)) = (op1 (e13) (e13)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H8f. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H96. % 47.07/47.24 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 47.07/47.24 cut (((op1 (e13) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 47.07/47.24 congruence. % 47.07/47.24 cut (((op1 (op1 (e11) (e10)) (op1 (e11) (e10))) = (e11)) = ((op1 (e13) (e13)) = (op1 (e10) (e13)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H98. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H75. % 47.07/47.24 cut (((e11) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H319]. % 47.07/47.24 cut (((op1 (op1 (e11) (e10)) (op1 (e11) (e10))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H31a]. % 47.07/47.24 congruence. % 47.07/47.24 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 47.07/47.24 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (op1 (e11) (e10)) (op1 (e11) (e10))) = (op1 (e13) (e13)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H31a. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H96. % 47.07/47.24 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 47.07/47.24 cut (((op1 (e13) (e13)) = (op1 (op1 (e11) (e10)) (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H318]. % 47.07/47.24 congruence. % 47.07/47.24 apply (zenon_L299_); trivial. % 47.07/47.24 apply zenon_H97. apply refl_equal. % 47.07/47.24 apply zenon_H97. apply refl_equal. % 47.07/47.24 apply zenon_H319. apply sym_equal. exact zenon_H14f. % 47.07/47.24 apply zenon_H97. apply refl_equal. % 47.07/47.24 apply zenon_H97. apply refl_equal. % 47.07/47.24 (* end of lemma zenon_L300_ *) % 47.07/47.24 assert (zenon_L301_ : (((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (e10))/\(((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (e11))/\(((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e12))/\((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e13)) = (e12)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H9b zenon_H115 zenon_Hb8. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9e. zenon_intro zenon_H9d. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H9d). zenon_intro zenon_H109. zenon_intro zenon_H108. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H10b. zenon_intro zenon_H10a. % 47.07/47.24 cut (((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e12)) = ((op1 (e12) (e12)) = (op1 (e12) (e13)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H115. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H10b. % 47.07/47.24 cut (((e12) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 47.07/47.24 cut (((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 47.07/47.24 congruence. % 47.07/47.24 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 47.07/47.24 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (op1 (e12) (e12)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H123. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H9f. % 47.07/47.24 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 47.07/47.24 cut (((op1 (e12) (e12)) = (op1 (op1 (e12) (e13)) (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 47.07/47.24 congruence. % 47.07/47.24 apply (zenon_L75_); trivial. % 47.07/47.24 apply zenon_Ha0. apply refl_equal. % 47.07/47.24 apply zenon_Ha0. apply refl_equal. % 47.07/47.24 apply zenon_Hb9. apply sym_equal. exact zenon_Hb8. % 47.07/47.24 (* end of lemma zenon_L301_ *) % 47.07/47.24 assert (zenon_L302_ : (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e10) (e13)) = (e11)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e12)) -> (~((e12) = (e13))) -> False). % 47.07/47.24 do 0 intro. intros zenon_Hac zenon_H3b zenon_H2c zenon_H1b zenon_H19 zenon_Hb4 zenon_H1c zenon_Hd4 zenon_H115 zenon_Hc5 zenon_H7d zenon_H5f zenon_H56 zenon_H34 zenon_H14f zenon_H8f zenon_Hb8 zenon_Hd8. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.24 apply (zenon_L10_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.24 apply (zenon_L41_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.24 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.07/47.24 apply (zenon_L300_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.07/47.24 apply (zenon_L21_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.07/47.24 apply (zenon_L74_); trivial. % 47.07/47.24 apply (zenon_L301_); trivial. % 47.07/47.24 apply (zenon_L84_); trivial. % 47.07/47.24 (* end of lemma zenon_L302_ *) % 47.07/47.24 assert (zenon_L303_ : (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e10) (e13)) = (e11)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> False). % 47.07/47.24 do 0 intro. intros zenon_H149 zenon_H150 zenon_H4b zenon_H130 zenon_H51 zenon_Hed zenon_Hf1 zenon_H5b zenon_H9c zenon_Hac zenon_H3b zenon_H2c zenon_H1b zenon_H19 zenon_Hb4 zenon_H1c zenon_Hd4 zenon_H115 zenon_Hc5 zenon_H5f zenon_H56 zenon_H34 zenon_H14f zenon_H8f zenon_Hd8. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H14a ]. % 47.07/47.24 apply (zenon_L105_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H145 | zenon_intro zenon_H14b ]. % 47.07/47.24 apply (zenon_L95_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H147 | zenon_intro zenon_H7d ]. % 47.07/47.24 apply (zenon_L96_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.24 apply (zenon_L50_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.24 apply (zenon_L51_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.24 apply (zenon_L137_); trivial. % 47.07/47.24 apply (zenon_L302_); trivial. % 47.07/47.24 (* end of lemma zenon_L303_ *) % 47.07/47.24 assert (zenon_L304_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> False). % 47.07/47.24 do 0 intro. intros zenon_H48 zenon_H2b zenon_Hd8 zenon_H8f zenon_H14f zenon_H56 zenon_H5f zenon_Hc5 zenon_H115 zenon_Hd4 zenon_Hb4 zenon_H19 zenon_H1b zenon_Hac zenon_H9c zenon_H5b zenon_Hf1 zenon_Hed zenon_H51 zenon_H130 zenon_H4b zenon_H150 zenon_H149 zenon_H3b zenon_H2c zenon_H1c zenon_H42. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.24 apply (zenon_L7_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.24 apply (zenon_L303_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.24 apply (zenon_L10_); trivial. % 47.07/47.24 apply (zenon_L11_); trivial. % 47.07/47.24 (* end of lemma zenon_L304_ *) % 47.07/47.24 assert (zenon_L305_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((op1 (e10) (e10)) = (e10)) -> (~((e11) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e10) (e13)) = (e11)) -> (~((e11) = (e12))) -> False). % 47.07/47.24 do 0 intro. intros zenon_H163 zenon_H5c zenon_H23 zenon_Ha9 zenon_Hd8 zenon_H48 zenon_H2b zenon_H8f zenon_H56 zenon_Hc5 zenon_H115 zenon_Hd4 zenon_Hb4 zenon_H19 zenon_H1b zenon_Hac zenon_H9c zenon_Hf1 zenon_Hed zenon_H130 zenon_H4b zenon_H150 zenon_H149 zenon_H3b zenon_H2c zenon_H1c zenon_H42 zenon_H164 zenon_H14f zenon_H51. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H50 | zenon_intro zenon_H168 ]. % 47.07/47.24 apply (zenon_L283_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H57 | zenon_intro zenon_H169 ]. % 47.07/47.24 apply (zenon_L15_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H5b | zenon_intro zenon_H8e ]. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.07/47.24 apply (zenon_L7_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.07/47.24 apply (zenon_L304_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.07/47.24 apply (zenon_L133_); trivial. % 47.07/47.24 apply (zenon_L123_); trivial. % 47.07/47.24 apply (zenon_L122_); trivial. % 47.07/47.24 (* end of lemma zenon_L305_ *) % 47.07/47.24 assert (zenon_L306_ : (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e12) = (e13))) -> (~((e11) = (e13))) -> ((op1 (e10) (e10)) = (e10)) -> (~((e10) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e13)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> False). % 47.07/47.24 do 0 intro. intros zenon_H162 zenon_H15b zenon_H51 zenon_H164 zenon_H42 zenon_H2c zenon_H3b zenon_H149 zenon_H4b zenon_H130 zenon_Hf1 zenon_H9c zenon_Hac zenon_H115 zenon_Hc5 zenon_H8f zenon_H2b zenon_H48 zenon_Hd8 zenon_Ha9 zenon_H23 zenon_H5c zenon_H163 zenon_Hd4 zenon_H1b zenon_H150 zenon_H14f zenon_H56 zenon_Hd0 zenon_H6a zenon_H1c zenon_H314 zenon_Hb0 zenon_H19 zenon_Hb4. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.07/47.24 apply (zenon_L280_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.07/47.24 apply (zenon_L282_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.07/47.24 apply (zenon_L305_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H1d | zenon_intro zenon_Hd5 ]. % 47.07/47.24 apply (zenon_L4_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd6 ]. % 47.07/47.24 apply (zenon_L105_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H57 | zenon_intro zenon_H5f ]. % 47.07/47.24 apply (zenon_L15_); trivial. % 47.07/47.24 apply (zenon_L297_); trivial. % 47.07/47.24 (* end of lemma zenon_L306_ *) % 47.07/47.24 assert (zenon_L307_ : ((op2 (e20) (e20)) = (e20)) -> ((op2 (e20) (e20)) = (e22)) -> (~((e20) = (e22))) -> False). % 47.07/47.24 do 0 intro. intros zenon_H18c zenon_H1b8 zenon_H1c4. % 47.07/47.24 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 47.07/47.24 cut (((e22) = (e22)) = ((e20) = (e22))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H1c4. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H1ba. % 47.07/47.24 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.07/47.24 cut (((e22) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1c5]. % 47.07/47.24 congruence. % 47.07/47.24 cut (((op2 (e20) (e20)) = (e20)) = ((e22) = (e20))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H1c5. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H18c. % 47.07/47.24 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 47.07/47.24 cut (((op2 (e20) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bd]. % 47.07/47.24 congruence. % 47.07/47.24 exact (zenon_H1bd zenon_H1b8). % 47.07/47.24 apply zenon_H19a. apply refl_equal. % 47.07/47.24 apply zenon_H1bb. apply refl_equal. % 47.07/47.24 apply zenon_H1bb. apply refl_equal. % 47.07/47.24 (* end of lemma zenon_L307_ *) % 47.07/47.24 assert (zenon_L308_ : ((op2 (e20) (e22)) = (e21)) -> ((op2 (e20) (e22)) = (e22)) -> (~((e21) = (e22))) -> False). % 47.07/47.24 do 0 intro. intros zenon_H2cf zenon_H1c3 zenon_H1b9. % 47.07/47.24 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 47.07/47.24 cut (((e22) = (e22)) = ((e21) = (e22))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H1b9. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H1ba. % 47.07/47.24 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.07/47.24 cut (((e22) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 47.07/47.24 congruence. % 47.07/47.24 cut (((op2 (e20) (e22)) = (e21)) = ((e22) = (e21))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H1bc. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H2cf. % 47.07/47.24 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.07/47.24 cut (((op2 (e20) (e22)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 47.07/47.24 congruence. % 47.07/47.24 exact (zenon_H1c6 zenon_H1c3). % 47.07/47.24 apply zenon_H181. apply refl_equal. % 47.07/47.24 apply zenon_H1bb. apply refl_equal. % 47.07/47.24 apply zenon_H1bb. apply refl_equal. % 47.07/47.24 (* end of lemma zenon_L308_ *) % 47.07/47.24 assert (zenon_L309_ : (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e22)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H25c zenon_H1db zenon_H23c. % 47.07/47.24 cut (((op2 (e20) (e23)) = (e22)) = ((op2 (e20) (e23)) = (op2 (e22) (e23)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H25c. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H1db. % 47.07/47.24 cut (((e22) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 47.07/47.24 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 47.07/47.24 congruence. % 47.07/47.24 apply zenon_H25e. apply refl_equal. % 47.07/47.24 apply zenon_H23d. apply sym_equal. exact zenon_H23c. % 47.07/47.24 (* end of lemma zenon_L309_ *) % 47.07/47.24 assert (zenon_L310_ : (~((op2 (e22) (e22)) = (op2 (op2 (e23) (e20)) (op2 (e23) (e20))))) -> ((op2 (e23) (e20)) = (e22)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H31b zenon_H257. % 47.07/47.24 cut (((e22) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H31c]. % 47.07/47.24 cut (((e22) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H31c]. % 47.07/47.24 congruence. % 47.07/47.24 apply zenon_H31c. apply sym_equal. exact zenon_H257. % 47.07/47.24 apply zenon_H31c. apply sym_equal. exact zenon_H257. % 47.07/47.24 (* end of lemma zenon_L310_ *) % 47.07/47.24 assert (zenon_L311_ : (((op2 (op2 (e20) (e20)) (op2 (e20) (e20))) = (e20))/\(((op2 (op2 (e21) (e20)) (op2 (e21) (e20))) = (e21))/\(((op2 (op2 (e22) (e20)) (op2 (e22) (e20))) = (e22))/\((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (e23))))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e20)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H1ec zenon_H265 zenon_H257 zenon_H223. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_H1ef. zenon_intro zenon_H1ee. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H1ee). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_H1f3. zenon_intro zenon_H1f2. % 47.07/47.24 cut (((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (e23)) = ((op2 (e22) (e22)) = (op2 (e22) (e23)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H265. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H1f2. % 47.07/47.24 cut (((e23) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 47.07/47.24 cut (((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H31d]. % 47.07/47.24 congruence. % 47.07/47.24 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H21c | zenon_intro zenon_H21d ]. % 47.07/47.24 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (op2 (e22) (e22)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H31d. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H21c. % 47.07/47.24 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 47.07/47.24 cut (((op2 (e22) (e22)) = (op2 (op2 (e23) (e20)) (op2 (e23) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H31b]. % 47.07/47.24 congruence. % 47.07/47.24 apply (zenon_L310_); trivial. % 47.07/47.24 apply zenon_H21d. apply refl_equal. % 47.07/47.24 apply zenon_H21d. apply refl_equal. % 47.07/47.24 apply zenon_H241. apply sym_equal. exact zenon_H223. % 47.07/47.24 (* end of lemma zenon_L311_ *) % 47.07/47.24 assert (zenon_L312_ : (((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (e20))/\(((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (e21))/\(((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (e22))/\((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e23)) = (e20)) -> ((op2 (e21) (e20)) = (e23)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H219 zenon_H193 zenon_H31e zenon_H19c. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H21b. zenon_intro zenon_H21a. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H21a). zenon_intro zenon_H245. zenon_intro zenon_H244. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H244). zenon_intro zenon_H247. zenon_intro zenon_H246. % 47.07/47.24 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23)) = ((op2 (e20) (e20)) = (op2 (e21) (e20)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H193. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H246. % 47.07/47.24 cut (((e23) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 47.07/47.24 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H31f]. % 47.07/47.24 congruence. % 47.07/47.24 elim (classic ((op2 (e20) (e20)) = (op2 (e20) (e20)))); [ zenon_intro zenon_H197 | zenon_intro zenon_H198 ]. % 47.07/47.24 cut (((op2 (e20) (e20)) = (op2 (e20) (e20))) = ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e20)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H31f. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H197. % 47.07/47.24 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 47.07/47.24 cut (((op2 (e20) (e20)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H320]. % 47.07/47.24 congruence. % 47.07/47.24 cut (((e20) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H321]. % 47.07/47.24 cut (((e20) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H321]. % 47.07/47.24 congruence. % 47.07/47.24 apply zenon_H321. apply sym_equal. exact zenon_H31e. % 47.07/47.24 apply zenon_H321. apply sym_equal. exact zenon_H31e. % 47.07/47.24 apply zenon_H198. apply refl_equal. % 47.07/47.24 apply zenon_H198. apply refl_equal. % 47.07/47.24 apply zenon_H1f4. apply sym_equal. exact zenon_H19c. % 47.07/47.24 (* end of lemma zenon_L312_ *) % 47.07/47.24 assert (zenon_L313_ : ((op2 (e22) (e23)) = (e23)) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e23)) = (e20)) -> ((op2 (e21) (e20)) = (e23)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H223 zenon_H257 zenon_H265 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H20a zenon_H1db zenon_H207 zenon_H193 zenon_H31e zenon_H19c. % 47.07/47.24 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.07/47.24 apply (zenon_L311_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.07/47.24 apply (zenon_L170_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.07/47.24 apply (zenon_L172_); trivial. % 47.07/47.24 apply (zenon_L312_); trivial. % 47.07/47.24 (* end of lemma zenon_L313_ *) % 47.07/47.24 assert (zenon_L314_ : (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e22)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e23)) = (e20)) -> ((op2 (e21) (e20)) = (e23)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H24b zenon_H234 zenon_H1a3 zenon_H14 zenon_H194 zenon_H299 zenon_H29a zenon_H23a zenon_H1b3 zenon_H183 zenon_H2b5 zenon_H25c zenon_H257 zenon_H265 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H20a zenon_H1db zenon_H207 zenon_H193 zenon_H31e zenon_H19c. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H233 | zenon_intro zenon_H24c ]. % 47.07/47.24 apply (zenon_L179_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H222 | zenon_intro zenon_H24d ]. % 47.07/47.24 apply (zenon_L234_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H23c | zenon_intro zenon_H223 ]. % 47.07/47.24 apply (zenon_L309_); trivial. % 47.07/47.24 apply (zenon_L313_); trivial. % 47.07/47.24 (* end of lemma zenon_L314_ *) % 47.07/47.24 assert (zenon_L315_ : ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e23)) = (e20)) -> ((op2 (e21) (e20)) = (e23)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H257 zenon_H270 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H23f zenon_H223 zenon_H26c zenon_H193 zenon_H31e zenon_H19c. % 47.07/47.24 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_H1ef. zenon_intro zenon_H1ee. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H1ee). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 47.07/47.24 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_H1f3. zenon_intro zenon_H1f2. % 47.07/47.24 cut (((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (e23)) = ((op2 (e22) (e22)) = (op2 (e23) (e22)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H270. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H1f2. % 47.07/47.24 cut (((e23) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 47.07/47.24 cut (((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H31d]. % 47.07/47.24 congruence. % 47.07/47.24 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H21c | zenon_intro zenon_H21d ]. % 47.07/47.24 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (op2 (e22) (e22)))). % 47.07/47.24 intro zenon_D_pnotp. % 47.07/47.24 apply zenon_H31d. % 47.07/47.24 rewrite <- zenon_D_pnotp. % 47.07/47.24 exact zenon_H21c. % 47.07/47.24 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 47.07/47.24 cut (((op2 (e22) (e22)) = (op2 (op2 (e23) (e20)) (op2 (e23) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H31b]. % 47.07/47.24 congruence. % 47.07/47.24 apply (zenon_L310_); trivial. % 47.07/47.24 apply zenon_H21d. apply refl_equal. % 47.07/47.24 apply zenon_H21d. apply refl_equal. % 47.07/47.24 apply zenon_H26f. apply sym_equal. exact zenon_H26c. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.07/47.24 apply (zenon_L170_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.07/47.24 apply (zenon_L197_); trivial. % 47.07/47.24 apply (zenon_L312_); trivial. % 47.07/47.24 (* end of lemma zenon_L315_ *) % 47.07/47.24 assert (zenon_L316_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e23)) = (e22)) -> (~((e20) = (e21))) -> ((op2 (e21) (e23)) = (e21)) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (e21) (e21))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e21) (e20)) = (e23)) -> False). % 47.07/47.24 do 0 intro. intros zenon_H322 zenon_H1c4 zenon_H1db zenon_H1df zenon_H1de zenon_H234 zenon_H183 zenon_H14 zenon_H257 zenon_H270 zenon_H1be zenon_H1d7 zenon_H1f9 zenon_H23f zenon_H223 zenon_H26c zenon_H193 zenon_H19c. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_H2e6 | zenon_intro zenon_H323 ]. % 47.07/47.24 apply (zenon_L261_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1dd | zenon_intro zenon_H324 ]. % 47.07/47.24 apply (zenon_L166_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H233 | zenon_intro zenon_H31e ]. % 47.07/47.24 apply (zenon_L179_); trivial. % 47.07/47.24 apply (zenon_L315_); trivial. % 47.07/47.24 (* end of lemma zenon_L316_ *) % 47.07/47.24 assert (zenon_L317_ : ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((op2 (e22) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (((op2 (e20) (e22)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e23) (e22)) = (e23))))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e21) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e21))\/((op2 (e23) (e20)) = (e21))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((e20) = (e23))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/((op2 (e21) (e23)) = (e20))))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e20) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e23) (e22)) = (e21))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e21)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/((op2 (e23) (e21)) = (e23))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e22))) -> ((e22) = (op2 (e21) (e21))) -> (~((op2 (e20) (e22)) = (op2 (e21) (e22)))) -> (~((e20) = (e21))) -> (~((e21) = (e23))) -> ((op2 (e20) (e22)) = (e21)) -> (~((e22) = (e23))) -> False). % 47.07/47.24 do 0 intro. intros zenon_H18c zenon_H1aa zenon_H14 zenon_H194 zenon_H1a3 zenon_H1e4 zenon_H2bc zenon_H2a8 zenon_H2ab zenon_H23f zenon_H1be zenon_H270 zenon_H234 zenon_H1c4 zenon_H322 zenon_H265 zenon_H20a zenon_H251 zenon_H2d5 zenon_H2ba zenon_H18d zenon_H2ef zenon_H2ec zenon_H2ee zenon_H19d zenon_H2bd zenon_H185 zenon_H287 zenon_H28d zenon_H27c zenon_H225 zenon_H271 zenon_H25f zenon_H259 zenon_H230 zenon_H229 zenon_H2eb zenon_H2f7 zenon_H2bb zenon_H2d7 zenon_H27b zenon_H2a0 zenon_H216 zenon_H2fc zenon_H1c7 zenon_H2d4 zenon_H27a zenon_H262 zenon_H27d zenon_H2d2 zenon_H2e7 zenon_H2d1 zenon_H24b zenon_H299 zenon_H23a zenon_H1b3 zenon_H2b5 zenon_H25c zenon_H2d3 zenon_H193 zenon_H1b0 zenon_H1b9 zenon_H183 zenon_H1cf zenon_H1df zenon_H1d3 zenon_H2cf zenon_H276. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.07/47.24 apply (zenon_L307_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.07/47.24 apply (zenon_L156_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.07/47.24 apply (zenon_L308_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H27d); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H280 ]. % 47.07/47.24 apply (zenon_L307_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H281 ]. % 47.07/47.24 apply (zenon_L158_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H23b | zenon_intro zenon_H257 ]. % 47.07/47.24 apply (zenon_L222_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.24 apply (zenon_L148_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.07/47.24 apply (zenon_L148_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H19b | zenon_intro zenon_H2db ]. % 47.07/47.24 apply (zenon_L150_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2dc ]. % 47.07/47.24 apply (zenon_L160_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H1dd ]. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.07/47.24 apply (zenon_L145_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.07/47.24 apply (zenon_L160_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2dd ]. % 47.07/47.24 apply (zenon_L162_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2de ]. % 47.07/47.24 apply (zenon_L163_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2de); [ zenon_intro zenon_H296 | zenon_intro zenon_H1de ]. % 47.07/47.24 apply (zenon_L253_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_H29f | zenon_intro zenon_H2c2 ]. % 47.07/47.24 apply (zenon_L220_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2c3 ]. % 47.07/47.24 apply (zenon_L163_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2c3); [ zenon_intro zenon_H2b1 | zenon_intro zenon_H1f9 ]. % 47.07/47.24 apply (zenon_L224_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2bc); [ zenon_intro zenon_H23b | zenon_intro zenon_H2c4 ]. % 47.07/47.24 apply (zenon_L222_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_H2aa | zenon_intro zenon_H2c5 ]. % 47.07/47.24 apply (zenon_L223_); trivial. % 47.07/47.24 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H29a | zenon_intro zenon_H23c ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.07/47.25 apply (zenon_L151_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.07/47.25 apply (zenon_L168_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_H2e6 | zenon_intro zenon_H323 ]. % 47.07/47.25 apply (zenon_L278_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1dd | zenon_intro zenon_H324 ]. % 47.07/47.25 apply (zenon_L276_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H233 | zenon_intro zenon_H31e ]. % 47.07/47.25 apply (zenon_L179_); trivial. % 47.07/47.25 apply (zenon_L314_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_H24e | zenon_intro zenon_H2df ]. % 47.07/47.25 apply (zenon_L262_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H250 | zenon_intro zenon_H2e0 ]. % 47.07/47.25 apply (zenon_L187_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H207 | zenon_intro zenon_H26c ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_H2e6 | zenon_intro zenon_H323 ]. % 47.07/47.25 apply (zenon_L261_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1dd | zenon_intro zenon_H324 ]. % 47.07/47.25 apply (zenon_L166_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H233 | zenon_intro zenon_H31e ]. % 47.07/47.25 apply (zenon_L179_); trivial. % 47.07/47.25 apply (zenon_L313_); trivial. % 47.07/47.25 apply (zenon_L316_); trivial. % 47.07/47.25 apply (zenon_L309_); trivial. % 47.07/47.25 apply (zenon_L167_); trivial. % 47.07/47.25 apply (zenon_L276_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.07/47.25 apply (zenon_L151_); trivial. % 47.07/47.25 apply (zenon_L152_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.25 apply (zenon_L262_); trivial. % 47.07/47.25 apply (zenon_L217_); trivial. % 47.07/47.25 (* end of lemma zenon_L317_ *) % 47.07/47.25 assert (zenon_L318_ : (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e20)) = (e21)) -> ((op2 (e23) (e21)) = (e21)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H325 zenon_H2b8 zenon_H1f9. % 47.07/47.25 cut (((op2 (e23) (e20)) = (e21)) = ((op2 (e23) (e20)) = (op2 (e23) (e21)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H325. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H2b8. % 47.07/47.25 cut (((e21) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H205]. % 47.07/47.25 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1ac]. % 47.07/47.25 congruence. % 47.07/47.25 apply zenon_H1ac. apply refl_equal. % 47.07/47.25 apply zenon_H205. apply sym_equal. exact zenon_H1f9. % 47.07/47.25 (* end of lemma zenon_L318_ *) % 47.07/47.25 assert (zenon_L319_ : (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e23) (e20)) = (e21)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H230 zenon_H1e4 zenon_H14 zenon_H2b8 zenon_H325 zenon_H229 zenon_H183 zenon_H22d zenon_H1d7. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H231 ]. % 47.07/47.25 apply (zenon_L167_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H232 ]. % 47.07/47.25 apply (zenon_L318_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H228 | zenon_intro zenon_H22e ]. % 47.07/47.25 apply (zenon_L176_); trivial. % 47.07/47.25 apply (zenon_L177_); trivial. % 47.07/47.25 (* end of lemma zenon_L319_ *) % 47.07/47.25 assert (zenon_L320_ : (~((e20) = (e21))) -> (~((op2 (e20) (e22)) = (op2 (e21) (e22)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e21)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e23) (e22)) = (e21))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/((op2 (e21) (e23)) = (e20))))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((e20) = (e23))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e21) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e21))\/((op2 (e23) (e20)) = (e21))))) -> (((op2 (e20) (e22)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e21) = (e22))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((e21) = (e23))) -> ((op2 (e20) (e22)) = (e21)) -> (~((e22) = (e23))) -> False). % 47.07/47.25 do 0 intro. intros zenon_H1df zenon_H1cf zenon_H1b0 zenon_H2d3 zenon_H25c zenon_H2b5 zenon_H1b3 zenon_H23a zenon_H299 zenon_H24b zenon_H2d1 zenon_H2e7 zenon_H2d2 zenon_H27d zenon_H262 zenon_H2d4 zenon_H1c7 zenon_H2fc zenon_H216 zenon_H2a0 zenon_H2d7 zenon_H2bb zenon_H2f7 zenon_H2eb zenon_H259 zenon_H25f zenon_H271 zenon_H225 zenon_H27c zenon_H28d zenon_H287 zenon_H185 zenon_H2bd zenon_H19d zenon_H2ee zenon_H2ec zenon_H2ef zenon_H18d zenon_H2ba zenon_H2d5 zenon_H251 zenon_H20a zenon_H265 zenon_H322 zenon_H234 zenon_H270 zenon_H23f zenon_H2ab zenon_H2bc zenon_H1a3 zenon_H1aa zenon_H27a zenon_H1c4 zenon_H18c zenon_H1be zenon_H1b9 zenon_H27b zenon_H194 zenon_H193 zenon_H22d zenon_H183 zenon_H229 zenon_H325 zenon_H14 zenon_H1e4 zenon_H230 zenon_H1d3 zenon_H2cf zenon_H276. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.07/47.25 apply (zenon_L279_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.07/47.25 apply (zenon_L219_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.07/47.25 apply (zenon_L317_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.07/47.25 apply (zenon_L307_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.07/47.25 apply (zenon_L156_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.07/47.25 apply (zenon_L308_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.25 apply (zenon_L148_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.25 apply (zenon_L319_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.25 apply (zenon_L262_); trivial. % 47.07/47.25 apply (zenon_L217_); trivial. % 47.07/47.25 (* end of lemma zenon_L320_ *) % 47.07/47.25 assert (zenon_L321_ : (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e22)) -> ((op2 (e22) (e22)) = (e22)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H216 zenon_H1c3 zenon_H29a. % 47.07/47.25 cut (((op2 (e20) (e22)) = (e22)) = ((op2 (e20) (e22)) = (op2 (e22) (e22)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H216. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H1c3. % 47.07/47.25 cut (((e22) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H29b]. % 47.07/47.25 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 47.07/47.25 congruence. % 47.07/47.25 apply zenon_H18f. apply refl_equal. % 47.07/47.25 apply zenon_H29b. apply sym_equal. exact zenon_H29a. % 47.07/47.25 (* end of lemma zenon_L321_ *) % 47.07/47.25 assert (zenon_L322_ : (~((op2 (e23) (e23)) = (op2 (op2 (e21) (e20)) (op2 (e21) (e20))))) -> ((op2 (e21) (e20)) = (e23)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H326 zenon_H19c. % 47.07/47.25 cut (((e23) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 47.07/47.25 cut (((e23) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 47.07/47.25 congruence. % 47.07/47.25 apply zenon_H1f4. apply sym_equal. exact zenon_H19c. % 47.07/47.25 apply zenon_H1f4. apply sym_equal. exact zenon_H19c. % 47.07/47.25 (* end of lemma zenon_L322_ *) % 47.07/47.25 assert (zenon_L323_ : (((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (e20))/\(((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (e21))/\(((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (e22))/\((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23))))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e23)) = (e22)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H219 zenon_H265 zenon_H23c. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H21b. zenon_intro zenon_H21a. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H21a). zenon_intro zenon_H245. zenon_intro zenon_H244. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H244). zenon_intro zenon_H247. zenon_intro zenon_H246. % 47.07/47.25 cut (((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (e22)) = ((op2 (e22) (e22)) = (op2 (e22) (e23)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H265. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H247. % 47.07/47.25 cut (((e22) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 47.07/47.25 cut (((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H2b4]. % 47.07/47.25 congruence. % 47.07/47.25 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H21c | zenon_intro zenon_H21d ]. % 47.07/47.25 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (op2 (e22) (e22)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H2b4. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H21c. % 47.07/47.25 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 47.07/47.25 cut (((op2 (e22) (e22)) = (op2 (op2 (e22) (e23)) (op2 (e22) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H2b3]. % 47.07/47.25 congruence. % 47.07/47.25 apply (zenon_L226_); trivial. % 47.07/47.25 apply zenon_H21d. apply refl_equal. % 47.07/47.25 apply zenon_H21d. apply refl_equal. % 47.07/47.25 apply zenon_H23d. apply sym_equal. exact zenon_H23c. % 47.07/47.25 (* end of lemma zenon_L323_ *) % 47.07/47.25 assert (zenon_L324_ : (((op2 (e20) (e20)) = (e21))\/(((op2 (e21) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e21))\/((op2 (e23) (e20)) = (e21))))) -> (~((e20) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((e20) = (e23))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e21) = (e23))) -> (~((e22) = (e23))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> ((op2 (e20) (e23)) = (e21)) -> (~((e21) = (e22))) -> False). % 47.07/47.25 do 0 intro. intros zenon_H2ba zenon_H1df zenon_H1aa zenon_H1a3 zenon_H2bd zenon_H185 zenon_H20a zenon_H23f zenon_H265 zenon_H19d zenon_H225 zenon_H216 zenon_H2ab zenon_H2bc zenon_H1b3 zenon_H2bb zenon_H1b0 zenon_H27a zenon_H1c4 zenon_H18c zenon_H1be zenon_H1d3 zenon_H276 zenon_H230 zenon_H1e4 zenon_H14 zenon_H325 zenon_H229 zenon_H183 zenon_H22d zenon_H193 zenon_H194 zenon_H27b zenon_H1da zenon_H1b9. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.07/47.25 apply (zenon_L279_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.07/47.25 apply (zenon_L219_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.07/47.25 apply (zenon_L307_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.07/47.25 apply (zenon_L156_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.25 apply (zenon_L148_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.07/47.25 apply (zenon_L148_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.07/47.25 apply (zenon_L145_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.07/47.25 apply (zenon_L160_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_H29f | zenon_intro zenon_H2c2 ]. % 47.07/47.25 apply (zenon_L220_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2c3 ]. % 47.07/47.25 apply (zenon_L163_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2c3); [ zenon_intro zenon_H2b1 | zenon_intro zenon_H1f9 ]. % 47.07/47.25 apply (zenon_L224_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2bc); [ zenon_intro zenon_H23b | zenon_intro zenon_H2c4 ]. % 47.07/47.25 apply (zenon_L222_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_H2aa | zenon_intro zenon_H2c5 ]. % 47.07/47.25 apply (zenon_L223_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H29a | zenon_intro zenon_H23c ]. % 47.07/47.25 apply (zenon_L321_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.07/47.25 apply (zenon_L151_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.07/47.25 apply (zenon_L168_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.07/47.25 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_H1ef. zenon_intro zenon_H1ee. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H1ee). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 47.07/47.25 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 47.07/47.25 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e20) (e23)) = (op2 (e23) (e23)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H20a. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H211. % 47.07/47.25 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 47.07/47.25 cut (((op2 (e23) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H213]. % 47.07/47.25 congruence. % 47.07/47.25 cut (((op2 (op2 (e21) (e20)) (op2 (e21) (e20))) = (e21)) = ((op2 (e23) (e23)) = (op2 (e20) (e23)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H213. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H1f1. % 47.07/47.25 cut (((e21) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H327]. % 47.07/47.25 cut (((op2 (op2 (e21) (e20)) (op2 (e21) (e20))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H328]. % 47.07/47.25 congruence. % 47.07/47.25 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 47.07/47.25 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (op2 (e21) (e20)) (op2 (e21) (e20))) = (op2 (e23) (e23)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H328. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H211. % 47.07/47.25 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 47.07/47.25 cut (((op2 (e23) (e23)) = (op2 (op2 (e21) (e20)) (op2 (e21) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H326]. % 47.07/47.25 congruence. % 47.07/47.25 apply (zenon_L322_); trivial. % 47.07/47.25 apply zenon_H212. apply refl_equal. % 47.07/47.25 apply zenon_H212. apply refl_equal. % 47.07/47.25 apply zenon_H327. apply sym_equal. exact zenon_H1da. % 47.07/47.25 apply zenon_H212. apply refl_equal. % 47.07/47.25 apply zenon_H212. apply refl_equal. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.07/47.25 apply (zenon_L170_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.07/47.25 apply (zenon_L225_); trivial. % 47.07/47.25 apply (zenon_L323_); trivial. % 47.07/47.25 apply (zenon_L210_); trivial. % 47.07/47.25 apply (zenon_L167_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.07/47.25 apply (zenon_L151_); trivial. % 47.07/47.25 apply (zenon_L152_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.25 apply (zenon_L206_); trivial. % 47.07/47.25 apply (zenon_L207_); trivial. % 47.07/47.25 apply (zenon_L165_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.07/47.25 apply (zenon_L307_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.07/47.25 apply (zenon_L156_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.25 apply (zenon_L148_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.25 apply (zenon_L319_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.25 apply (zenon_L206_); trivial. % 47.07/47.25 apply (zenon_L207_); trivial. % 47.07/47.25 apply (zenon_L165_); trivial. % 47.07/47.25 (* end of lemma zenon_L324_ *) % 47.07/47.25 assert (zenon_L325_ : (~((h2 (e12)) = (e22))) -> ((h2 (e12)) = (op2 (e21) (e21))) -> ((e22) = (op2 (e21) (e21))) -> False). % 47.07/47.25 do 0 intro. intros zenon_H329 zenon_H32a zenon_H183. % 47.07/47.25 cut (((h2 (e12)) = (op2 (e21) (e21))) = ((h2 (e12)) = (e22))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H329. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H32a. % 47.07/47.25 cut (((op2 (e21) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 47.07/47.25 cut (((h2 (e12)) = (h2 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H32b]. % 47.07/47.25 congruence. % 47.07/47.25 apply zenon_H32b. apply refl_equal. % 47.07/47.25 apply zenon_H184. apply sym_equal. exact zenon_H183. % 47.07/47.25 (* end of lemma zenon_L325_ *) % 47.07/47.25 assert (zenon_L326_ : ((e12) = (op1 (e11) (e11))) -> ((op1 (e11) (e11)) = (e10)) -> (~((e10) = (e12))) -> False). % 47.07/47.25 do 0 intro. intros zenon_H19 zenon_H32c zenon_H5c. % 47.07/47.25 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 47.07/47.25 cut (((e12) = (e12)) = ((e10) = (e12))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H5c. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H52. % 47.07/47.25 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.07/47.25 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 47.07/47.25 congruence. % 47.07/47.25 cut (((e12) = (op1 (e11) (e11))) = ((e12) = (e10))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H5d. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H19. % 47.07/47.25 cut (((op1 (e11) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32d]. % 47.07/47.25 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.07/47.25 congruence. % 47.07/47.25 apply zenon_H53. apply refl_equal. % 47.07/47.25 exact (zenon_H32d zenon_H32c). % 47.07/47.25 apply zenon_H53. apply refl_equal. % 47.07/47.25 apply zenon_H53. apply refl_equal. % 47.07/47.25 (* end of lemma zenon_L326_ *) % 47.07/47.25 assert (zenon_L327_ : ((op1 (e12) (e11)) = (e10)) -> ((op1 (e12) (e11)) = (e13)) -> (~((e10) = (e13))) -> False). % 47.07/47.25 do 0 intro. intros zenon_H32e zenon_H60 zenon_H35. % 47.07/47.25 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 47.07/47.25 cut (((e13) = (e13)) = ((e10) = (e13))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H35. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H36. % 47.07/47.25 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 47.07/47.25 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 47.07/47.25 congruence. % 47.07/47.25 cut (((op1 (e12) (e11)) = (e10)) = ((e13) = (e10))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H38. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H32e. % 47.07/47.25 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 47.07/47.25 cut (((op1 (e12) (e11)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H32f]. % 47.07/47.25 congruence. % 47.07/47.25 exact (zenon_H32f zenon_H60). % 47.07/47.25 apply zenon_H32. apply refl_equal. % 47.07/47.25 apply zenon_H37. apply refl_equal. % 47.07/47.25 apply zenon_H37. apply refl_equal. % 47.07/47.25 (* end of lemma zenon_L327_ *) % 47.07/47.25 assert (zenon_L328_ : ((op1 (e13) (e10)) = (e11)) -> ((op1 (e13) (e10)) = (e12)) -> (~((e11) = (e12))) -> False). % 47.07/47.25 do 0 intro. intros zenon_H15a zenon_Hf7 zenon_H51. % 47.07/47.25 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 47.07/47.25 cut (((e12) = (e12)) = ((e11) = (e12))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H51. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H52. % 47.07/47.25 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 47.07/47.25 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 47.07/47.25 congruence. % 47.07/47.25 cut (((op1 (e13) (e10)) = (e11)) = ((e12) = (e11))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H54. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H15a. % 47.07/47.25 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 47.07/47.25 cut (((op1 (e13) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 47.07/47.25 congruence. % 47.07/47.25 exact (zenon_Hf8 zenon_Hf7). % 47.07/47.25 apply zenon_H17. apply refl_equal. % 47.07/47.25 apply zenon_H53. apply refl_equal. % 47.07/47.25 apply zenon_H53. apply refl_equal. % 47.07/47.25 (* end of lemma zenon_L328_ *) % 47.07/47.25 assert (zenon_L329_ : (((op1 (op1 (e10) (e10)) (op1 (e10) (e10))) = (e10))/\(((op1 (op1 (e11) (e10)) (op1 (e11) (e10))) = (e11))/\(((op1 (op1 (e12) (e10)) (op1 (e12) (e10))) = (e12))/\((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e13)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H70 zenon_Hb0 zenon_H15a zenon_Hb5. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H73. zenon_intro zenon_H72. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H75. zenon_intro zenon_H74. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H74). zenon_intro zenon_H77. zenon_intro zenon_H76. % 47.07/47.25 cut (((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (e13)) = ((op1 (e11) (e11)) = (op1 (e13) (e11)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_Hb0. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H76. % 47.07/47.25 cut (((e13) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 47.07/47.25 cut (((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H330]. % 47.07/47.25 congruence. % 47.07/47.25 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H84 | zenon_intro zenon_H58 ]. % 47.07/47.25 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (op1 (e11) (e11)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H330. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H84. % 47.07/47.25 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 47.07/47.25 cut (((op1 (e11) (e11)) = (op1 (op1 (e13) (e10)) (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H331]. % 47.07/47.25 congruence. % 47.07/47.25 cut (((e11) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H332]. % 47.07/47.25 cut (((e11) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H332]. % 47.07/47.25 congruence. % 47.07/47.25 apply zenon_H332. apply sym_equal. exact zenon_H15a. % 47.07/47.25 apply zenon_H332. apply sym_equal. exact zenon_H15a. % 47.07/47.25 apply zenon_H58. apply refl_equal. % 47.07/47.25 apply zenon_H58. apply refl_equal. % 47.07/47.25 apply zenon_Hb6. apply sym_equal. exact zenon_Hb5. % 47.07/47.25 (* end of lemma zenon_L329_ *) % 47.07/47.25 assert (zenon_L330_ : (((op1 (op1 (e10) (e12)) (op1 (e10) (e12))) = (e10))/\(((op1 (op1 (e11) (e12)) (op1 (e11) (e12))) = (e11))/\(((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (e12))/\((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e12)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H8d zenon_H2b zenon_H102 zenon_H34. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H91. zenon_intro zenon_H90. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H93. zenon_intro zenon_H92. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H92). zenon_intro zenon_H95. zenon_intro zenon_H94. % 47.07/47.25 cut (((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (e13)) = ((op1 (e10) (e10)) = (op1 (e11) (e10)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H2b. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H94. % 47.07/47.25 cut (((e13) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 47.07/47.25 cut (((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H333]. % 47.07/47.25 congruence. % 47.07/47.25 elim (classic ((op1 (e10) (e10)) = (op1 (e10) (e10)))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 47.07/47.25 cut (((op1 (e10) (e10)) = (op1 (e10) (e10))) = ((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (op1 (e10) (e10)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H333. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H2f. % 47.07/47.25 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 47.07/47.25 cut (((op1 (e10) (e10)) = (op1 (op1 (e13) (e12)) (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H334]. % 47.07/47.25 congruence. % 47.07/47.25 cut (((e10) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 47.07/47.25 cut (((e10) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 47.07/47.25 congruence. % 47.07/47.25 apply zenon_H103. apply sym_equal. exact zenon_H102. % 47.07/47.25 apply zenon_H103. apply sym_equal. exact zenon_H102. % 47.07/47.25 apply zenon_H30. apply refl_equal. % 47.07/47.25 apply zenon_H30. apply refl_equal. % 47.07/47.25 apply zenon_H78. apply sym_equal. exact zenon_H34. % 47.07/47.25 (* end of lemma zenon_L330_ *) % 47.07/47.25 assert (zenon_L331_ : (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e12)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e13) (e10)) = (e11)) -> False). % 47.07/47.25 do 0 intro. intros zenon_Hb0 zenon_H8f zenon_Hd7 zenon_Hb5 zenon_H34 zenon_H102 zenon_H2b zenon_H335 zenon_H172 zenon_H15a. % 47.07/47.25 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.07/47.25 apply (zenon_L329_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.07/47.25 apply (zenon_L82_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.07/47.25 apply (zenon_L330_); trivial. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9e. zenon_intro zenon_H9d. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H9d). zenon_intro zenon_H109. zenon_intro zenon_H108. % 47.07/47.25 cut (((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (e11)) = ((op1 (e10) (e10)) = (op1 (e13) (e10)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H335. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H109. % 47.07/47.25 cut (((e11) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H332]. % 47.07/47.25 cut (((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H336]. % 47.07/47.25 congruence. % 47.07/47.25 elim (classic ((op1 (e10) (e10)) = (op1 (e10) (e10)))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 47.07/47.25 cut (((op1 (e10) (e10)) = (op1 (e10) (e10))) = ((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (op1 (e10) (e10)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H336. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H2f. % 47.07/47.25 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 47.07/47.25 cut (((op1 (e10) (e10)) = (op1 (op1 (e11) (e13)) (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H337]. % 47.07/47.25 congruence. % 47.07/47.25 cut (((e10) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H173]. % 47.07/47.25 cut (((e10) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H173]. % 47.07/47.25 congruence. % 47.07/47.25 apply zenon_H173. apply sym_equal. exact zenon_H172. % 47.07/47.25 apply zenon_H173. apply sym_equal. exact zenon_H172. % 47.07/47.25 apply zenon_H30. apply refl_equal. % 47.07/47.25 apply zenon_H30. apply refl_equal. % 47.07/47.25 apply zenon_H332. apply sym_equal. exact zenon_H15a. % 47.07/47.25 (* end of lemma zenon_L331_ *) % 47.07/47.25 assert (zenon_L332_ : (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e13) (e13)) = (e10)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H338 zenon_H172 zenon_H30a. % 47.07/47.25 cut (((op1 (e11) (e13)) = (e10)) = ((op1 (e11) (e13)) = (op1 (e13) (e13)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H338. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H172. % 47.07/47.25 cut (((e10) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H30d]. % 47.07/47.25 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 47.07/47.25 congruence. % 47.07/47.25 apply zenon_H139. apply refl_equal. % 47.07/47.25 apply zenon_H30d. apply sym_equal. exact zenon_H30a. % 47.07/47.25 (* end of lemma zenon_L332_ *) % 47.07/47.25 assert (zenon_L333_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e13) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H339 zenon_H15b zenon_H6a zenon_H19 zenon_H1c zenon_H15a zenon_H335 zenon_H2b zenon_H34 zenon_Hb5 zenon_Hd7 zenon_H8f zenon_Hb0 zenon_H338 zenon_H172. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.25 apply (zenon_L119_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.25 apply (zenon_L331_); trivial. % 47.07/47.25 apply (zenon_L332_); trivial. % 47.07/47.25 (* end of lemma zenon_L333_ *) % 47.07/47.25 assert (zenon_L334_ : ((op1 (e13) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H15a zenon_Hb0 zenon_Hc5 zenon_Hb5 zenon_Ha8 zenon_Hfb zenon_H115 zenon_H2b zenon_H30a zenon_H34. % 47.07/47.25 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.07/47.25 apply (zenon_L329_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.07/47.25 apply (zenon_L37_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H91. zenon_intro zenon_H90. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H93. zenon_intro zenon_H92. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H92). zenon_intro zenon_H95. zenon_intro zenon_H94. % 47.07/47.25 cut (((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (e13)) = ((op1 (e12) (e12)) = (op1 (e12) (e13)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H115. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H94. % 47.07/47.25 cut (((e13) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 47.07/47.25 cut (((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H33c]. % 47.07/47.25 congruence. % 47.07/47.25 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 47.07/47.25 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (op1 (e12) (e12)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H33c. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H9f. % 47.07/47.25 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 47.07/47.25 cut (((op1 (e12) (e12)) = (op1 (op1 (e13) (e12)) (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H33d]. % 47.07/47.25 congruence. % 47.07/47.25 cut (((e12) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 47.07/47.25 cut (((e12) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 47.07/47.25 congruence. % 47.07/47.25 apply zenon_Hfc. apply sym_equal. exact zenon_Hfb. % 47.07/47.25 apply zenon_Hfc. apply sym_equal. exact zenon_Hfb. % 47.07/47.25 apply zenon_Ha0. apply refl_equal. % 47.07/47.25 apply zenon_Ha0. apply refl_equal. % 47.07/47.25 apply zenon_Hc7. apply sym_equal. exact zenon_Ha8. % 47.07/47.25 apply (zenon_L291_); trivial. % 47.07/47.25 (* end of lemma zenon_L334_ *) % 47.07/47.25 assert (zenon_L335_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H339 zenon_H15b zenon_H6a zenon_H19 zenon_H1c zenon_Hdf zenon_H306 zenon_H15a zenon_Hb0 zenon_Hc5 zenon_Hb5 zenon_Ha8 zenon_Hfb zenon_H115 zenon_H2b zenon_H34. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.25 apply (zenon_L119_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.25 apply (zenon_L288_); trivial. % 47.07/47.25 apply (zenon_L334_); trivial. % 47.07/47.25 (* end of lemma zenon_L335_ *) % 47.07/47.25 assert (zenon_L336_ : (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e13)) = (e12)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H10d zenon_Hdf zenon_H306 zenon_H34 zenon_H30a zenon_H2b zenon_H115 zenon_H15a zenon_Hb0 zenon_Hb5 zenon_Hc5 zenon_Ha8 zenon_Hf9 zenon_Hff. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H102 | zenon_intro zenon_H10e ]. % 47.07/47.25 apply (zenon_L288_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H105 | zenon_intro zenon_H10f ]. % 47.07/47.25 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.07/47.25 apply (zenon_L329_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.07/47.25 apply (zenon_L37_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.07/47.25 apply (zenon_L63_); trivial. % 47.07/47.25 apply (zenon_L291_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hc4 ]. % 47.07/47.25 apply (zenon_L334_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.07/47.25 apply (zenon_L329_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.07/47.25 apply (zenon_L37_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.07/47.25 apply (zenon_L33_); trivial. % 47.07/47.25 apply (zenon_L59_); trivial. % 47.07/47.25 (* end of lemma zenon_L336_ *) % 47.07/47.25 assert (zenon_L337_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e12))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((e10) = (e11))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> False). % 47.07/47.25 do 0 intro. intros zenon_H116 zenon_H51 zenon_H1c zenon_H19 zenon_H6a zenon_H15b zenon_H339 zenon_H10d zenon_Hdf zenon_H306 zenon_H34 zenon_H30a zenon_H2b zenon_H115 zenon_H15a zenon_Hb0 zenon_Hb5 zenon_Hc5 zenon_Ha8 zenon_Hf9. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.07/47.25 apply (zenon_L328_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.07/47.25 apply (zenon_L28_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.07/47.25 apply (zenon_L335_); trivial. % 47.07/47.25 apply (zenon_L336_); trivial. % 47.07/47.25 (* end of lemma zenon_L337_ *) % 47.07/47.25 assert (zenon_L338_ : (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e13)) = (e12)) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e12))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((e10) = (e11))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> False). % 47.07/47.25 do 0 intro. intros zenon_H110 zenon_H63 zenon_H175 zenon_H174 zenon_Hff zenon_H116 zenon_H51 zenon_H1c zenon_H19 zenon_H6a zenon_H15b zenon_H339 zenon_H10d zenon_Hdf zenon_H306 zenon_H34 zenon_H30a zenon_H2b zenon_H115 zenon_H15a zenon_Hb0 zenon_Hb5 zenon_Hc5 zenon_Hf9. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H62 | zenon_intro zenon_H111 ]. % 47.07/47.25 apply (zenon_L18_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H112 ]. % 47.07/47.25 apply (zenon_L127_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Ha8 ]. % 47.07/47.25 apply (zenon_L55_); trivial. % 47.07/47.25 apply (zenon_L337_); trivial. % 47.07/47.25 (* end of lemma zenon_L338_ *) % 47.07/47.25 assert (zenon_L339_ : (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((e10) = (e13))) -> ((op1 (e12) (e11)) = (e10)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H12d zenon_Hd8 zenon_He6 zenon_Hf9 zenon_H10d zenon_H51 zenon_H116 zenon_Hac zenon_H3b zenon_H2c zenon_H35 zenon_H32e zenon_Hbb zenon_H9c zenon_H339 zenon_H15b zenon_H6a zenon_H19 zenon_H1c zenon_Hdf zenon_H306 zenon_H15a zenon_Hb0 zenon_Hc5 zenon_Hb5 zenon_H115 zenon_H2b zenon_H34. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H5b | zenon_intro zenon_H12e ]. % 47.07/47.25 apply (zenon_L133_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_He5 | zenon_intro zenon_H12f ]. % 47.07/47.25 apply (zenon_L48_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.25 apply (zenon_L10_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.25 apply (zenon_L327_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.25 apply (zenon_L102_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.25 apply (zenon_L119_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.25 apply (zenon_L288_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.07/47.25 apply (zenon_L328_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.07/47.25 apply (zenon_L28_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.07/47.25 apply (zenon_L53_); trivial. % 47.07/47.25 apply (zenon_L336_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.25 apply (zenon_L10_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.25 apply (zenon_L327_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.25 apply (zenon_L102_); trivial. % 47.07/47.25 apply (zenon_L335_); trivial. % 47.07/47.25 (* end of lemma zenon_L339_ *) % 47.07/47.25 assert (zenon_L340_ : (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((e10) = (e13))) -> ((op1 (e12) (e11)) = (e10)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H133 zenon_Hb4 zenon_H314 zenon_Hd0 zenon_H129 zenon_H12d zenon_Hd8 zenon_He6 zenon_Hf9 zenon_H10d zenon_H51 zenon_H116 zenon_Hac zenon_H3b zenon_H2c zenon_H35 zenon_H32e zenon_Hbb zenon_H9c zenon_H339 zenon_H15b zenon_H6a zenon_H19 zenon_H1c zenon_Hdf zenon_H306 zenon_H15a zenon_Hb0 zenon_Hc5 zenon_H115 zenon_H2b zenon_H34. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H5f | zenon_intro zenon_H134 ]. % 47.07/47.25 apply (zenon_L297_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H128 | zenon_intro zenon_H135 ]. % 47.07/47.25 apply (zenon_L87_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H60 | zenon_intro zenon_Hb5 ]. % 47.07/47.25 apply (zenon_L327_); trivial. % 47.07/47.25 apply (zenon_L339_); trivial. % 47.07/47.25 (* end of lemma zenon_L340_ *) % 47.07/47.25 assert (zenon_L341_ : (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e11)) = (e11)) -> (~((e10) = (e11))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e11) = (e13))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e11)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H33e zenon_H150 zenon_Hd3 zenon_H15b zenon_H172 zenon_Ha9 zenon_Ha8 zenon_H33f zenon_H15a. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H14f | zenon_intro zenon_H340 ]. % 47.07/47.25 apply (zenon_L105_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H175 | zenon_intro zenon_H341 ]. % 47.07/47.25 apply (zenon_L287_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H342 ]. % 47.07/47.25 apply (zenon_L26_); trivial. % 47.07/47.25 cut (((op1 (e13) (e10)) = (e11)) = ((op1 (e13) (e10)) = (op1 (e13) (e13)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H33f. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H15a. % 47.07/47.25 cut (((e11) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H343]. % 47.07/47.25 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 47.07/47.25 congruence. % 47.07/47.25 apply zenon_H44. apply refl_equal. % 47.07/47.25 apply zenon_H343. apply sym_equal. exact zenon_H342. % 47.07/47.25 (* end of lemma zenon_L341_ *) % 47.07/47.25 assert (zenon_L342_ : (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((e10) = (e13))) -> ((op1 (e12) (e11)) = (e10)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e11)) = (e11)) -> (~((e10) = (e11))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e11)) -> False). % 47.07/47.25 do 0 intro. intros zenon_Hac zenon_H3b zenon_H1c zenon_H2c zenon_H35 zenon_H32e zenon_Hbb zenon_H9c zenon_H33e zenon_H150 zenon_Hd3 zenon_H15b zenon_H172 zenon_Ha9 zenon_H33f zenon_H15a. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.25 apply (zenon_L10_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.25 apply (zenon_L327_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.25 apply (zenon_L102_); trivial. % 47.07/47.25 apply (zenon_L341_); trivial. % 47.07/47.25 (* end of lemma zenon_L342_ *) % 47.07/47.25 assert (zenon_L343_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e13) (e10)) = (e11)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e11) = (e13))) -> (~((e10) = (e11))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((e10) = (e13))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e12) = (e13))) -> False). % 47.07/47.25 do 0 intro. intros zenon_H163 zenon_H23 zenon_H56 zenon_H119 zenon_H17b zenon_H174 zenon_H110 zenon_H177 zenon_H137 zenon_H344 zenon_H1b zenon_H338 zenon_H8f zenon_H335 zenon_H164 zenon_H42 zenon_H1c zenon_H2c zenon_H3b zenon_H345 zenon_H5c zenon_H133 zenon_Hb4 zenon_H314 zenon_Hd0 zenon_H129 zenon_H12d zenon_He6 zenon_Hf9 zenon_H10d zenon_H51 zenon_H116 zenon_H339 zenon_H6a zenon_H306 zenon_Hb0 zenon_Hc5 zenon_H115 zenon_H2b zenon_H346 zenon_H4b zenon_H15a zenon_H33f zenon_Ha9 zenon_H15b zenon_Hd3 zenon_H150 zenon_H33e zenon_H9c zenon_H35 zenon_Hac zenon_H11b zenon_H19 zenon_H63 zenon_H48 zenon_Hd8. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H50 | zenon_intro zenon_H168 ]. % 47.07/47.25 apply (zenon_L283_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H57 | zenon_intro zenon_H169 ]. % 47.07/47.25 apply (zenon_L15_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H5b | zenon_intro zenon_H8e ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.07/47.25 apply (zenon_L7_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.07/47.25 apply (zenon_L297_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.07/47.25 apply (zenon_L133_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.25 apply (zenon_L7_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H33 | zenon_intro zenon_H347 ]. % 47.07/47.25 apply (zenon_L9_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H32c | zenon_intro zenon_H348 ]. % 47.07/47.25 apply (zenon_L326_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H348); [ zenon_intro zenon_Hdf | zenon_intro zenon_H172 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.25 apply (zenon_L4_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.25 apply (zenon_L326_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H5f | zenon_intro zenon_H134 ]. % 47.07/47.25 apply (zenon_L297_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H128 | zenon_intro zenon_H135 ]. % 47.07/47.25 apply (zenon_L87_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H60 | zenon_intro zenon_Hb5 ]. % 47.07/47.25 apply (zenon_L327_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.25 apply (zenon_L119_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.25 apply (zenon_L288_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.07/47.25 apply (zenon_L328_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.07/47.25 apply (zenon_L28_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.07/47.25 apply (zenon_L70_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H17b); [ zenon_intro zenon_H172 | zenon_intro zenon_H17c ]. % 47.07/47.25 apply (zenon_L333_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H17c); [ zenon_intro zenon_H175 | zenon_intro zenon_H17d ]. % 47.07/47.25 apply (zenon_L338_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H176 | zenon_intro zenon_H136 ]. % 47.07/47.25 apply (zenon_L132_); trivial. % 47.07/47.25 apply (zenon_L92_); trivial. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.25 apply (zenon_L4_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.25 apply (zenon_L326_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H5f | zenon_intro zenon_H134 ]. % 47.07/47.25 apply (zenon_L297_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H128 | zenon_intro zenon_H135 ]. % 47.07/47.25 apply (zenon_L87_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H60 | zenon_intro zenon_Hb5 ]. % 47.07/47.25 apply (zenon_L327_); trivial. % 47.07/47.25 apply (zenon_L333_); trivial. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.25 apply (zenon_L10_); trivial. % 47.07/47.25 apply (zenon_L11_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.07/47.25 apply (zenon_L7_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.07/47.25 apply (zenon_L297_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.25 apply (zenon_L7_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H33 | zenon_intro zenon_H347 ]. % 47.07/47.25 apply (zenon_L9_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H32c | zenon_intro zenon_H348 ]. % 47.07/47.25 apply (zenon_L326_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H348); [ zenon_intro zenon_Hdf | zenon_intro zenon_H172 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H346); [ zenon_intro zenon_H4c | zenon_intro zenon_H34b ]. % 47.07/47.25 apply (zenon_L13_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H34b); [ zenon_intro zenon_H32e | zenon_intro zenon_H34c ]. % 47.07/47.25 apply (zenon_L340_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H34c); [ zenon_intro zenon_H11a | zenon_intro zenon_H62 ]. % 47.07/47.25 apply (zenon_L72_); trivial. % 47.07/47.25 apply (zenon_L18_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H346); [ zenon_intro zenon_H4c | zenon_intro zenon_H34b ]. % 47.07/47.25 apply (zenon_L13_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H34b); [ zenon_intro zenon_H32e | zenon_intro zenon_H34c ]. % 47.07/47.25 apply (zenon_L342_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H34c); [ zenon_intro zenon_H11a | zenon_intro zenon_H62 ]. % 47.07/47.25 apply (zenon_L72_); trivial. % 47.07/47.25 apply (zenon_L18_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.25 apply (zenon_L10_); trivial. % 47.07/47.25 apply (zenon_L11_); trivial. % 47.07/47.25 apply (zenon_L44_); trivial. % 47.07/47.25 (* end of lemma zenon_L343_ *) % 47.07/47.25 assert (zenon_L344_ : (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e13) (e11)) = (e11)) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> False). % 47.07/47.25 do 0 intro. intros zenon_Hd4 zenon_H1c zenon_H1b zenon_H7d zenon_H19 zenon_H56 zenon_Hb4 zenon_Hb5. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H1d | zenon_intro zenon_Hd5 ]. % 47.07/47.25 apply (zenon_L4_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd6 ]. % 47.07/47.25 apply (zenon_L40_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H57 | zenon_intro zenon_H5f ]. % 47.07/47.25 apply (zenon_L15_); trivial. % 47.07/47.25 apply (zenon_L29_); trivial. % 47.07/47.25 (* end of lemma zenon_L344_ *) % 47.07/47.25 assert (zenon_L345_ : (((op1 (op1 (e10) (e10)) (op1 (e10) (e10))) = (e10))/\(((op1 (op1 (e11) (e10)) (op1 (e11) (e10))) = (e11))/\(((op1 (op1 (e12) (e10)) (op1 (e12) (e10))) = (e12))/\((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> ((op1 (e12) (e13)) = (e13)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H70 zenon_H115 zenon_Hf7 zenon_Ha8. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H73. zenon_intro zenon_H72. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H75. zenon_intro zenon_H74. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H74). zenon_intro zenon_H77. zenon_intro zenon_H76. % 47.07/47.25 cut (((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (e13)) = ((op1 (e12) (e12)) = (op1 (e12) (e13)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H115. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H76. % 47.07/47.25 cut (((e13) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 47.07/47.25 cut (((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H309]. % 47.07/47.25 congruence. % 47.07/47.25 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 47.07/47.25 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (op1 (e12) (e12)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H309. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H9f. % 47.07/47.25 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 47.07/47.25 cut (((op1 (e12) (e12)) = (op1 (op1 (e13) (e10)) (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H307]. % 47.07/47.25 congruence. % 47.07/47.25 apply (zenon_L289_); trivial. % 47.07/47.25 apply zenon_Ha0. apply refl_equal. % 47.07/47.25 apply zenon_Ha0. apply refl_equal. % 47.07/47.25 apply zenon_Hc7. apply sym_equal. exact zenon_Ha8. % 47.07/47.25 (* end of lemma zenon_L345_ *) % 47.07/47.25 assert (zenon_L346_ : ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e13) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.07/47.25 do 0 intro. intros zenon_Hf7 zenon_H115 zenon_Hc5 zenon_Ha8 zenon_Hb5 zenon_H105 zenon_Hb0 zenon_H2b zenon_H30a zenon_H34. % 47.07/47.25 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.07/47.25 apply (zenon_L345_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.07/47.25 apply (zenon_L37_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.07/47.25 apply (zenon_L63_); trivial. % 47.07/47.25 apply (zenon_L291_); trivial. % 47.07/47.25 (* end of lemma zenon_L346_ *) % 47.07/47.25 assert (zenon_L347_ : (((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (e10))/\(((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (e11))/\(((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e12))/\((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e13)) = (e11)) -> ((op1 (e13) (e11)) = (e13)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H9b zenon_Hb0 zenon_H342 zenon_Hb5. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9e. zenon_intro zenon_H9d. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H9d). zenon_intro zenon_H109. zenon_intro zenon_H108. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H10b. zenon_intro zenon_H10a. % 47.07/47.25 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13)) = ((op1 (e11) (e11)) = (op1 (e13) (e11)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_Hb0. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H10a. % 47.07/47.25 cut (((e13) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 47.07/47.25 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H34d]. % 47.07/47.25 congruence. % 47.07/47.25 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H84 | zenon_intro zenon_H58 ]. % 47.07/47.25 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H34d. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H84. % 47.07/47.25 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 47.07/47.25 cut (((op1 (e11) (e11)) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H34e]. % 47.07/47.25 congruence. % 47.07/47.25 cut (((e11) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H343]. % 47.07/47.25 cut (((e11) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H343]. % 47.07/47.25 congruence. % 47.07/47.25 apply zenon_H343. apply sym_equal. exact zenon_H342. % 47.07/47.25 apply zenon_H343. apply sym_equal. exact zenon_H342. % 47.07/47.25 apply zenon_H58. apply refl_equal. % 47.07/47.25 apply zenon_H58. apply refl_equal. % 47.07/47.25 apply zenon_Hb6. apply sym_equal. exact zenon_Hb5. % 47.07/47.25 (* end of lemma zenon_L347_ *) % 47.07/47.25 assert (zenon_L348_ : ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e12)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e13)) = (e11)) -> ((op1 (e13) (e11)) = (e13)) -> False). % 47.07/47.25 do 0 intro. intros zenon_Hf7 zenon_H115 zenon_Hc5 zenon_Ha8 zenon_H34 zenon_H102 zenon_H2b zenon_Hb0 zenon_H342 zenon_Hb5. % 47.07/47.25 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.07/47.25 apply (zenon_L345_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.07/47.25 apply (zenon_L37_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.07/47.25 apply (zenon_L330_); trivial. % 47.07/47.25 apply (zenon_L347_); trivial. % 47.07/47.25 (* end of lemma zenon_L348_ *) % 47.07/47.25 assert (zenon_L349_ : (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e12)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e13)) = (e11)) -> False). % 47.07/47.25 do 0 intro. intros zenon_Hd0 zenon_H6a zenon_H1c zenon_Hd3 zenon_Hb4 zenon_H19 zenon_Hf7 zenon_H115 zenon_Hc5 zenon_Ha8 zenon_H34 zenon_H102 zenon_H2b zenon_Hb0 zenon_H342. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.07/47.25 apply (zenon_L40_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.07/47.25 apply (zenon_L28_); trivial. % 47.07/47.25 apply (zenon_L348_); trivial. % 47.07/47.25 (* end of lemma zenon_L349_ *) % 47.07/47.25 assert (zenon_L350_ : (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e13)) = (e11)) -> ((op1 (e13) (e11)) = (e13)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H10d zenon_H19 zenon_Hb4 zenon_Hd3 zenon_H1c zenon_H6a zenon_Hd0 zenon_H34 zenon_H30a zenon_H2b zenon_H115 zenon_Hfa zenon_Hf7 zenon_Hf9 zenon_Hc5 zenon_Ha8 zenon_Hb0 zenon_H342 zenon_Hb5. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H102 | zenon_intro zenon_H10e ]. % 47.07/47.25 apply (zenon_L349_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H105 | zenon_intro zenon_H10f ]. % 47.07/47.25 apply (zenon_L346_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hc4 ]. % 47.07/47.25 apply (zenon_L53_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.07/47.25 apply (zenon_L290_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.07/47.25 apply (zenon_L37_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.07/47.25 apply (zenon_L33_); trivial. % 47.07/47.25 apply (zenon_L347_); trivial. % 47.07/47.25 (* end of lemma zenon_L350_ *) % 47.07/47.25 assert (zenon_L351_ : (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (~((e10) = (e11))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> ((op1 (e12) (e11)) = (e10)) -> (~((e10) = (e13))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H34f zenon_H306 zenon_Hdf zenon_H15b zenon_H339 zenon_H9c zenon_Hbb zenon_H32e zenon_H35 zenon_H2c zenon_H3b zenon_Hac zenon_H116 zenon_H51 zenon_He6 zenon_Hd8 zenon_H12d zenon_H129 zenon_H314 zenon_H133 zenon_H56 zenon_H1b zenon_Hd4 zenon_H10d zenon_H19 zenon_Hb4 zenon_Hd3 zenon_H1c zenon_H6a zenon_Hd0 zenon_H34 zenon_H30a zenon_H2b zenon_H115 zenon_Hfa zenon_Hf7 zenon_Hf9 zenon_Hc5 zenon_Ha8 zenon_Hb0 zenon_Hb5. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H34f); [ zenon_intro zenon_H15a | zenon_intro zenon_H350 ]. % 47.07/47.25 apply (zenon_L340_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H350); [ zenon_intro zenon_H7d | zenon_intro zenon_H351 ]. % 47.07/47.25 apply (zenon_L344_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H351); [ zenon_intro zenon_H105 | zenon_intro zenon_H342 ]. % 47.07/47.25 apply (zenon_L346_); trivial. % 47.07/47.25 apply (zenon_L350_); trivial. % 47.07/47.25 (* end of lemma zenon_L351_ *) % 47.07/47.25 assert (zenon_L352_ : ((op1 (e13) (e12)) = (e11)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (~((e10) = (e11))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> ((op1 (e12) (e11)) = (e10)) -> (~((e10) = (e13))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False). % 47.07/47.25 do 0 intro. intros zenon_H105 zenon_H104 zenon_H34f zenon_H306 zenon_Hdf zenon_H15b zenon_H339 zenon_H9c zenon_Hbb zenon_H32e zenon_H35 zenon_H2c zenon_H3b zenon_Hac zenon_H116 zenon_H51 zenon_He6 zenon_Hd8 zenon_H12d zenon_H129 zenon_H314 zenon_H133 zenon_H56 zenon_H1b zenon_Hd4 zenon_H10d zenon_H19 zenon_Hb4 zenon_Hd3 zenon_H1c zenon_H6a zenon_Hd0 zenon_H34 zenon_H30a zenon_H2b zenon_H115 zenon_Hfa zenon_Hf7 zenon_Hf9 zenon_Hc5 zenon_Ha8 zenon_Hb0. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.07/47.25 apply (zenon_L57_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.07/47.25 apply (zenon_L28_); trivial. % 47.07/47.25 apply (zenon_L351_); trivial. % 47.07/47.25 (* end of lemma zenon_L352_ *) % 47.07/47.25 assert (zenon_L353_ : (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((e10) = (e13))) -> ((op1 (e12) (e11)) = (e10)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e11))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False). % 47.07/47.25 do 0 intro. intros zenon_H101 zenon_Hfd zenon_Hed zenon_H5f zenon_H48 zenon_H63 zenon_H11b zenon_H33e zenon_H150 zenon_Ha9 zenon_H33f zenon_H4b zenon_H346 zenon_H5c zenon_H345 zenon_H42 zenon_H164 zenon_H335 zenon_H8f zenon_H338 zenon_H344 zenon_H137 zenon_H177 zenon_H110 zenon_H174 zenon_H17b zenon_H119 zenon_H23 zenon_H163 zenon_Hd4 zenon_H1b zenon_H56 zenon_H133 zenon_H314 zenon_H129 zenon_H12d zenon_Hd8 zenon_He6 zenon_H51 zenon_H116 zenon_Hac zenon_H3b zenon_H2c zenon_H35 zenon_H32e zenon_Hbb zenon_H9c zenon_H339 zenon_H15b zenon_Hdf zenon_H306 zenon_H34f zenon_H104 zenon_H10d zenon_H19 zenon_Hb4 zenon_Hd3 zenon_H1c zenon_H6a zenon_Hd0 zenon_H34 zenon_H2b zenon_H115 zenon_Hfa zenon_Hf7 zenon_Hf9 zenon_Hc5 zenon_Hb0. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.25 apply (zenon_L10_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.25 apply (zenon_L17_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.25 apply (zenon_L102_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.25 apply (zenon_L69_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.25 apply (zenon_L288_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H34f); [ zenon_intro zenon_H15a | zenon_intro zenon_H350 ]. % 47.07/47.25 apply (zenon_L343_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H350); [ zenon_intro zenon_H7d | zenon_intro zenon_H351 ]. % 47.07/47.25 apply (zenon_L40_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H351); [ zenon_intro zenon_H105 | zenon_intro zenon_H342 ]. % 47.07/47.25 apply (zenon_L352_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.07/47.25 apply (zenon_L40_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.07/47.25 apply (zenon_L28_); trivial. % 47.07/47.25 apply (zenon_L350_); trivial. % 47.07/47.25 (* end of lemma zenon_L353_ *) % 47.07/47.25 assert (zenon_L354_ : (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (~((e10) = (e11))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e11)) = (e10)) -> (~((e10) = (e13))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> False). % 47.07/47.25 do 0 intro. intros zenon_Hb0 zenon_Hc5 zenon_Hf9 zenon_Hf7 zenon_H115 zenon_H2b zenon_H34 zenon_Hd0 zenon_H6a zenon_H1c zenon_Hd3 zenon_Hb4 zenon_H19 zenon_H10d zenon_H104 zenon_H34f zenon_H306 zenon_Hdf zenon_H15b zenon_H339 zenon_H9c zenon_H32e zenon_H35 zenon_H2c zenon_H3b zenon_Hac zenon_H116 zenon_H51 zenon_He6 zenon_Hd8 zenon_H12d zenon_H129 zenon_H314 zenon_H133 zenon_H56 zenon_H1b zenon_Hd4 zenon_H163 zenon_H23 zenon_H119 zenon_H17b zenon_H174 zenon_H110 zenon_H177 zenon_H137 zenon_H344 zenon_H338 zenon_H8f zenon_H335 zenon_H164 zenon_H42 zenon_H345 zenon_H5c zenon_H346 zenon_H4b zenon_H33f zenon_Ha9 zenon_H150 zenon_H33e zenon_H11b zenon_H63 zenon_H48 zenon_H5f zenon_Hed zenon_Hfd zenon_H101 zenon_H30e zenon_H149 zenon_H142 zenon_H130 zenon_Hf1 zenon_Hbe zenon_Hde zenon_Hea zenon_H16f zenon_H30f zenon_H14c zenon_Hb7 zenon_H8e. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.25 apply (zenon_L50_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.25 apply (zenon_L51_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H22 | zenon_intro zenon_H14d ]. % 47.07/47.25 apply (zenon_L46_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H141 | zenon_intro zenon_H14e ]. % 47.07/47.25 apply (zenon_L295_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbb ]. % 47.07/47.25 apply (zenon_L137_); trivial. % 47.07/47.25 apply (zenon_L353_); trivial. % 47.07/47.25 apply (zenon_L30_); trivial. % 47.07/47.25 (* end of lemma zenon_L354_ *) % 47.07/47.25 assert (zenon_L355_ : (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((e10) = (e11))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e11) = (e13))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e12)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False). % 47.07/47.25 do 0 intro. intros zenon_H33e zenon_H150 zenon_H15b zenon_H172 zenon_Ha9 zenon_Hd0 zenon_H6a zenon_H1c zenon_Hd3 zenon_Hb4 zenon_H19 zenon_Hf7 zenon_H115 zenon_Hc5 zenon_Ha8 zenon_H34 zenon_H102 zenon_H2b zenon_Hb0. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H14f | zenon_intro zenon_H340 ]. % 47.07/47.25 apply (zenon_L105_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H175 | zenon_intro zenon_H341 ]. % 47.07/47.25 apply (zenon_L287_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H342 ]. % 47.07/47.25 apply (zenon_L26_); trivial. % 47.07/47.25 apply (zenon_L349_); trivial. % 47.07/47.25 (* end of lemma zenon_L355_ *) % 47.07/47.25 assert (zenon_L356_ : (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((e10) = (e13))) -> ((op1 (e12) (e11)) = (e10)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((e10) = (e11))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e11) = (e13))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e12)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False). % 47.07/47.25 do 0 intro. intros zenon_Hac zenon_H3b zenon_H2c zenon_H35 zenon_H32e zenon_Hbb zenon_H9c zenon_H33e zenon_H150 zenon_H15b zenon_H172 zenon_Ha9 zenon_Hd0 zenon_H6a zenon_H1c zenon_Hd3 zenon_Hb4 zenon_H19 zenon_Hf7 zenon_H115 zenon_Hc5 zenon_H34 zenon_H102 zenon_H2b zenon_Hb0. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.25 apply (zenon_L10_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.25 apply (zenon_L327_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.25 apply (zenon_L102_); trivial. % 47.07/47.25 apply (zenon_L355_); trivial. % 47.07/47.25 (* end of lemma zenon_L356_ *) % 47.07/47.25 assert (zenon_L357_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e12) (e12)) = (e12)) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((e10) = (e13))) -> ((op1 (e12) (e11)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((e10) = (e11))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e11) = (e13))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e12)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False). % 47.07/47.25 do 0 intro. intros zenon_H14c zenon_H24 zenon_H8e zenon_Hb7 zenon_H30f zenon_H16f zenon_H23 zenon_Hea zenon_H5f zenon_H56 zenon_Hf9 zenon_H119 zenon_H306 zenon_H10d zenon_H174 zenon_H63 zenon_H110 zenon_Hde zenon_He6 zenon_Hbe zenon_Hf1 zenon_Hed zenon_H51 zenon_H130 zenon_H4b zenon_H142 zenon_H149 zenon_H30e zenon_Hfa zenon_Hac zenon_H3b zenon_H2c zenon_H35 zenon_H32e zenon_H9c zenon_H33e zenon_H150 zenon_H15b zenon_H172 zenon_Ha9 zenon_Hd0 zenon_H6a zenon_H1c zenon_Hd3 zenon_Hb4 zenon_H19 zenon_Hf7 zenon_H115 zenon_Hc5 zenon_H34 zenon_H102 zenon_H2b zenon_Hb0. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H22 | zenon_intro zenon_H14d ]. % 47.07/47.25 apply (zenon_L5_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H141 | zenon_intro zenon_H14e ]. % 47.07/47.25 apply (zenon_L295_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbb ]. % 47.07/47.25 apply (zenon_L137_); trivial. % 47.07/47.25 apply (zenon_L356_); trivial. % 47.07/47.25 (* end of lemma zenon_L357_ *) % 47.07/47.25 assert (zenon_L358_ : (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e13))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> False). % 47.07/47.25 do 0 intro. intros zenon_H6a zenon_H19 zenon_H338 zenon_H14c zenon_H24 zenon_H30f zenon_H16f zenon_H23 zenon_Hea zenon_H5f zenon_H56 zenon_Hf9 zenon_H119 zenon_H306 zenon_H10d zenon_H174 zenon_H63 zenon_H110 zenon_Hde zenon_He6 zenon_Hbe zenon_Hf1 zenon_Hed zenon_H51 zenon_H130 zenon_H4b zenon_H142 zenon_H149 zenon_H30e zenon_Hac zenon_H35 zenon_H9c zenon_H33e zenon_H150 zenon_H15b zenon_Ha9 zenon_Hd0 zenon_Hd3 zenon_Hb4 zenon_Hf7 zenon_H115 zenon_Hc5 zenon_H2b zenon_Hb0 zenon_H116 zenon_H5c zenon_H104 zenon_Hfd zenon_H101 zenon_H339 zenon_Hb7 zenon_H8e zenon_H1b zenon_H344 zenon_H48 zenon_H11b zenon_H33f zenon_H346 zenon_H345 zenon_H164 zenon_H335 zenon_H8f zenon_H137 zenon_H177 zenon_H17b zenon_H163 zenon_Hd4 zenon_H133 zenon_H314 zenon_H129 zenon_H12d zenon_Hd8 zenon_H34f zenon_H3b zenon_H2c zenon_H1c zenon_H42. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.25 apply (zenon_L7_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H33 | zenon_intro zenon_H347 ]. % 47.07/47.25 apply (zenon_L9_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H32c | zenon_intro zenon_H348 ]. % 47.07/47.25 apply (zenon_L326_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H348); [ zenon_intro zenon_Hdf | zenon_intro zenon_H172 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.25 apply (zenon_L4_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.25 apply (zenon_L326_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.25 apply (zenon_L354_); trivial. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.25 apply (zenon_L4_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.25 apply (zenon_L326_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.25 apply (zenon_L50_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.25 apply (zenon_L51_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.25 apply (zenon_L69_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.25 apply (zenon_L357_); trivial. % 47.07/47.25 apply (zenon_L332_); trivial. % 47.07/47.25 apply (zenon_L30_); trivial. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.25 apply (zenon_L10_); trivial. % 47.07/47.25 apply (zenon_L11_); trivial. % 47.07/47.25 (* end of lemma zenon_L358_ *) % 47.07/47.25 assert (zenon_L359_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((e11) = (e13))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H339 zenon_Hf9 zenon_Hfa zenon_H101 zenon_H10d zenon_Hfd zenon_Hed zenon_H63 zenon_H110 zenon_H104 zenon_H56 zenon_H5f zenon_H5c zenon_H116 zenon_Hb0 zenon_H2b zenon_H34 zenon_Ha8 zenon_Hc5 zenon_H115 zenon_Hf7 zenon_H19 zenon_Hb4 zenon_Hd3 zenon_H1c zenon_H6a zenon_Hd0 zenon_Ha9 zenon_H15b zenon_H150 zenon_H33e zenon_H338 zenon_H172. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.25 apply (zenon_L69_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.25 apply (zenon_L355_); trivial. % 47.07/47.25 apply (zenon_L332_); trivial. % 47.07/47.25 (* end of lemma zenon_L359_ *) % 47.07/47.25 assert (zenon_L360_ : (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e10) (e10)) = (e10)) -> (~((e10) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e11) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e12)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H33e zenon_H51 zenon_H164 zenon_H42 zenon_H1c zenon_H2c zenon_H3b zenon_H149 zenon_H150 zenon_H4b zenon_H130 zenon_Hed zenon_Hf1 zenon_H9c zenon_Hac zenon_H1b zenon_H19 zenon_Hb4 zenon_Hd4 zenon_H56 zenon_H8f zenon_H48 zenon_Hd8 zenon_H23 zenon_H5c zenon_H163 zenon_H15b zenon_H172 zenon_Ha9 zenon_Hf7 zenon_H115 zenon_Hc5 zenon_Ha8 zenon_H34 zenon_H102 zenon_H2b zenon_Hb0 zenon_Hb5. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H14f | zenon_intro zenon_H340 ]. % 47.07/47.25 apply (zenon_L305_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H175 | zenon_intro zenon_H341 ]. % 47.07/47.25 apply (zenon_L287_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H342 ]. % 47.07/47.25 apply (zenon_L26_); trivial. % 47.07/47.25 apply (zenon_L348_); trivial. % 47.07/47.25 (* end of lemma zenon_L360_ *) % 47.07/47.25 assert (zenon_L361_ : (((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 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((e11) = (e13))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e12) = (e13))) -> False). % 47.07/47.25 do 0 intro. intros zenon_H315 zenon_H30e zenon_H142 zenon_Hbe zenon_Hde zenon_Hea zenon_H16f zenon_H30f zenon_H24 zenon_H14c zenon_H42 zenon_H1c zenon_H2c zenon_H3b zenon_H11b zenon_H33f zenon_H346 zenon_H345 zenon_H335 zenon_H137 zenon_H177 zenon_H174 zenon_H17b zenon_H119 zenon_H314 zenon_H12d zenon_He6 zenon_H306 zenon_H34f zenon_H344 zenon_Hb7 zenon_H35 zenon_H339 zenon_Hf9 zenon_H101 zenon_H10d zenon_H116 zenon_Hb0 zenon_H2b zenon_Hc5 zenon_H115 zenon_Ha9 zenon_H15b zenon_H163 zenon_H5c zenon_H23 zenon_H48 zenon_H8f zenon_H56 zenon_Hd4 zenon_Hb4 zenon_H1b zenon_Hac zenon_H9c zenon_Hf1 zenon_Hed zenon_H130 zenon_H4b zenon_H150 zenon_H149 zenon_H164 zenon_H51 zenon_H33e zenon_H338 zenon_H129 zenon_Hd0 zenon_Hd3 zenon_H104 zenon_H110 zenon_H63 zenon_Hfd zenon_H133 zenon_H19 zenon_H6a zenon_H8e zenon_Hd8. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H50 | zenon_intro zenon_H316 ]. % 47.07/47.25 apply (zenon_L283_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H316); [ zenon_intro zenon_H301 | zenon_intro zenon_H317 ]. % 47.07/47.25 apply (zenon_L285_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H317); [ zenon_intro zenon_Hee | zenon_intro zenon_Hf7 ]. % 47.07/47.25 apply (zenon_L50_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.07/47.25 apply (zenon_L7_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.07/47.25 apply (zenon_L358_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.25 apply (zenon_L7_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H33 | zenon_intro zenon_H347 ]. % 47.07/47.25 apply (zenon_L9_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H32c | zenon_intro zenon_H348 ]. % 47.07/47.25 apply (zenon_L326_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H348); [ zenon_intro zenon_Hdf | zenon_intro zenon_H172 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.25 apply (zenon_L4_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.25 apply (zenon_L326_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H5f | zenon_intro zenon_H134 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.25 apply (zenon_L50_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.25 apply (zenon_L51_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.25 apply (zenon_L353_); trivial. % 47.07/47.25 apply (zenon_L30_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H128 | zenon_intro zenon_H135 ]. % 47.07/47.25 apply (zenon_L87_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H60 | zenon_intro zenon_Hb5 ]. % 47.07/47.25 apply (zenon_L327_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.25 apply (zenon_L50_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.25 apply (zenon_L51_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.25 apply (zenon_L10_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.25 apply (zenon_L327_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.25 apply (zenon_L102_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.25 apply (zenon_L79_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.25 apply (zenon_L288_); trivial. % 47.07/47.25 apply (zenon_L351_); trivial. % 47.07/47.25 apply (zenon_L30_); trivial. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.25 apply (zenon_L4_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.25 apply (zenon_L326_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H5f | zenon_intro zenon_H134 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.25 apply (zenon_L50_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.25 apply (zenon_L51_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.25 apply (zenon_L10_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.25 apply (zenon_L17_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.25 apply (zenon_L102_); trivial. % 47.07/47.25 apply (zenon_L359_); trivial. % 47.07/47.25 apply (zenon_L30_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H128 | zenon_intro zenon_H135 ]. % 47.07/47.25 apply (zenon_L87_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H60 | zenon_intro zenon_Hb5 ]. % 47.07/47.25 apply (zenon_L327_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.25 apply (zenon_L50_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.25 apply (zenon_L51_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.25 apply (zenon_L10_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.25 apply (zenon_L327_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.25 apply (zenon_L102_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.25 apply (zenon_L79_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.25 apply (zenon_L360_); trivial. % 47.07/47.25 apply (zenon_L332_); trivial. % 47.07/47.25 apply (zenon_L30_); trivial. % 47.07/47.25 apply (zenon_L19_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.25 apply (zenon_L10_); trivial. % 47.07/47.25 apply (zenon_L11_); trivial. % 47.07/47.25 apply (zenon_L44_); trivial. % 47.07/47.25 (* end of lemma zenon_L361_ *) % 47.07/47.25 assert (zenon_L362_ : (((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (e20))/\(((op2 (op2 (e21) (e22)) (op2 (e21) (e22))) = (e21))/\(((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (e22))/\((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e22)) = (e20)) -> ((op2 (e21) (e20)) = (e23)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H209 zenon_H193 zenon_H260 zenon_H19c. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H209). zenon_intro zenon_H20c. zenon_intro zenon_H20b. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_H20e. zenon_intro zenon_H20d. % 47.07/47.25 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H210. zenon_intro zenon_H20f. % 47.07/47.25 cut (((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e23)) = ((op2 (e20) (e20)) = (op2 (e21) (e20)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H193. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H20f. % 47.07/47.25 cut (((e23) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 47.07/47.25 cut (((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H352]. % 47.07/47.25 congruence. % 47.07/47.25 elim (classic ((op2 (e20) (e20)) = (op2 (e20) (e20)))); [ zenon_intro zenon_H197 | zenon_intro zenon_H198 ]. % 47.07/47.25 cut (((op2 (e20) (e20)) = (op2 (e20) (e20))) = ((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (op2 (e20) (e20)))). % 47.07/47.25 intro zenon_D_pnotp. % 47.07/47.25 apply zenon_H352. % 47.07/47.25 rewrite <- zenon_D_pnotp. % 47.07/47.25 exact zenon_H197. % 47.07/47.25 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 47.07/47.25 cut (((op2 (e20) (e20)) = (op2 (op2 (e23) (e22)) (op2 (e23) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H353]. % 47.07/47.25 congruence. % 47.07/47.25 cut (((e20) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H261]. % 47.07/47.25 cut (((e20) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H261]. % 47.07/47.25 congruence. % 47.07/47.25 apply zenon_H261. apply sym_equal. exact zenon_H260. % 47.07/47.25 apply zenon_H261. apply sym_equal. exact zenon_H260. % 47.07/47.25 apply zenon_H198. apply refl_equal. % 47.07/47.25 apply zenon_H198. apply refl_equal. % 47.07/47.25 apply zenon_H1f4. apply sym_equal. exact zenon_H19c. % 47.07/47.25 (* end of lemma zenon_L362_ *) % 47.07/47.25 assert (zenon_L363_ : ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e22)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e23)) = (e21)) -> ((op2 (e23) (e21)) = (e23)) -> False). % 47.07/47.25 do 0 intro. intros zenon_H257 zenon_H265 zenon_H23f zenon_H223 zenon_H19c zenon_H260 zenon_H193 zenon_H229 zenon_H243 zenon_H22e. % 47.07/47.25 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.07/47.25 apply (zenon_L311_); trivial. % 47.07/47.25 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.07/47.26 apply (zenon_L182_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.07/47.26 apply (zenon_L362_); trivial. % 47.07/47.26 apply (zenon_L183_); trivial. % 47.07/47.26 (* end of lemma zenon_L363_ *) % 47.07/47.26 assert (zenon_L364_ : (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((e20) = (e23))) -> ((op2 (e22) (e21)) = (e20)) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((e21) = (e22))) -> ((op2 (e20) (e23)) = (e22)) -> (~((e20) = (e21))) -> ((op2 (e21) (e23)) = (e20)) -> (~((e21) = (e23))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e22)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e23)) -> False). % 47.07/47.26 do 0 intro. intros zenon_H225 zenon_H1a3 zenon_H14 zenon_H194 zenon_H19d zenon_H1ea zenon_H24e zenon_H216 zenon_H2c7 zenon_H1b9 zenon_H1db zenon_H1df zenon_H1dd zenon_H1d3 zenon_H257 zenon_H265 zenon_H23f zenon_H19c zenon_H260 zenon_H193 zenon_H229 zenon_H22e. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.07/47.26 apply (zenon_L151_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.07/47.26 apply (zenon_L168_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.07/47.26 apply (zenon_L264_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_H1da | zenon_intro zenon_H2c8 ]. % 47.07/47.26 apply (zenon_L165_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2c8); [ zenon_intro zenon_H1de | zenon_intro zenon_H2c9 ]. % 47.07/47.26 apply (zenon_L166_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2c9); [ zenon_intro zenon_H222 | zenon_intro zenon_H243 ]. % 47.07/47.26 apply (zenon_L174_); trivial. % 47.07/47.26 apply (zenon_L363_); trivial. % 47.07/47.26 (* end of lemma zenon_L364_ *) % 47.07/47.26 assert (zenon_L365_ : ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> ((op2 (e23) (e21)) = (e23)) -> ((op2 (e23) (e22)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e23)) = (e20)) -> ((op2 (e21) (e20)) = (e23)) -> False). % 47.07/47.26 do 0 intro. intros zenon_H257 zenon_H265 zenon_H23f zenon_H223 zenon_H22e zenon_H263 zenon_H229 zenon_H193 zenon_H31e zenon_H19c. % 47.07/47.26 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.07/47.26 apply (zenon_L311_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.07/47.26 apply (zenon_L182_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.07/47.26 apply (zenon_L201_); trivial. % 47.07/47.26 apply (zenon_L312_); trivial. % 47.07/47.26 (* end of lemma zenon_L365_ *) % 47.07/47.26 assert (zenon_L366_ : (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e20) (e22)) = (op2 (e21) (e22)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (((op2 (e20) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e23) (e22)) = (e21))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/((op2 (e21) (e23)) = (e20))))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e21) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e21))\/((op2 (e23) (e20)) = (e21))))) -> (((op2 (e20) (e22)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((op2 (e20) (e20)) = (e20)) -> ((op2 (e22) (e20)) = (e21)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((e20) = (e22))) -> (~((e20) = (e21))) -> (((op2 (e20) (e21)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> ((op2 (e20) (e21)) = (e21)) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((e21) = (e22))) -> (~((e21) = (e23))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> ((e22) = (op2 (e21) (e21))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((e22) = (e23))) -> False). % 47.07/47.26 do 0 intro. intros zenon_H1aa zenon_H14 zenon_H194 zenon_H1a3 zenon_H1cf zenon_H1b0 zenon_H25c zenon_H2b5 zenon_H1b3 zenon_H23a zenon_H24b zenon_H2d1 zenon_H2e7 zenon_H2d2 zenon_H27d zenon_H262 zenon_H27a zenon_H2fc zenon_H2a0 zenon_H2d7 zenon_H2bb zenon_H2f7 zenon_H2eb zenon_H230 zenon_H259 zenon_H25f zenon_H271 zenon_H27c zenon_H28d zenon_H287 zenon_H2ee zenon_H2ec zenon_H2ef zenon_H18d zenon_H2ba zenon_H2d5 zenon_H251 zenon_H20a zenon_H270 zenon_H1be zenon_H2ab zenon_H2bc zenon_H18c zenon_H2a8 zenon_H299 zenon_H354 zenon_H234 zenon_H322 zenon_H2bd zenon_H185 zenon_H1c4 zenon_H1df zenon_H2d4 zenon_H1c7 zenon_H355 zenon_H29f zenon_H27b zenon_H291 zenon_H225 zenon_H19d zenon_H216 zenon_H2c7 zenon_H1b9 zenon_H1d3 zenon_H265 zenon_H23f zenon_H193 zenon_H229 zenon_H2d3 zenon_H183 zenon_H1e4 zenon_H1db zenon_H276. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H27d); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H280 ]. % 47.07/47.26 apply (zenon_L307_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H281 ]. % 47.07/47.26 apply (zenon_L158_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H23b | zenon_intro zenon_H257 ]. % 47.07/47.26 apply (zenon_L222_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.26 apply (zenon_L148_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.26 apply (zenon_L220_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.07/47.26 apply (zenon_L148_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H19b | zenon_intro zenon_H2db ]. % 47.07/47.26 apply (zenon_L150_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2dc ]. % 47.07/47.26 apply (zenon_L160_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H1dd ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.07/47.26 apply (zenon_L145_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.07/47.26 apply (zenon_L160_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H2e2 ]. % 47.07/47.26 apply (zenon_L220_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2a4 | zenon_intro zenon_H2e3 ]. % 47.07/47.26 apply (zenon_L221_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H22e ]. % 47.07/47.26 apply (zenon_L168_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H2cf | zenon_intro zenon_H2fd ]. % 47.07/47.26 apply (zenon_L317_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2fd); [ zenon_intro zenon_H296 | zenon_intro zenon_H2fe ]. % 47.07/47.26 apply (zenon_L253_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H297 | zenon_intro zenon_H263 ]. % 47.07/47.26 apply (zenon_L263_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.07/47.26 apply (zenon_L151_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.07/47.26 apply (zenon_L168_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.07/47.26 apply (zenon_L264_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H354); [ zenon_intro zenon_H1ed | zenon_intro zenon_H356 ]. % 47.07/47.26 apply (zenon_L188_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H356); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H357 ]. % 47.07/47.26 apply (zenon_L167_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H357); [ zenon_intro zenon_H260 | zenon_intro zenon_H31e ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_H2e6 | zenon_intro zenon_H323 ]. % 47.07/47.26 apply (zenon_L261_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1dd | zenon_intro zenon_H324 ]. % 47.07/47.26 apply (zenon_L364_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H233 | zenon_intro zenon_H31e ]. % 47.07/47.26 apply (zenon_L179_); trivial. % 47.07/47.26 apply (zenon_L365_); trivial. % 47.07/47.26 apply (zenon_L365_); trivial. % 47.07/47.26 apply (zenon_L167_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.07/47.26 apply (zenon_L145_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.07/47.26 apply (zenon_L160_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2dd ]. % 47.07/47.26 apply (zenon_L162_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2de ]. % 47.07/47.26 apply (zenon_L163_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2de); [ zenon_intro zenon_H296 | zenon_intro zenon_H1de ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H2e2 ]. % 47.07/47.26 apply (zenon_L220_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2a4 | zenon_intro zenon_H2e3 ]. % 47.07/47.26 apply (zenon_L221_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H22e ]. % 47.07/47.26 apply (zenon_L168_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H355); [ zenon_intro zenon_H18b | zenon_intro zenon_H358 ]. % 47.07/47.26 apply (zenon_L238_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H358); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H359 ]. % 47.07/47.26 apply (zenon_L253_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H359); [ zenon_intro zenon_H290 | zenon_intro zenon_H260 ]. % 47.07/47.26 apply (zenon_L213_); trivial. % 47.07/47.26 apply (zenon_L364_); trivial. % 47.07/47.26 apply (zenon_L166_); trivial. % 47.07/47.26 apply (zenon_L167_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.07/47.26 apply (zenon_L151_); trivial. % 47.07/47.26 apply (zenon_L152_); trivial. % 47.07/47.26 apply (zenon_L217_); trivial. % 47.07/47.26 (* end of lemma zenon_L366_ *) % 47.07/47.26 assert (zenon_L367_ : (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((e21) = (e23))) -> ((op2 (e20) (e21)) = (e21)) -> (~((e22) = (e23))) -> ((op2 (e20) (e22)) = (e22)) -> ((op2 (e20) (e23)) = (e20)) -> (~((e20) = (e23))) -> False). % 47.07/47.26 do 0 intro. intros zenon_H27b zenon_H14 zenon_H194 zenon_H193 zenon_H1d3 zenon_H29f zenon_H276 zenon_H1c3 zenon_H2e6 zenon_H19d. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.26 apply (zenon_L148_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.26 apply (zenon_L220_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.26 apply (zenon_L206_); trivial. % 47.07/47.26 apply (zenon_L260_); trivial. % 47.07/47.26 (* end of lemma zenon_L367_ *) % 47.07/47.26 assert (zenon_L368_ : (((op2 (op2 (e20) (e20)) (op2 (e20) (e20))) = (e20))/\(((op2 (op2 (e21) (e20)) (op2 (e21) (e20))) = (e21))/\(((op2 (op2 (e22) (e20)) (op2 (e22) (e20))) = (e22))/\((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e20)) = (e21)) -> ((op2 (e23) (e21)) = (e23)) -> False). % 47.07/47.26 do 0 intro. intros zenon_H1ec zenon_H229 zenon_H2b8 zenon_H22e. % 47.07/47.26 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_H1ef. zenon_intro zenon_H1ee. % 47.07/47.26 apply (zenon_and_s _ _ zenon_H1ee). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 47.07/47.26 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_H1f3. zenon_intro zenon_H1f2. % 47.07/47.26 cut (((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (e23)) = ((op2 (e21) (e21)) = (op2 (e23) (e21)))). % 47.07/47.26 intro zenon_D_pnotp. % 47.07/47.26 apply zenon_H229. % 47.07/47.26 rewrite <- zenon_D_pnotp. % 47.07/47.26 exact zenon_H1f2. % 47.07/47.26 cut (((e23) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H22f]. % 47.07/47.26 cut (((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H35a]. % 47.07/47.26 congruence. % 47.07/47.26 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H200 | zenon_intro zenon_H1c0 ]. % 47.07/47.26 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (op2 (e21) (e21)))). % 47.07/47.26 intro zenon_D_pnotp. % 47.07/47.26 apply zenon_H35a. % 47.07/47.26 rewrite <- zenon_D_pnotp. % 47.07/47.26 exact zenon_H200. % 47.07/47.26 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 47.07/47.26 cut (((op2 (e21) (e21)) = (op2 (op2 (e23) (e20)) (op2 (e23) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H35b]. % 47.07/47.26 congruence. % 47.07/47.26 cut (((e21) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H35c]. % 47.07/47.26 cut (((e21) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H35c]. % 47.07/47.26 congruence. % 47.07/47.26 apply zenon_H35c. apply sym_equal. exact zenon_H2b8. % 47.07/47.26 apply zenon_H35c. apply sym_equal. exact zenon_H2b8. % 47.07/47.26 apply zenon_H1c0. apply refl_equal. % 47.07/47.26 apply zenon_H1c0. apply refl_equal. % 47.07/47.26 apply zenon_H22f. apply sym_equal. exact zenon_H22e. % 47.07/47.26 (* end of lemma zenon_L368_ *) % 47.07/47.26 assert (zenon_L369_ : (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e23)) -> ((op2 (e23) (e21)) = (e23)) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e22)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e21) (e23)) = (e20)) -> ((op2 (e23) (e20)) = (e21)) -> False). % 47.07/47.26 do 0 intro. intros zenon_H229 zenon_H20a zenon_H278 zenon_H22e zenon_H19c zenon_H260 zenon_H193 zenon_H35d zenon_H1dd zenon_H2b8. % 47.07/47.26 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.07/47.26 apply (zenon_L368_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.07/47.26 apply (zenon_L239_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.07/47.26 apply (zenon_L362_); trivial. % 47.07/47.26 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H21b. zenon_intro zenon_H21a. % 47.07/47.26 apply (zenon_and_s _ _ zenon_H21a). zenon_intro zenon_H245. zenon_intro zenon_H244. % 47.07/47.26 cut (((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (e21)) = ((op2 (e20) (e20)) = (op2 (e23) (e20)))). % 47.07/47.26 intro zenon_D_pnotp. % 47.07/47.26 apply zenon_H35d. % 47.07/47.26 rewrite <- zenon_D_pnotp. % 47.07/47.26 exact zenon_H245. % 47.07/47.26 cut (((e21) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H35c]. % 47.07/47.26 cut (((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H35e]. % 47.07/47.26 congruence. % 47.07/47.26 elim (classic ((op2 (e20) (e20)) = (op2 (e20) (e20)))); [ zenon_intro zenon_H197 | zenon_intro zenon_H198 ]. % 47.07/47.26 cut (((op2 (e20) (e20)) = (op2 (e20) (e20))) = ((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (op2 (e20) (e20)))). % 47.07/47.26 intro zenon_D_pnotp. % 47.07/47.26 apply zenon_H35e. % 47.07/47.26 rewrite <- zenon_D_pnotp. % 47.07/47.26 exact zenon_H197. % 47.07/47.26 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 47.07/47.26 cut (((op2 (e20) (e20)) = (op2 (op2 (e21) (e23)) (op2 (e21) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H35f]. % 47.07/47.26 congruence. % 47.07/47.26 cut (((e20) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2ed]. % 47.07/47.26 cut (((e20) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2ed]. % 47.07/47.26 congruence. % 47.07/47.26 apply zenon_H2ed. apply sym_equal. exact zenon_H1dd. % 47.07/47.26 apply zenon_H2ed. apply sym_equal. exact zenon_H1dd. % 47.07/47.26 apply zenon_H198. apply refl_equal. % 47.07/47.26 apply zenon_H198. apply refl_equal. % 47.07/47.26 apply zenon_H35c. apply sym_equal. exact zenon_H2b8. % 47.07/47.26 (* end of lemma zenon_L369_ *) % 47.07/47.26 assert (zenon_L370_ : ((op2 (e23) (e20)) = (e21)) -> ((op2 (e23) (e20)) = (e22)) -> (~((e21) = (e22))) -> False). % 47.07/47.26 do 0 intro. intros zenon_H2b8 zenon_H257 zenon_H1b9. % 47.07/47.26 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 47.07/47.26 cut (((e22) = (e22)) = ((e21) = (e22))). % 47.07/47.26 intro zenon_D_pnotp. % 47.07/47.26 apply zenon_H1b9. % 47.07/47.26 rewrite <- zenon_D_pnotp. % 47.07/47.26 exact zenon_H1ba. % 47.07/47.26 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 47.07/47.26 cut (((e22) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 47.07/47.26 congruence. % 47.07/47.26 cut (((op2 (e23) (e20)) = (e21)) = ((e22) = (e21))). % 47.07/47.26 intro zenon_D_pnotp. % 47.07/47.26 apply zenon_H1bc. % 47.07/47.26 rewrite <- zenon_D_pnotp. % 47.07/47.26 exact zenon_H2b8. % 47.07/47.26 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.07/47.26 cut (((op2 (e23) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H258]. % 47.07/47.26 congruence. % 47.07/47.26 exact (zenon_H258 zenon_H257). % 47.07/47.26 apply zenon_H181. apply refl_equal. % 47.07/47.26 apply zenon_H1bb. apply refl_equal. % 47.07/47.26 apply zenon_H1bb. apply refl_equal. % 47.07/47.26 (* end of lemma zenon_L370_ *) % 47.07/47.26 assert (zenon_L371_ : ((op2 (e23) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> ((op2 (e23) (e21)) = (e23)) -> ((op2 (e23) (e22)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e23)) = (e20)) -> ((op2 (e21) (e20)) = (e23)) -> False). % 47.07/47.26 do 0 intro. intros zenon_H2b8 zenon_H229 zenon_H23f zenon_H223 zenon_H22e zenon_H260 zenon_H193 zenon_H31e zenon_H19c. % 47.07/47.26 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.07/47.26 apply (zenon_L368_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.07/47.26 apply (zenon_L182_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.07/47.26 apply (zenon_L362_); trivial. % 47.07/47.26 apply (zenon_L312_); trivial. % 47.07/47.26 (* end of lemma zenon_L371_ *) % 47.07/47.26 assert (zenon_L372_ : (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e21)) -> ((op2 (e23) (e22)) = (e21)) -> False). % 47.07/47.26 do 0 intro. intros zenon_H25f zenon_H2b8 zenon_H263. % 47.07/47.26 cut (((op2 (e23) (e20)) = (e21)) = ((op2 (e23) (e20)) = (op2 (e23) (e22)))). % 47.07/47.26 intro zenon_D_pnotp. % 47.07/47.26 apply zenon_H25f. % 47.07/47.26 rewrite <- zenon_D_pnotp. % 47.07/47.26 exact zenon_H2b8. % 47.07/47.26 cut (((e21) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 47.07/47.26 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1ac]. % 47.07/47.26 congruence. % 47.07/47.26 apply zenon_H1ac. apply refl_equal. % 47.07/47.26 apply zenon_H264. apply sym_equal. exact zenon_H263. % 47.07/47.26 (* end of lemma zenon_L372_ *) % 47.07/47.26 assert (zenon_L373_ : ((op2 (e23) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e23)) -> ((op2 (e22) (e23)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e23)) = (e20)) -> ((op2 (e21) (e20)) = (e23)) -> False). % 47.07/47.26 do 0 intro. intros zenon_H2b8 zenon_H229 zenon_H23f zenon_H22e zenon_H223 zenon_H25a zenon_H265 zenon_H193 zenon_H31e zenon_H19c. % 47.07/47.26 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.07/47.26 apply (zenon_L368_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.07/47.26 apply (zenon_L182_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.07/47.26 apply (zenon_L193_); trivial. % 47.07/47.26 apply (zenon_L312_); trivial. % 47.07/47.26 (* end of lemma zenon_L373_ *) % 47.07/47.26 assert (zenon_L374_ : ((op2 (e23) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> False). % 47.07/47.26 do 0 intro. intros zenon_H2b8 zenon_H229 zenon_H22e zenon_H23f zenon_H26c zenon_H265 zenon_H269 zenon_H223. % 47.07/47.26 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.07/47.26 apply (zenon_L368_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.07/47.26 apply (zenon_L182_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.07/47.26 apply (zenon_L197_); trivial. % 47.07/47.26 apply (zenon_L195_); trivial. % 47.07/47.26 (* end of lemma zenon_L374_ *) % 47.07/47.26 assert (zenon_L375_ : (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e23) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> False). % 47.07/47.26 do 0 intro. intros zenon_H230 zenon_H1e4 zenon_H14 zenon_H325 zenon_H183 zenon_H2b8 zenon_H229 zenon_H23f zenon_H26c zenon_H265 zenon_H269 zenon_H223. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H231 ]. % 47.07/47.26 apply (zenon_L167_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H232 ]. % 47.07/47.26 apply (zenon_L318_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H228 | zenon_intro zenon_H22e ]. % 47.07/47.26 apply (zenon_L176_); trivial. % 47.07/47.26 apply (zenon_L374_); trivial. % 47.07/47.26 (* end of lemma zenon_L375_ *) % 47.07/47.26 assert (zenon_L376_ : (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e21)) = (e23)) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e23) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> False). % 47.07/47.26 do 0 intro. intros zenon_H271 zenon_H25f zenon_H19c zenon_H31e zenon_H193 zenon_H22e zenon_H230 zenon_H1e4 zenon_H14 zenon_H325 zenon_H183 zenon_H2b8 zenon_H229 zenon_H23f zenon_H265 zenon_H269 zenon_H223. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H260 | zenon_intro zenon_H272 ]. % 47.07/47.26 apply (zenon_L371_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H263 | zenon_intro zenon_H273 ]. % 47.07/47.26 apply (zenon_L372_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H25a | zenon_intro zenon_H26c ]. % 47.07/47.26 apply (zenon_L373_); trivial. % 47.07/47.26 apply (zenon_L375_); trivial. % 47.07/47.26 (* end of lemma zenon_L376_ *) % 47.07/47.26 assert (zenon_L377_ : (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e21) = (e22))) -> ((op2 (e20) (e22)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((op2 (e21) (e23)) = (e21)) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e23) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e21)) = (e23)) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e23) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> False). % 47.07/47.26 do 0 intro. intros zenon_H27c zenon_H1b9 zenon_H1c3 zenon_H259 zenon_H24b zenon_H234 zenon_H1de zenon_H2eb zenon_H23b zenon_H23a zenon_H271 zenon_H25f zenon_H19c zenon_H31e zenon_H193 zenon_H22e zenon_H230 zenon_H1e4 zenon_H14 zenon_H325 zenon_H183 zenon_H2b8 zenon_H229 zenon_H23f zenon_H265. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H257 | zenon_intro zenon_H284 ]. % 47.07/47.26 apply (zenon_L370_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H228 | zenon_intro zenon_H285 ]. % 47.07/47.26 apply (zenon_L176_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H25a | zenon_intro zenon_H269 ]. % 47.07/47.26 apply (zenon_L189_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H233 | zenon_intro zenon_H24c ]. % 47.07/47.26 apply (zenon_L179_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H222 | zenon_intro zenon_H24d ]. % 47.07/47.26 apply (zenon_L254_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H23c | zenon_intro zenon_H223 ]. % 47.07/47.26 apply (zenon_L180_); trivial. % 47.07/47.26 apply (zenon_L376_); trivial. % 47.07/47.26 (* end of lemma zenon_L377_ *) % 47.07/47.26 assert (zenon_L378_ : (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> ((e22) = (op2 (e21) (e21))) -> ((op2 (e22) (e21)) = (e21)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> False). % 47.07/47.26 do 0 intro. intros zenon_H2b5 zenon_H183 zenon_H2b1 zenon_H1b3 zenon_H29a zenon_H299 zenon_H194 zenon_H14 zenon_H1a3. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H2b6 ]. % 47.07/47.26 apply (zenon_L154_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b7 ]. % 47.07/47.26 apply (zenon_L224_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H23b | zenon_intro zenon_H1a2 ]. % 47.07/47.26 apply (zenon_L215_); trivial. % 47.07/47.26 apply (zenon_L151_); trivial. % 47.07/47.26 (* end of lemma zenon_L378_ *) % 47.07/47.26 assert (zenon_L379_ : (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((e21) = (e22))) -> ((op2 (e22) (e20)) = (e22)) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> ((e22) = (op2 (e21) (e21))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> ((op2 (e21) (e22)) = (e21)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((e20) = (e23))) -> ((op2 (e22) (e21)) = (e20)) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((e21) = (e23))) -> False). % 47.07/47.26 do 0 intro. intros zenon_H360 zenon_H1b9 zenon_H23b zenon_H2b5 zenon_H183 zenon_H1b3 zenon_H299 zenon_H291 zenon_H29c zenon_H296 zenon_H295 zenon_H225 zenon_H1a3 zenon_H14 zenon_H194 zenon_H19d zenon_H1ea zenon_H24e zenon_H216 zenon_H1d3. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H361 ]. % 47.07/47.26 apply (zenon_L222_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H2b1 | zenon_intro zenon_H362 ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H29c); [ zenon_intro zenon_H290 | zenon_intro zenon_H29d ]. % 47.07/47.26 apply (zenon_L213_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H29d); [ zenon_intro zenon_H297 | zenon_intro zenon_H29e ]. % 47.07/47.26 apply (zenon_L214_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H29e); [ zenon_intro zenon_H29a | zenon_intro zenon_H207 ]. % 47.07/47.26 apply (zenon_L378_); trivial. % 47.07/47.26 apply (zenon_L264_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H297 | zenon_intro zenon_H222 ]. % 47.07/47.26 apply (zenon_L214_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.07/47.26 apply (zenon_L151_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.07/47.26 apply (zenon_L168_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.07/47.26 apply (zenon_L264_); trivial. % 47.07/47.26 apply (zenon_L174_); trivial. % 47.07/47.26 (* end of lemma zenon_L379_ *) % 47.07/47.26 assert (zenon_L380_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e23)) = (e22)) -> (~((e20) = (e21))) -> ((op2 (e21) (e23)) = (e21)) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (e21) (e21))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e23) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e23)) -> ((op2 (e22) (e23)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e21) (e20)) = (e23)) -> False). % 47.07/47.26 do 0 intro. intros zenon_H322 zenon_H1c4 zenon_H1db zenon_H1df zenon_H1de zenon_H234 zenon_H183 zenon_H14 zenon_H2b8 zenon_H229 zenon_H23f zenon_H22e zenon_H223 zenon_H25a zenon_H265 zenon_H193 zenon_H19c. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_H2e6 | zenon_intro zenon_H323 ]. % 47.07/47.26 apply (zenon_L261_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1dd | zenon_intro zenon_H324 ]. % 47.07/47.26 apply (zenon_L166_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H233 | zenon_intro zenon_H31e ]. % 47.07/47.26 apply (zenon_L179_); trivial. % 47.07/47.26 apply (zenon_L373_); trivial. % 47.07/47.26 (* end of lemma zenon_L380_ *) % 47.07/47.26 assert (zenon_L381_ : (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> ((op2 (e20) (e21)) = (e21)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/((op2 (e21) (e23)) = (e20))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> ((op2 (e20) (e20)) = (e20)) -> (~((e22) = (e23))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (e21) (e21))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e23))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (((op2 (e20) (e21)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e22)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e22)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e21))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> ((op2 (e23) (e20)) = (e21)) -> (~((e21) = (e22))) -> False). % 47.07/47.26 do 0 intro. intros zenon_H27a zenon_H1be zenon_H35d zenon_H20a zenon_H355 zenon_H29f zenon_H25f zenon_H271 zenon_H23a zenon_H2eb zenon_H24b zenon_H259 zenon_H27c zenon_H354 zenon_H2d7 zenon_H27d zenon_H18c zenon_H276 zenon_H1e4 zenon_H183 zenon_H2d3 zenon_H1b0 zenon_H1d3 zenon_H295 zenon_H29c zenon_H291 zenon_H1b3 zenon_H2b5 zenon_H360 zenon_H2d4 zenon_H22d zenon_H325 zenon_H230 zenon_H1c7 zenon_H2d6 zenon_H2cb zenon_H299 zenon_H225 zenon_H19d zenon_H216 zenon_H322 zenon_H1c4 zenon_H1df zenon_H234 zenon_H229 zenon_H23f zenon_H265 zenon_H193 zenon_H185 zenon_H2bd zenon_H1a3 zenon_H194 zenon_H14 zenon_H1aa zenon_H27b zenon_H2b8 zenon_H1b9. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.07/47.26 apply (zenon_L307_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.07/47.26 apply (zenon_L156_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H27d); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H280 ]. % 47.07/47.26 apply (zenon_L307_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H281 ]. % 47.07/47.26 apply (zenon_L158_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H23b | zenon_intro zenon_H257 ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.26 apply (zenon_L148_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.26 apply (zenon_L319_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.26 apply (zenon_L206_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.07/47.26 apply (zenon_L148_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H19b | zenon_intro zenon_H2db ]. % 47.07/47.26 apply (zenon_L150_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2dc ]. % 47.07/47.26 apply (zenon_L160_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H1dd ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.07/47.26 apply (zenon_L145_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.07/47.26 apply (zenon_L160_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2dd ]. % 47.07/47.26 apply (zenon_L219_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2de ]. % 47.07/47.26 apply (zenon_L163_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2de); [ zenon_intro zenon_H296 | zenon_intro zenon_H1de ]. % 47.07/47.26 apply (zenon_L253_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H2e2 ]. % 47.07/47.26 apply (zenon_L319_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2a4 | zenon_intro zenon_H2e3 ]. % 47.07/47.26 apply (zenon_L221_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H22e ]. % 47.07/47.26 apply (zenon_L168_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H354); [ zenon_intro zenon_H1ed | zenon_intro zenon_H356 ]. % 47.07/47.26 apply (zenon_L236_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H356); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H357 ]. % 47.07/47.26 apply (zenon_L167_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H357); [ zenon_intro zenon_H260 | zenon_intro zenon_H31e ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_H2e6 | zenon_intro zenon_H323 ]. % 47.07/47.26 apply (zenon_L367_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1dd | zenon_intro zenon_H324 ]. % 47.07/47.26 apply (zenon_L369_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H233 | zenon_intro zenon_H31e ]. % 47.07/47.26 apply (zenon_L179_); trivial. % 47.07/47.26 apply (zenon_L377_); trivial. % 47.07/47.26 apply (zenon_L377_); trivial. % 47.07/47.26 apply (zenon_L167_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.07/47.26 apply (zenon_L145_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.07/47.26 apply (zenon_L160_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2dd ]. % 47.07/47.26 apply (zenon_L162_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2de ]. % 47.07/47.26 apply (zenon_L163_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2de); [ zenon_intro zenon_H296 | zenon_intro zenon_H1de ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H2e2 ]. % 47.07/47.26 apply (zenon_L220_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2a4 | zenon_intro zenon_H2e3 ]. % 47.07/47.26 apply (zenon_L221_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H22e ]. % 47.07/47.26 apply (zenon_L168_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H355); [ zenon_intro zenon_H18b | zenon_intro zenon_H358 ]. % 47.07/47.26 apply (zenon_L157_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H358); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H359 ]. % 47.07/47.26 apply (zenon_L253_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H359); [ zenon_intro zenon_H290 | zenon_intro zenon_H260 ]. % 47.07/47.26 apply (zenon_L213_); trivial. % 47.07/47.26 apply (zenon_L369_); trivial. % 47.07/47.26 apply (zenon_L166_); trivial. % 47.07/47.26 apply (zenon_L167_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.07/47.26 apply (zenon_L151_); trivial. % 47.07/47.26 apply (zenon_L152_); trivial. % 47.07/47.26 apply (zenon_L370_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H27d); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H280 ]. % 47.07/47.26 apply (zenon_L307_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H281 ]. % 47.07/47.26 apply (zenon_L158_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H23b | zenon_intro zenon_H257 ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.26 apply (zenon_L148_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.26 apply (zenon_L319_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.07/47.26 apply (zenon_L148_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.07/47.26 apply (zenon_L145_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.07/47.26 apply (zenon_L160_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2dd ]. % 47.07/47.26 apply (zenon_L219_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2de ]. % 47.07/47.26 apply (zenon_L163_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2de); [ zenon_intro zenon_H296 | zenon_intro zenon_H1de ]. % 47.07/47.26 apply (zenon_L379_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H2e2 ]. % 47.07/47.26 apply (zenon_L319_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2a4 | zenon_intro zenon_H2e3 ]. % 47.07/47.26 apply (zenon_L221_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H22e ]. % 47.07/47.26 apply (zenon_L168_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H2e4 ]. % 47.07/47.26 apply (zenon_L206_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2ca | zenon_intro zenon_H2e5 ]. % 47.07/47.26 apply (zenon_L249_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H29a | zenon_intro zenon_H25a ]. % 47.07/47.26 apply (zenon_L215_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.07/47.26 apply (zenon_L151_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.07/47.26 apply (zenon_L168_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.07/47.26 apply (zenon_L264_); trivial. % 47.07/47.26 apply (zenon_L380_); trivial. % 47.07/47.26 apply (zenon_L167_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.07/47.26 apply (zenon_L151_); trivial. % 47.07/47.26 apply (zenon_L152_); trivial. % 47.07/47.26 apply (zenon_L217_); trivial. % 47.07/47.26 apply (zenon_L370_); trivial. % 47.07/47.26 (* end of lemma zenon_L381_ *) % 47.07/47.26 assert (zenon_L382_ : (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e11)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e13) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.07/47.26 do 0 intro. intros zenon_H338 zenon_H175 zenon_H8f zenon_Hd7 zenon_Hb5 zenon_H105 zenon_Hb0 zenon_H2b zenon_H30a zenon_H34. % 47.07/47.26 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.07/47.26 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H73. zenon_intro zenon_H72. % 47.07/47.26 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H75. zenon_intro zenon_H74. % 47.07/47.26 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 47.07/47.26 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e11) (e13)) = (op1 (e13) (e13)))). % 47.07/47.26 intro zenon_D_pnotp. % 47.07/47.26 apply zenon_H338. % 47.07/47.26 rewrite <- zenon_D_pnotp. % 47.07/47.26 exact zenon_H96. % 47.07/47.26 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 47.07/47.26 cut (((op1 (e13) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H363]. % 47.07/47.26 congruence. % 47.07/47.26 cut (((op1 (op1 (e11) (e10)) (op1 (e11) (e10))) = (e11)) = ((op1 (e13) (e13)) = (op1 (e11) (e13)))). % 47.07/47.26 intro zenon_D_pnotp. % 47.07/47.26 apply zenon_H363. % 47.07/47.26 rewrite <- zenon_D_pnotp. % 47.07/47.26 exact zenon_H75. % 47.07/47.26 cut (((e11) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 47.07/47.26 cut (((op1 (op1 (e11) (e10)) (op1 (e11) (e10))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H31a]. % 47.07/47.26 congruence. % 47.07/47.26 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 47.07/47.26 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (op1 (e11) (e10)) (op1 (e11) (e10))) = (op1 (e13) (e13)))). % 47.07/47.26 intro zenon_D_pnotp. % 47.07/47.26 apply zenon_H31a. % 47.07/47.26 rewrite <- zenon_D_pnotp. % 47.07/47.26 exact zenon_H96. % 47.07/47.26 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 47.07/47.26 cut (((op1 (e13) (e13)) = (op1 (op1 (e11) (e10)) (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H318]. % 47.07/47.26 congruence. % 47.07/47.26 apply (zenon_L299_); trivial. % 47.07/47.26 apply zenon_H97. apply refl_equal. % 47.07/47.26 apply zenon_H97. apply refl_equal. % 47.07/47.26 apply zenon_H17e. apply sym_equal. exact zenon_H175. % 47.07/47.26 apply zenon_H97. apply refl_equal. % 47.07/47.26 apply zenon_H97. apply refl_equal. % 47.07/47.26 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.07/47.26 apply (zenon_L82_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.07/47.26 apply (zenon_L63_); trivial. % 47.07/47.26 apply (zenon_L291_); trivial. % 47.07/47.26 (* end of lemma zenon_L382_ *) % 47.07/47.26 assert (zenon_L383_ : ((op1 (e13) (e12)) = (e13)) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e12)) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.07/47.26 do 0 intro. intros zenon_Hc4 zenon_Hf7 zenon_Hf9 zenon_H8f zenon_Hd7 zenon_Hb5 zenon_Hc5 zenon_Hb8 zenon_H8b zenon_H2b zenon_H30a zenon_H34. % 47.07/47.26 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H70 | zenon_intro zenon_Ha5 ]. % 47.07/47.26 apply (zenon_L290_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha6 ]. % 47.07/47.26 apply (zenon_L82_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H8d | zenon_intro zenon_H9b ]. % 47.07/47.26 apply (zenon_L74_); trivial. % 47.07/47.26 apply (zenon_L291_); trivial. % 47.07/47.26 (* end of lemma zenon_L383_ *) % 47.07/47.26 assert (zenon_L384_ : (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e13)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e12)) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.07/47.26 do 0 intro. intros zenon_H10d zenon_Hdf zenon_H306 zenon_Hb0 zenon_H175 zenon_H338 zenon_H5b zenon_H119 zenon_Hf7 zenon_Hf9 zenon_H8f zenon_Hd7 zenon_Hb5 zenon_Hc5 zenon_Hb8 zenon_H8b zenon_H2b zenon_H30a zenon_H34. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H102 | zenon_intro zenon_H10e ]. % 47.07/47.26 apply (zenon_L288_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H105 | zenon_intro zenon_H10f ]. % 47.07/47.26 apply (zenon_L382_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hc4 ]. % 47.07/47.26 apply (zenon_L70_); trivial. % 47.07/47.26 apply (zenon_L383_); trivial. % 47.07/47.26 (* end of lemma zenon_L384_ *) % 47.07/47.26 assert (zenon_L385_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e12) (e12)) = (e13)) -> ((op1 (e12) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (e11) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> False). % 47.07/47.26 do 0 intro. intros zenon_H339 zenon_H5c zenon_H116 zenon_H6a zenon_H17b zenon_H34 zenon_H2b zenon_H8b zenon_Hb8 zenon_Hc5 zenon_Hb5 zenon_Hd7 zenon_H8f zenon_Hf9 zenon_Hf7 zenon_H119 zenon_H5b zenon_H338 zenon_Hb0 zenon_H306 zenon_Hdf zenon_H10d zenon_H177 zenon_H19 zenon_H2c zenon_H1c zenon_H137. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.26 apply (zenon_L71_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.26 apply (zenon_L19_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.26 apply (zenon_L288_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H17b); [ zenon_intro zenon_H172 | zenon_intro zenon_H17c ]. % 47.07/47.26 apply (zenon_L332_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H17c); [ zenon_intro zenon_H175 | zenon_intro zenon_H17d ]. % 47.07/47.26 apply (zenon_L384_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H176 | zenon_intro zenon_H136 ]. % 47.07/47.26 apply (zenon_L132_); trivial. % 47.07/47.26 apply (zenon_L92_); trivial. % 47.07/47.26 (* end of lemma zenon_L385_ *) % 47.07/47.26 assert (zenon_L386_ : (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e12)) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> False). % 47.07/47.26 do 0 intro. intros zenon_Hd0 zenon_H6a zenon_H1c zenon_Hd3 zenon_Hb4 zenon_Hb0 zenon_H19 zenon_Hc4 zenon_Hf7 zenon_Hf9 zenon_H8f zenon_Hd7 zenon_Hc5 zenon_Hb8 zenon_H8b zenon_H2b zenon_H30a zenon_H34. % 47.07/47.26 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.07/47.26 apply (zenon_L19_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.07/47.26 apply (zenon_L40_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.07/47.26 apply (zenon_L28_); trivial. % 47.07/47.26 apply (zenon_L383_); trivial. % 47.07/47.26 (* end of lemma zenon_L386_ *) % 47.07/47.26 assert (zenon_L387_ : (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e10)) -> ((op1 (e13) (e13)) = (e10)) -> False). % 47.07/47.26 do 0 intro. intros zenon_H8f zenon_H13d zenon_H30a. % 47.07/47.26 cut (((op1 (e10) (e13)) = (e10)) = ((op1 (e10) (e13)) = (op1 (e13) (e13)))). % 47.07/47.26 intro zenon_D_pnotp. % 47.07/47.26 apply zenon_H8f. % 47.07/47.26 rewrite <- zenon_D_pnotp. % 47.07/47.26 exact zenon_H13d. % 47.07/47.26 cut (((e10) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H30d]. % 47.07/47.26 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 47.07/47.26 congruence. % 47.07/47.26 apply zenon_Hba. apply refl_equal. % 47.07/47.26 apply zenon_H30d. apply sym_equal. exact zenon_H30a. % 47.07/47.26 (* end of lemma zenon_L387_ *) % 47.07/47.26 assert (zenon_L388_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((e10) = (e13))) -> ((op1 (e12) (e11)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e11))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e13)) = (e13)) -> False). % 47.07/47.26 do 0 intro. intros zenon_H154 zenon_H30a zenon_H5b zenon_Hb7 zenon_H14c zenon_H30f zenon_H16f zenon_Hea zenon_Hde zenon_Hbe zenon_Hf1 zenon_H130 zenon_H142 zenon_H149 zenon_H30e zenon_H101 zenon_Hfd zenon_Hed zenon_H5f zenon_H48 zenon_H63 zenon_H11b zenon_H33e zenon_H150 zenon_Ha9 zenon_H33f zenon_H4b zenon_H346 zenon_H5c zenon_H345 zenon_H42 zenon_H164 zenon_H335 zenon_H338 zenon_H344 zenon_H137 zenon_H177 zenon_H110 zenon_H174 zenon_H17b zenon_H119 zenon_H23 zenon_H163 zenon_Hd4 zenon_H1b zenon_H56 zenon_H133 zenon_H314 zenon_H129 zenon_H12d zenon_Hd8 zenon_He6 zenon_H51 zenon_H116 zenon_Hac zenon_H3b zenon_H2c zenon_H35 zenon_H32e zenon_H9c zenon_H339 zenon_H15b zenon_Hdf zenon_H306 zenon_H34f zenon_H104 zenon_H10d zenon_H19 zenon_Hb4 zenon_Hd3 zenon_H1c zenon_H6a zenon_Hd0 zenon_H34 zenon_H2b zenon_H115 zenon_Hf7 zenon_Hf9 zenon_Hc5 zenon_Hb0 zenon_H8f zenon_H152. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H13d | zenon_intro zenon_H155 ]. % 47.07/47.26 apply (zenon_L387_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H14f | zenon_intro zenon_H156 ]. % 47.07/47.26 apply (zenon_L304_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H8e | zenon_intro zenon_Hd7 ]. % 47.07/47.26 apply (zenon_L354_); trivial. % 47.07/47.26 apply (zenon_L111_); trivial. % 47.07/47.26 (* end of lemma zenon_L388_ *) % 47.07/47.26 assert (zenon_L389_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e12) (e12)) = (e13)) -> ((op1 (e12) (e13)) = (e12)) -> ((op1 (e10) (e13)) = (e13)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((e10) = (e13))) -> ((op1 (e12) (e11)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e11))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 47.07/47.26 do 0 intro. intros zenon_H364 zenon_H8b zenon_Hb8 zenon_Hd7 zenon_H154 zenon_H30a zenon_H5b zenon_Hb7 zenon_H14c zenon_H30f zenon_H16f zenon_Hea zenon_Hde zenon_Hbe zenon_Hf1 zenon_H130 zenon_H142 zenon_H149 zenon_H30e zenon_H101 zenon_Hfd zenon_Hed zenon_H5f zenon_H48 zenon_H63 zenon_H11b zenon_H33e zenon_H150 zenon_Ha9 zenon_H33f zenon_H4b zenon_H346 zenon_H5c zenon_H345 zenon_H42 zenon_H164 zenon_H335 zenon_H338 zenon_H344 zenon_H137 zenon_H177 zenon_H110 zenon_H174 zenon_H17b zenon_H119 zenon_H23 zenon_H163 zenon_Hd4 zenon_H1b zenon_H56 zenon_H133 zenon_H314 zenon_H129 zenon_H12d zenon_Hd8 zenon_He6 zenon_H51 zenon_H116 zenon_Hac zenon_H3b zenon_H2c zenon_H35 zenon_H32e zenon_H9c zenon_H339 zenon_H15b zenon_Hdf zenon_H306 zenon_H34f zenon_H104 zenon_H10d zenon_H19 zenon_Hb4 zenon_Hd3 zenon_H1c zenon_H6a zenon_Hd0 zenon_H34 zenon_H2b zenon_H115 zenon_Hf7 zenon_Hf9 zenon_Hc5 zenon_Hb0 zenon_H8f. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H364); [ zenon_intro zenon_H41 | zenon_intro zenon_H365 ]. % 47.07/47.26 apply (zenon_L11_); trivial. % 47.07/47.26 apply (zenon_or_s _ _ zenon_H365); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H366 ]. % 47.07/47.27 apply (zenon_L385_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H366); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H152 ]. % 47.07/47.27 apply (zenon_L386_); trivial. % 47.07/47.27 apply (zenon_L388_); trivial. % 47.07/47.27 (* end of lemma zenon_L389_ *) % 47.07/47.27 assert (zenon_L390_ : (~((e12) = (e13))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e11))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_Hd8 zenon_H13e zenon_H125 zenon_H11f zenon_H157 zenon_H364 zenon_H154 zenon_H5b zenon_Hb7 zenon_H14c zenon_H30f zenon_H16f zenon_Hea zenon_Hde zenon_Hbe zenon_Hf1 zenon_H130 zenon_H142 zenon_H149 zenon_H30e zenon_H101 zenon_Hfd zenon_Hed zenon_H5f zenon_H48 zenon_H63 zenon_H11b zenon_H33e zenon_H150 zenon_Ha9 zenon_H33f zenon_H4b zenon_H346 zenon_H5c zenon_H345 zenon_H42 zenon_H164 zenon_H335 zenon_H338 zenon_H344 zenon_H137 zenon_H177 zenon_H110 zenon_H174 zenon_H17b zenon_H119 zenon_H23 zenon_H163 zenon_Hd4 zenon_H1b zenon_H56 zenon_H133 zenon_H314 zenon_H129 zenon_H12d zenon_He6 zenon_H51 zenon_H116 zenon_Hac zenon_H3b zenon_H2c zenon_H35 zenon_H9c zenon_H339 zenon_H15b zenon_Hdf zenon_H306 zenon_H34f zenon_H104 zenon_H10d zenon_Hb4 zenon_Hd3 zenon_Hd0 zenon_H34 zenon_H2b zenon_H115 zenon_Hf7 zenon_Hf9 zenon_Hc5 zenon_Hb0 zenon_H8f zenon_H1c zenon_H19 zenon_H6a. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.27 apply (zenon_L4_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.27 apply (zenon_L326_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.27 apply (zenon_L50_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.27 apply (zenon_L51_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.27 apply (zenon_L137_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.27 apply (zenon_L10_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.27 apply (zenon_L17_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.27 apply (zenon_L113_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.27 apply (zenon_L19_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.27 apply (zenon_L288_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H158 ]. % 47.07/47.27 apply (zenon_L389_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H136 | zenon_intro zenon_H159 ]. % 47.07/47.27 apply (zenon_L92_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H152 ]. % 47.07/47.27 apply (zenon_L84_); trivial. % 47.07/47.27 apply (zenon_L388_); trivial. % 47.07/47.27 apply (zenon_L84_); trivial. % 47.07/47.27 apply (zenon_L19_); trivial. % 47.07/47.27 (* end of lemma zenon_L390_ *) % 47.07/47.27 assert (zenon_L391_ : (~((h2 (e13)) = (e23))) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H367 zenon_H368 zenon_H194. % 47.07/47.27 cut (((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) = ((h2 (e13)) = (e23))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H367. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H368. % 47.07/47.27 cut (((op2 (e21) (op2 (op2 (e21) (e21)) (e21))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H369]. % 47.07/47.27 cut (((h2 (e13)) = (h2 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H36a]. % 47.07/47.27 congruence. % 47.07/47.27 apply zenon_H36a. apply refl_equal. % 47.07/47.27 apply zenon_H369. apply sym_equal. exact zenon_H194. % 47.07/47.27 (* end of lemma zenon_L391_ *) % 47.07/47.27 assert (zenon_L392_ : (~((h2 (op1 (e10) (e13))) = (op2 (h2 (e10)) (h2 (e13))))) -> ((op1 (e10) (e13)) = (e13)) -> ((op2 (e20) (e23)) = (e23)) -> ((h2 (e10)) = (op2 (op2 (e21) (e21)) (e21))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H36b zenon_Hd7 zenon_H278 zenon_H13 zenon_H14 zenon_H368 zenon_H194. % 47.07/47.27 cut (((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) = ((h2 (op1 (e10) (e13))) = (op2 (h2 (e10)) (h2 (e13))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H36b. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H368. % 47.07/47.27 cut (((op2 (e21) (op2 (op2 (e21) (e21)) (e21))) = (op2 (h2 (e10)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H36c]. % 47.07/47.27 cut (((h2 (e13)) = (h2 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H36d]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((h2 (op1 (e10) (e13))) = (h2 (op1 (e10) (e13))))); [ zenon_intro zenon_H36e | zenon_intro zenon_H36f ]. % 47.07/47.27 cut (((h2 (op1 (e10) (e13))) = (h2 (op1 (e10) (e13)))) = ((h2 (e13)) = (h2 (op1 (e10) (e13))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H36d. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H36e. % 47.07/47.27 cut (((h2 (op1 (e10) (e13))) = (h2 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H36f]. % 47.07/47.27 cut (((h2 (op1 (e10) (e13))) = (h2 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H370]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op1 (e10) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 47.07/47.27 congruence. % 47.07/47.27 exact (zenon_Hda zenon_Hd7). % 47.07/47.27 apply zenon_H36f. apply refl_equal. % 47.07/47.27 apply zenon_H36f. apply refl_equal. % 47.07/47.27 elim (classic ((op2 (h2 (e10)) (h2 (e13))) = (op2 (h2 (e10)) (h2 (e13))))); [ zenon_intro zenon_H371 | zenon_intro zenon_H372 ]. % 47.07/47.27 cut (((op2 (h2 (e10)) (h2 (e13))) = (op2 (h2 (e10)) (h2 (e13)))) = ((op2 (e21) (op2 (op2 (e21) (e21)) (e21))) = (op2 (h2 (e10)) (h2 (e13))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H36c. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H371. % 47.07/47.27 cut (((op2 (h2 (e10)) (h2 (e13))) = (op2 (h2 (e10)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H372]. % 47.07/47.27 cut (((op2 (h2 (e10)) (h2 (e13))) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H373]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op2 (e20) (e23)) = (e23)) = ((op2 (h2 (e10)) (h2 (e13))) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H373. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H278. % 47.07/47.27 cut (((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H374]. % 47.07/47.27 cut (((op2 (e20) (e23)) = (op2 (h2 (e10)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H375]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((op2 (h2 (e10)) (h2 (e13))) = (op2 (h2 (e10)) (h2 (e13))))); [ zenon_intro zenon_H371 | zenon_intro zenon_H372 ]. % 47.07/47.27 cut (((op2 (h2 (e10)) (h2 (e13))) = (op2 (h2 (e10)) (h2 (e13)))) = ((op2 (e20) (e23)) = (op2 (h2 (e10)) (h2 (e13))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H375. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H371. % 47.07/47.27 cut (((op2 (h2 (e10)) (h2 (e13))) = (op2 (h2 (e10)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H372]. % 47.07/47.27 cut (((op2 (h2 (e10)) (h2 (e13))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H376]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((h2 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H367]. % 47.07/47.27 cut (((h2 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 47.07/47.27 congruence. % 47.07/47.27 apply (zenon_L1_); trivial. % 47.07/47.27 apply (zenon_L391_); trivial. % 47.07/47.27 apply zenon_H372. apply refl_equal. % 47.07/47.27 apply zenon_H372. apply refl_equal. % 47.07/47.27 exact (zenon_H374 zenon_H194). % 47.07/47.27 apply zenon_H372. apply refl_equal. % 47.07/47.27 apply zenon_H372. apply refl_equal. % 47.07/47.27 (* end of lemma zenon_L392_ *) % 47.07/47.27 assert (zenon_L393_ : (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e12)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e11)) = (e10)) -> (~((e10) = (e13))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> False). % 47.07/47.27 do 0 intro. intros zenon_Hb0 zenon_H2b zenon_H102 zenon_H34 zenon_Hc5 zenon_H115 zenon_Hf7 zenon_H19 zenon_Hb4 zenon_Hd3 zenon_H1c zenon_H6a zenon_Hd0 zenon_Ha9 zenon_H172 zenon_H15b zenon_H150 zenon_H33e zenon_H9c zenon_H32e zenon_H35 zenon_H2c zenon_H3b zenon_Hac zenon_H30e zenon_H149 zenon_H142 zenon_H4b zenon_H130 zenon_H51 zenon_Hed zenon_Hf1 zenon_Hbe zenon_He6 zenon_Hde zenon_H110 zenon_H63 zenon_H174 zenon_H10d zenon_H306 zenon_H119 zenon_Hf9 zenon_H56 zenon_H5f zenon_Hea zenon_H23 zenon_H16f zenon_H30f zenon_H24 zenon_H14c zenon_Hb7 zenon_H8e. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.27 apply (zenon_L50_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.27 apply (zenon_L51_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.27 apply (zenon_L357_); trivial. % 47.07/47.27 apply (zenon_L30_); trivial. % 47.07/47.27 (* end of lemma zenon_L393_ *) % 47.07/47.27 assert (zenon_L394_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((e10) = (e13))) -> ((op1 (e12) (e11)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((e10) = (e11))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e11) = (e13))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e12)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e13)) = (e13)) -> False). % 47.07/47.27 do 0 intro. intros zenon_H154 zenon_H171 zenon_H42 zenon_H5b zenon_H1b zenon_Hd4 zenon_Hd8 zenon_H48 zenon_Hb7 zenon_H14c zenon_H24 zenon_H30f zenon_H16f zenon_H23 zenon_Hea zenon_H5f zenon_H56 zenon_Hf9 zenon_H119 zenon_H306 zenon_H10d zenon_H174 zenon_H63 zenon_H110 zenon_Hde zenon_He6 zenon_Hbe zenon_Hf1 zenon_Hed zenon_H51 zenon_H130 zenon_H4b zenon_H142 zenon_H149 zenon_H30e zenon_Hac zenon_H3b zenon_H2c zenon_H35 zenon_H32e zenon_H9c zenon_H33e zenon_H150 zenon_H15b zenon_H172 zenon_Ha9 zenon_Hd0 zenon_H6a zenon_H1c zenon_Hd3 zenon_Hb4 zenon_H19 zenon_Hf7 zenon_H115 zenon_Hc5 zenon_H34 zenon_H102 zenon_H2b zenon_Hb0 zenon_H8f zenon_H152. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H13d | zenon_intro zenon_H155 ]. % 47.07/47.27 apply (zenon_L126_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H14f | zenon_intro zenon_H156 ]. % 47.07/47.27 apply (zenon_L304_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H8e | zenon_intro zenon_Hd7 ]. % 47.07/47.27 apply (zenon_L393_); trivial. % 47.07/47.27 apply (zenon_L111_); trivial. % 47.07/47.27 (* end of lemma zenon_L394_ *) % 47.07/47.27 assert (zenon_L395_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((h2 (e10)) = (op2 (op2 (e21) (e21)) (e21))) -> ((op2 (e20) (e23)) = (e23)) -> (~((h2 (op1 (e10) (e13))) = (op2 (h2 (e10)) (h2 (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e13)) = (e11)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((e10) = (e13))) -> ((op1 (e12) (e11)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((e10) = (e11))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e11) = (e13))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e12)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H157 zenon_H194 zenon_H368 zenon_H14 zenon_H13 zenon_H278 zenon_H36b zenon_H137 zenon_H342 zenon_H154 zenon_H171 zenon_H42 zenon_H5b zenon_H1b zenon_Hd4 zenon_Hd8 zenon_H48 zenon_Hb7 zenon_H14c zenon_H24 zenon_H30f zenon_H16f zenon_H23 zenon_Hea zenon_H5f zenon_H56 zenon_Hf9 zenon_H119 zenon_H306 zenon_H10d zenon_H174 zenon_H63 zenon_H110 zenon_Hde zenon_He6 zenon_Hbe zenon_Hf1 zenon_Hed zenon_H51 zenon_H130 zenon_H4b zenon_H142 zenon_H149 zenon_H30e zenon_Hac zenon_H3b zenon_H2c zenon_H35 zenon_H32e zenon_H9c zenon_H33e zenon_H150 zenon_H15b zenon_H172 zenon_Ha9 zenon_Hd0 zenon_H6a zenon_H1c zenon_Hd3 zenon_Hb4 zenon_H19 zenon_Hf7 zenon_H115 zenon_Hc5 zenon_H34 zenon_H102 zenon_H2b zenon_Hb0 zenon_H8f. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H158 ]. % 47.07/47.27 apply (zenon_L392_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H136 | zenon_intro zenon_H159 ]. % 47.07/47.27 apply (zenon_L92_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H152 ]. % 47.07/47.27 apply (zenon_L349_); trivial. % 47.07/47.27 apply (zenon_L394_); trivial. % 47.07/47.27 (* end of lemma zenon_L395_ *) % 47.07/47.27 assert (zenon_L396_ : (~((op2 (e23) (e23)) = (op2 (e20) (e21)))) -> ((op2 (op2 (e21) (e20)) (op2 (e21) (e20))) = (e21)) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e20) (e21)) = (e21)) -> False). % 47.07/47.27 do 0 intro. intros zenon_H377 zenon_H1f1 zenon_H19c zenon_H29f. % 47.07/47.27 cut (((op2 (op2 (e21) (e20)) (op2 (e21) (e20))) = (e21)) = ((op2 (e23) (e23)) = (op2 (e20) (e21)))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H377. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H1f1. % 47.07/47.27 cut (((e21) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2f9]. % 47.07/47.27 cut (((op2 (op2 (e21) (e20)) (op2 (e21) (e20))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H328]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 47.07/47.27 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (op2 (e21) (e20)) (op2 (e21) (e20))) = (op2 (e23) (e23)))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H328. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H211. % 47.07/47.27 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 47.07/47.27 cut (((op2 (e23) (e23)) = (op2 (op2 (e21) (e20)) (op2 (e21) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H326]. % 47.07/47.27 congruence. % 47.07/47.27 apply (zenon_L322_); trivial. % 47.07/47.27 apply zenon_H212. apply refl_equal. % 47.07/47.27 apply zenon_H212. apply refl_equal. % 47.07/47.27 apply zenon_H2f9. apply sym_equal. exact zenon_H29f. % 47.07/47.27 (* end of lemma zenon_L396_ *) % 47.07/47.27 assert (zenon_L397_ : (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e21)) -> ((op2 (e20) (e21)) = (e21)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e23)) -> ((op2 (e23) (e21)) = (e23)) -> ((op2 (e23) (e22)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e23) (e23)) = (e20)) -> ((op2 (e21) (e20)) = (e23)) -> False). % 47.07/47.27 do 0 intro. intros zenon_H378 zenon_H1de zenon_H29f zenon_H20a zenon_H278 zenon_H22e zenon_H263 zenon_H229 zenon_H193 zenon_H31e zenon_H19c. % 47.07/47.27 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1ec | zenon_intro zenon_H217 ]. % 47.07/47.27 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_H1ef. zenon_intro zenon_H1ee. % 47.07/47.27 apply (zenon_and_s _ _ zenon_H1ee). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 47.07/47.27 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 47.07/47.27 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e21) (e23)) = (op2 (e23) (e23)))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H378. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H211. % 47.07/47.27 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 47.07/47.27 cut (((op2 (e23) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H379]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op2 (e20) (e21)) = (e21)) = ((op2 (e23) (e23)) = (op2 (e21) (e23)))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H379. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H29f. % 47.07/47.27 cut (((e21) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2f2]. % 47.07/47.27 cut (((op2 (e20) (e21)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H37a]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H212 ]. % 47.07/47.27 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e20) (e21)) = (op2 (e23) (e23)))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H37a. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H211. % 47.07/47.27 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 47.07/47.27 cut (((op2 (e23) (e23)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H377]. % 47.07/47.27 congruence. % 47.07/47.27 apply (zenon_L396_); trivial. % 47.07/47.27 apply zenon_H212. apply refl_equal. % 47.07/47.27 apply zenon_H212. apply refl_equal. % 47.07/47.27 apply zenon_H2f2. apply sym_equal. exact zenon_H1de. % 47.07/47.27 apply zenon_H212. apply refl_equal. % 47.07/47.27 apply zenon_H212. apply refl_equal. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H218 ]. % 47.07/47.27 apply (zenon_L239_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H209 | zenon_intro zenon_H219 ]. % 47.07/47.27 apply (zenon_L201_); trivial. % 47.07/47.27 apply (zenon_L312_); trivial. % 47.07/47.27 (* end of lemma zenon_L397_ *) % 47.07/47.27 assert (zenon_L398_ : (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (((op2 (e20) (e21)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/((op2 (e23) (e21)) = (e23))))) -> (~((e21) = (e23))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((op2 (e22) (e21)) = (e20)) -> (((op2 (e20) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e23) (e22)) = (e21))))) -> (~((e21) = (e22))) -> ((op2 (e20) (e22)) = (e22)) -> ((op2 (e21) (e22)) = (e20)) -> ((op2 (e22) (e20)) = (e21)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e23))) -> (~((e20) = (e21))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (e21) (e21))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e21)) = (e21)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e23)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e21) (e20)) = (e23)) -> False). % 47.07/47.27 do 0 intro. intros zenon_H2d3 zenon_H1aa zenon_H1a3 zenon_H1b0 zenon_H2d4 zenon_H1d3 zenon_H1c7 zenon_H194 zenon_H1ea zenon_H2fc zenon_H1b9 zenon_H1c3 zenon_H1d0 zenon_H2a8 zenon_H299 zenon_H322 zenon_H19d zenon_H1df zenon_H234 zenon_H183 zenon_H14 zenon_H378 zenon_H29f zenon_H20a zenon_H278 zenon_H229 zenon_H193 zenon_H19c. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2dd ]. % 47.07/47.27 apply (zenon_L219_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2de ]. % 47.07/47.27 apply (zenon_L163_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H2de); [ zenon_intro zenon_H296 | zenon_intro zenon_H1de ]. % 47.07/47.27 apply (zenon_L253_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H2e2 ]. % 47.07/47.27 apply (zenon_L220_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2a4 | zenon_intro zenon_H2e3 ]. % 47.07/47.27 apply (zenon_L221_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H22e ]. % 47.07/47.27 apply (zenon_L168_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H2cf | zenon_intro zenon_H2fd ]. % 47.07/47.27 apply (zenon_L308_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H2fd); [ zenon_intro zenon_H296 | zenon_intro zenon_H2fe ]. % 47.07/47.27 apply (zenon_L253_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_H297 | zenon_intro zenon_H263 ]. % 47.07/47.27 apply (zenon_L263_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_H2e6 | zenon_intro zenon_H323 ]. % 47.07/47.27 apply (zenon_L260_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1dd | zenon_intro zenon_H324 ]. % 47.07/47.27 apply (zenon_L166_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H233 | zenon_intro zenon_H31e ]. % 47.07/47.27 apply (zenon_L179_); trivial. % 47.07/47.27 apply (zenon_L397_); trivial. % 47.07/47.27 (* end of lemma zenon_L398_ *) % 47.07/47.27 assert (zenon_L399_ : (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((e20) = (e22))) -> ((op2 (e21) (e20)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e20) (e23)) = (e23)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e21)) = (e21)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((e20) = (e21))) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e20)) = (e21)) -> ((op2 (e21) (e22)) = (e20)) -> ((op2 (e20) (e22)) = (e22)) -> (~((e21) = (e22))) -> (((op2 (e20) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e23) (e22)) = (e21))))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (~((e21) = (e23))) -> (((op2 (e20) (e21)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/((op2 (e23) (e21)) = (e23))))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((e22) = (op2 (e21) (e21))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H2bd zenon_H185 zenon_H1c4 zenon_H19c zenon_H193 zenon_H229 zenon_H278 zenon_H20a zenon_H29f zenon_H378 zenon_H234 zenon_H1df zenon_H19d zenon_H322 zenon_H299 zenon_H2a8 zenon_H1d0 zenon_H1c3 zenon_H1b9 zenon_H2fc zenon_H194 zenon_H1c7 zenon_H1d3 zenon_H2d4 zenon_H1b0 zenon_H1a3 zenon_H1aa zenon_H2d3 zenon_H14 zenon_H183 zenon_H1e4. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.07/47.27 apply (zenon_L145_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.07/47.27 apply (zenon_L160_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.07/47.27 apply (zenon_L398_); trivial. % 47.07/47.27 apply (zenon_L167_); trivial. % 47.07/47.27 (* end of lemma zenon_L399_ *) % 47.07/47.27 assert (zenon_L400_ : (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((e11) = (e13))) -> ((op1 (e11) (e10)) = (e13)) -> (~((e11) = (e12))) -> ((e12) = (op1 (e11) (e11))) -> ((e22) = (op2 (e21) (e21))) -> ((h2 (e12)) = (op2 (e21) (e21))) -> ((h2 (e11)) = (e21)) -> ((op2 (e21) (e22)) = (e21)) -> (~((h2 (op1 (e11) (e12))) = (op2 (h2 (e11)) (h2 (e12))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e11))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H30e zenon_Ha9 zenon_H34 zenon_H51 zenon_H19 zenon_H183 zenon_H32a zenon_H37b zenon_H296 zenon_H37c zenon_H172 zenon_H15b. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H30e); [ zenon_intro zenon_He1 | zenon_intro zenon_H310 ]. % 47.07/47.27 apply (zenon_L281_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H310); [ zenon_intro zenon_H145 | zenon_intro zenon_H311 ]. % 47.07/47.27 apply (zenon_L95_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H311); [ zenon_intro zenon_He2 | zenon_intro zenon_H175 ]. % 47.07/47.27 cut (((h2 (e11)) = (e21)) = ((h2 (op1 (e11) (e12))) = (op2 (h2 (e11)) (h2 (e12))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H37c. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H37b. % 47.07/47.27 cut (((e21) = (op2 (h2 (e11)) (h2 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H37d]. % 47.07/47.27 cut (((h2 (e11)) = (h2 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H37e]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((h2 (op1 (e11) (e12))) = (h2 (op1 (e11) (e12))))); [ zenon_intro zenon_H37f | zenon_intro zenon_H380 ]. % 47.07/47.27 cut (((h2 (op1 (e11) (e12))) = (h2 (op1 (e11) (e12)))) = ((h2 (e11)) = (h2 (op1 (e11) (e12))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H37e. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H37f. % 47.07/47.27 cut (((h2 (op1 (e11) (e12))) = (h2 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H380]. % 47.07/47.27 cut (((h2 (op1 (e11) (e12))) = (h2 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H381]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op1 (e11) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H382]. % 47.07/47.27 congruence. % 47.07/47.27 exact (zenon_H382 zenon_He2). % 47.07/47.27 apply zenon_H380. apply refl_equal. % 47.07/47.27 apply zenon_H380. apply refl_equal. % 47.07/47.27 elim (classic ((op2 (h2 (e11)) (h2 (e12))) = (op2 (h2 (e11)) (h2 (e12))))); [ zenon_intro zenon_H383 | zenon_intro zenon_H384 ]. % 47.07/47.27 cut (((op2 (h2 (e11)) (h2 (e12))) = (op2 (h2 (e11)) (h2 (e12)))) = ((e21) = (op2 (h2 (e11)) (h2 (e12))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H37d. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H383. % 47.07/47.27 cut (((op2 (h2 (e11)) (h2 (e12))) = (op2 (h2 (e11)) (h2 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H384]. % 47.07/47.27 cut (((op2 (h2 (e11)) (h2 (e12))) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H385]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op2 (e21) (e22)) = (e21)) = ((op2 (h2 (e11)) (h2 (e12))) = (e21))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H385. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H296. % 47.07/47.27 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.07/47.27 cut (((op2 (e21) (e22)) = (op2 (h2 (e11)) (h2 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H386]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((op2 (h2 (e11)) (h2 (e12))) = (op2 (h2 (e11)) (h2 (e12))))); [ zenon_intro zenon_H383 | zenon_intro zenon_H384 ]. % 47.07/47.27 cut (((op2 (h2 (e11)) (h2 (e12))) = (op2 (h2 (e11)) (h2 (e12)))) = ((op2 (e21) (e22)) = (op2 (h2 (e11)) (h2 (e12))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H386. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H383. % 47.07/47.27 cut (((op2 (h2 (e11)) (h2 (e12))) = (op2 (h2 (e11)) (h2 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H384]. % 47.07/47.27 cut (((op2 (h2 (e11)) (h2 (e12))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H387]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((h2 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H329]. % 47.07/47.27 cut (((h2 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H388]. % 47.07/47.27 congruence. % 47.07/47.27 exact (zenon_H388 zenon_H37b). % 47.07/47.27 apply (zenon_L325_); trivial. % 47.07/47.27 apply zenon_H384. apply refl_equal. % 47.07/47.27 apply zenon_H384. apply refl_equal. % 47.07/47.27 apply zenon_H181. apply refl_equal. % 47.07/47.27 apply zenon_H384. apply refl_equal. % 47.07/47.27 apply zenon_H384. apply refl_equal. % 47.07/47.27 apply (zenon_L287_); trivial. % 47.07/47.27 (* end of lemma zenon_L400_ *) % 47.07/47.27 assert (zenon_L401_ : (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((e10) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_Hd8 zenon_H339 zenon_H5c zenon_H116 zenon_H17b zenon_H34 zenon_H2b zenon_Hc5 zenon_Hd7 zenon_H8f zenon_Hf9 zenon_Hf7 zenon_H119 zenon_H5b zenon_H338 zenon_Hb0 zenon_H306 zenon_Hdf zenon_H10d zenon_H177 zenon_H2c zenon_H137 zenon_H35 zenon_H3b zenon_Hac zenon_H9c zenon_Hf1 zenon_Hed zenon_H51 zenon_H130 zenon_H129 zenon_H115 zenon_Hd0 zenon_Hd3 zenon_Hb4 zenon_H104 zenon_H34f zenon_H15b zenon_He6 zenon_H12d zenon_H314 zenon_H133 zenon_H56 zenon_H1b zenon_Hd4 zenon_H163 zenon_H23 zenon_H174 zenon_H110 zenon_H344 zenon_H335 zenon_H164 zenon_H42 zenon_H345 zenon_H346 zenon_H4b zenon_H33f zenon_Ha9 zenon_H150 zenon_H33e zenon_H11b zenon_H63 zenon_H48 zenon_Hfd zenon_H101 zenon_H30e zenon_H149 zenon_H142 zenon_Hbe zenon_Hde zenon_Hea zenon_H16f zenon_H30f zenon_H14c zenon_Hb7 zenon_H154 zenon_H364 zenon_H157 zenon_H11f zenon_H125 zenon_H13e zenon_H1c zenon_H19 zenon_H6a. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.27 apply (zenon_L4_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.27 apply (zenon_L326_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H5f | zenon_intro zenon_H134 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.27 apply (zenon_L50_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.27 apply (zenon_L51_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.27 apply (zenon_L137_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.27 apply (zenon_L10_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.27 apply (zenon_L327_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.27 apply (zenon_L113_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.27 apply (zenon_L19_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.27 apply (zenon_L288_); trivial. % 47.07/47.27 apply (zenon_L389_); trivial. % 47.07/47.27 apply (zenon_L84_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H128 | zenon_intro zenon_H135 ]. % 47.07/47.27 apply (zenon_L87_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H60 | zenon_intro zenon_Hb5 ]. % 47.07/47.27 apply (zenon_L327_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.27 apply (zenon_L50_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.27 apply (zenon_L51_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.27 apply (zenon_L137_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.27 apply (zenon_L10_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.27 apply (zenon_L327_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.27 apply (zenon_L385_); trivial. % 47.07/47.27 apply (zenon_L84_); trivial. % 47.07/47.27 apply (zenon_L19_); trivial. % 47.07/47.27 (* end of lemma zenon_L401_ *) % 47.07/47.27 assert (zenon_L402_ : (~((h2 (op1 (e11) (e13))) = (op2 (h2 (e11)) (h2 (e13))))) -> ((h2 (e10)) = (op2 (op2 (e21) (e21)) (e21))) -> ((op1 (e11) (e13)) = (e10)) -> ((op2 (e21) (e23)) = (e20)) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((h2 (e11)) = (e21)) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H389 zenon_H13 zenon_H172 zenon_H1dd zenon_H14 zenon_H37b zenon_H368 zenon_H194. % 47.07/47.27 cut (((h2 (e10)) = (op2 (op2 (e21) (e21)) (e21))) = ((h2 (op1 (e11) (e13))) = (op2 (h2 (e11)) (h2 (e13))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H389. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H13. % 47.07/47.27 cut (((op2 (op2 (e21) (e21)) (e21)) = (op2 (h2 (e11)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H38a]. % 47.07/47.27 cut (((h2 (e10)) = (h2 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H38b]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((h2 (op1 (e11) (e13))) = (h2 (op1 (e11) (e13))))); [ zenon_intro zenon_H38c | zenon_intro zenon_H38d ]. % 47.07/47.27 cut (((h2 (op1 (e11) (e13))) = (h2 (op1 (e11) (e13)))) = ((h2 (e10)) = (h2 (op1 (e11) (e13))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H38b. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H38c. % 47.07/47.27 cut (((h2 (op1 (e11) (e13))) = (h2 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H38d]. % 47.07/47.27 cut (((h2 (op1 (e11) (e13))) = (h2 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H38e]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op1 (e11) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H38f]. % 47.07/47.27 congruence. % 47.07/47.27 exact (zenon_H38f zenon_H172). % 47.07/47.27 apply zenon_H38d. apply refl_equal. % 47.07/47.27 apply zenon_H38d. apply refl_equal. % 47.07/47.27 elim (classic ((op2 (h2 (e11)) (h2 (e13))) = (op2 (h2 (e11)) (h2 (e13))))); [ zenon_intro zenon_H390 | zenon_intro zenon_H391 ]. % 47.07/47.27 cut (((op2 (h2 (e11)) (h2 (e13))) = (op2 (h2 (e11)) (h2 (e13)))) = ((op2 (op2 (e21) (e21)) (e21)) = (op2 (h2 (e11)) (h2 (e13))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H38a. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H390. % 47.07/47.27 cut (((op2 (h2 (e11)) (h2 (e13))) = (op2 (h2 (e11)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H391]. % 47.07/47.27 cut (((op2 (h2 (e11)) (h2 (e13))) = (op2 (op2 (e21) (e21)) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H392]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op2 (e21) (e23)) = (e20)) = ((op2 (h2 (e11)) (h2 (e13))) = (op2 (op2 (e21) (e21)) (e21)))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H392. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H1dd. % 47.07/47.27 cut (((e20) = (op2 (op2 (e21) (e21)) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H393]. % 47.07/47.27 cut (((op2 (e21) (e23)) = (op2 (h2 (e11)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H394]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((op2 (h2 (e11)) (h2 (e13))) = (op2 (h2 (e11)) (h2 (e13))))); [ zenon_intro zenon_H390 | zenon_intro zenon_H391 ]. % 47.07/47.27 cut (((op2 (h2 (e11)) (h2 (e13))) = (op2 (h2 (e11)) (h2 (e13)))) = ((op2 (e21) (e23)) = (op2 (h2 (e11)) (h2 (e13))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H394. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H390. % 47.07/47.27 cut (((op2 (h2 (e11)) (h2 (e13))) = (op2 (h2 (e11)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H391]. % 47.07/47.27 cut (((op2 (h2 (e11)) (h2 (e13))) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H395]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((h2 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H367]. % 47.07/47.27 cut (((h2 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H388]. % 47.07/47.27 congruence. % 47.07/47.27 exact (zenon_H388 zenon_H37b). % 47.07/47.27 apply (zenon_L391_); trivial. % 47.07/47.27 apply zenon_H391. apply refl_equal. % 47.07/47.27 apply zenon_H391. apply refl_equal. % 47.07/47.27 exact (zenon_H393 zenon_H14). % 47.07/47.27 apply zenon_H391. apply refl_equal. % 47.07/47.27 apply zenon_H391. apply refl_equal. % 47.07/47.27 (* end of lemma zenon_L402_ *) % 47.07/47.27 assert (zenon_L403_ : (~((h2 (op1 (e12) (e12))) = (op2 (h2 (e12)) (h2 (e12))))) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((op1 (e12) (e12)) = (e13)) -> ((op2 (e22) (e22)) = (e23)) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((h2 (e12)) = (op2 (e21) (e21))) -> ((e22) = (op2 (e21) (e21))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H396 zenon_H368 zenon_H8b zenon_H207 zenon_H194 zenon_H32a zenon_H183. % 47.07/47.27 cut (((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) = ((h2 (op1 (e12) (e12))) = (op2 (h2 (e12)) (h2 (e12))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H396. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H368. % 47.07/47.27 cut (((op2 (e21) (op2 (op2 (e21) (e21)) (e21))) = (op2 (h2 (e12)) (h2 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H397]. % 47.07/47.27 cut (((h2 (e13)) = (h2 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H398]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((h2 (op1 (e12) (e12))) = (h2 (op1 (e12) (e12))))); [ zenon_intro zenon_H399 | zenon_intro zenon_H39a ]. % 47.07/47.27 cut (((h2 (op1 (e12) (e12))) = (h2 (op1 (e12) (e12)))) = ((h2 (e13)) = (h2 (op1 (e12) (e12))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H398. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H399. % 47.07/47.27 cut (((h2 (op1 (e12) (e12))) = (h2 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H39a]. % 47.07/47.27 cut (((h2 (op1 (e12) (e12))) = (h2 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H39b]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op1 (e12) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H39c]. % 47.07/47.27 congruence. % 47.07/47.27 exact (zenon_H39c zenon_H8b). % 47.07/47.27 apply zenon_H39a. apply refl_equal. % 47.07/47.27 apply zenon_H39a. apply refl_equal. % 47.07/47.27 elim (classic ((op2 (h2 (e12)) (h2 (e12))) = (op2 (h2 (e12)) (h2 (e12))))); [ zenon_intro zenon_H39d | zenon_intro zenon_H39e ]. % 47.07/47.27 cut (((op2 (h2 (e12)) (h2 (e12))) = (op2 (h2 (e12)) (h2 (e12)))) = ((op2 (e21) (op2 (op2 (e21) (e21)) (e21))) = (op2 (h2 (e12)) (h2 (e12))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H397. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H39d. % 47.07/47.27 cut (((op2 (h2 (e12)) (h2 (e12))) = (op2 (h2 (e12)) (h2 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H39e]. % 47.07/47.27 cut (((op2 (h2 (e12)) (h2 (e12))) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H39f]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op2 (e22) (e22)) = (e23)) = ((op2 (h2 (e12)) (h2 (e12))) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H39f. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H207. % 47.07/47.27 cut (((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H374]. % 47.07/47.27 cut (((op2 (e22) (e22)) = (op2 (h2 (e12)) (h2 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3a0]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((op2 (h2 (e12)) (h2 (e12))) = (op2 (h2 (e12)) (h2 (e12))))); [ zenon_intro zenon_H39d | zenon_intro zenon_H39e ]. % 47.07/47.27 cut (((op2 (h2 (e12)) (h2 (e12))) = (op2 (h2 (e12)) (h2 (e12)))) = ((op2 (e22) (e22)) = (op2 (h2 (e12)) (h2 (e12))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3a0. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H39d. % 47.07/47.27 cut (((op2 (h2 (e12)) (h2 (e12))) = (op2 (h2 (e12)) (h2 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H39e]. % 47.07/47.27 cut (((op2 (h2 (e12)) (h2 (e12))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3a1]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((h2 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H329]. % 47.07/47.27 cut (((h2 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H329]. % 47.07/47.27 congruence. % 47.07/47.27 apply (zenon_L325_); trivial. % 47.07/47.27 apply (zenon_L325_); trivial. % 47.07/47.27 apply zenon_H39e. apply refl_equal. % 47.07/47.27 apply zenon_H39e. apply refl_equal. % 47.07/47.27 exact (zenon_H374 zenon_H194). % 47.07/47.27 apply zenon_H39e. apply refl_equal. % 47.07/47.27 apply zenon_H39e. apply refl_equal. % 47.07/47.27 (* end of lemma zenon_L403_ *) % 47.07/47.27 assert (zenon_L404_ : ((h2 (e12)) = (op2 (e21) (e21))) -> ((op1 (e13) (e10)) = (e12)) -> ((e22) = (op2 (e21) (e21))) -> (~((e22) = (h2 (op1 (e13) (e10))))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H32a zenon_Hf7 zenon_H183 zenon_H3a2. % 47.07/47.27 elim (classic ((h2 (op1 (e13) (e10))) = (h2 (op1 (e13) (e10))))); [ zenon_intro zenon_H3a3 | zenon_intro zenon_H3a4 ]. % 47.07/47.27 cut (((h2 (op1 (e13) (e10))) = (h2 (op1 (e13) (e10)))) = ((e22) = (h2 (op1 (e13) (e10))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3a2. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H3a3. % 47.07/47.27 cut (((h2 (op1 (e13) (e10))) = (h2 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3a4]. % 47.07/47.27 cut (((h2 (op1 (e13) (e10))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H3a5]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((h2 (e12)) = (op2 (e21) (e21))) = ((h2 (op1 (e13) (e10))) = (e22))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3a5. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H32a. % 47.07/47.27 cut (((op2 (e21) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 47.07/47.27 cut (((h2 (e12)) = (h2 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3a6]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((h2 (op1 (e13) (e10))) = (h2 (op1 (e13) (e10))))); [ zenon_intro zenon_H3a3 | zenon_intro zenon_H3a4 ]. % 47.07/47.27 cut (((h2 (op1 (e13) (e10))) = (h2 (op1 (e13) (e10)))) = ((h2 (e12)) = (h2 (op1 (e13) (e10))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3a6. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H3a3. % 47.07/47.27 cut (((h2 (op1 (e13) (e10))) = (h2 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3a4]. % 47.07/47.27 cut (((h2 (op1 (e13) (e10))) = (h2 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H3a7]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op1 (e13) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 47.07/47.27 congruence. % 47.07/47.27 exact (zenon_Hf8 zenon_Hf7). % 47.07/47.27 apply zenon_H3a4. apply refl_equal. % 47.07/47.27 apply zenon_H3a4. apply refl_equal. % 47.07/47.27 apply zenon_H184. apply sym_equal. exact zenon_H183. % 47.07/47.27 apply zenon_H3a4. apply refl_equal. % 47.07/47.27 apply zenon_H3a4. apply refl_equal. % 47.07/47.27 (* end of lemma zenon_L404_ *) % 47.07/47.27 assert (zenon_L405_ : (~((h2 (op1 (e13) (e11))) = (op2 (h2 (e13)) (h2 (e11))))) -> ((op1 (e13) (e11)) = (e13)) -> ((op2 (e23) (e21)) = (e23)) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((h2 (e11)) = (e21)) -> False). % 47.07/47.27 do 0 intro. intros zenon_H3a8 zenon_Hb5 zenon_H22e zenon_H368 zenon_H194 zenon_H37b. % 47.07/47.27 cut (((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) = ((h2 (op1 (e13) (e11))) = (op2 (h2 (e13)) (h2 (e11))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3a8. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H368. % 47.07/47.27 cut (((op2 (e21) (op2 (op2 (e21) (e21)) (e21))) = (op2 (h2 (e13)) (h2 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3a9]. % 47.07/47.27 cut (((h2 (e13)) = (h2 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3aa]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((h2 (op1 (e13) (e11))) = (h2 (op1 (e13) (e11))))); [ zenon_intro zenon_H3ab | zenon_intro zenon_H3ac ]. % 47.07/47.27 cut (((h2 (op1 (e13) (e11))) = (h2 (op1 (e13) (e11)))) = ((h2 (e13)) = (h2 (op1 (e13) (e11))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3aa. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H3ab. % 47.07/47.27 cut (((h2 (op1 (e13) (e11))) = (h2 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3ac]. % 47.07/47.27 cut (((h2 (op1 (e13) (e11))) = (h2 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H3ad]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op1 (e13) (e11)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H3ae]. % 47.07/47.27 congruence. % 47.07/47.27 exact (zenon_H3ae zenon_Hb5). % 47.07/47.27 apply zenon_H3ac. apply refl_equal. % 47.07/47.27 apply zenon_H3ac. apply refl_equal. % 47.07/47.27 elim (classic ((op2 (h2 (e13)) (h2 (e11))) = (op2 (h2 (e13)) (h2 (e11))))); [ zenon_intro zenon_H3af | zenon_intro zenon_H3b0 ]. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e11))) = (op2 (h2 (e13)) (h2 (e11)))) = ((op2 (e21) (op2 (op2 (e21) (e21)) (e21))) = (op2 (h2 (e13)) (h2 (e11))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3a9. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H3af. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e11))) = (op2 (h2 (e13)) (h2 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3b0]. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e11))) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H3b1]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op2 (e23) (e21)) = (e23)) = ((op2 (h2 (e13)) (h2 (e11))) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3b1. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H22e. % 47.07/47.27 cut (((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H374]. % 47.07/47.27 cut (((op2 (e23) (e21)) = (op2 (h2 (e13)) (h2 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3b2]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((op2 (h2 (e13)) (h2 (e11))) = (op2 (h2 (e13)) (h2 (e11))))); [ zenon_intro zenon_H3af | zenon_intro zenon_H3b0 ]. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e11))) = (op2 (h2 (e13)) (h2 (e11)))) = ((op2 (e23) (e21)) = (op2 (h2 (e13)) (h2 (e11))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3b2. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H3af. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e11))) = (op2 (h2 (e13)) (h2 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3b0]. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e11))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H3b3]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((h2 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H388]. % 47.07/47.27 cut (((h2 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H367]. % 47.07/47.27 congruence. % 47.07/47.27 apply (zenon_L391_); trivial. % 47.07/47.27 exact (zenon_H388 zenon_H37b). % 47.07/47.27 apply zenon_H3b0. apply refl_equal. % 47.07/47.27 apply zenon_H3b0. apply refl_equal. % 47.07/47.27 exact (zenon_H374 zenon_H194). % 47.07/47.27 apply zenon_H3b0. apply refl_equal. % 47.07/47.27 apply zenon_H3b0. apply refl_equal. % 47.07/47.27 (* end of lemma zenon_L405_ *) % 47.07/47.27 assert (zenon_L406_ : ((h2 (e10)) = (op2 (op2 (e21) (e21)) (e21))) -> ((op1 (e13) (e12)) = (e10)) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((e20) = (h2 (op1 (e13) (e12))))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H13 zenon_H102 zenon_H14 zenon_H3b4. % 47.07/47.27 elim (classic ((h2 (op1 (e13) (e12))) = (h2 (op1 (e13) (e12))))); [ zenon_intro zenon_H3b5 | zenon_intro zenon_H3b6 ]. % 47.07/47.27 cut (((h2 (op1 (e13) (e12))) = (h2 (op1 (e13) (e12)))) = ((e20) = (h2 (op1 (e13) (e12))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3b4. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H3b5. % 47.07/47.27 cut (((h2 (op1 (e13) (e12))) = (h2 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3b6]. % 47.07/47.27 cut (((h2 (op1 (e13) (e12))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H3b7]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((h2 (e10)) = (op2 (op2 (e21) (e21)) (e21))) = ((h2 (op1 (e13) (e12))) = (e20))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3b7. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H13. % 47.07/47.27 cut (((op2 (op2 (e21) (e21)) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 47.07/47.27 cut (((h2 (e10)) = (h2 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3b8]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((h2 (op1 (e13) (e12))) = (h2 (op1 (e13) (e12))))); [ zenon_intro zenon_H3b5 | zenon_intro zenon_H3b6 ]. % 47.07/47.27 cut (((h2 (op1 (e13) (e12))) = (h2 (op1 (e13) (e12)))) = ((h2 (e10)) = (h2 (op1 (e13) (e12))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3b8. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H3b5. % 47.07/47.27 cut (((h2 (op1 (e13) (e12))) = (h2 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3b6]. % 47.07/47.27 cut (((h2 (op1 (e13) (e12))) = (h2 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3b9]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op1 (e13) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H3ba]. % 47.07/47.27 congruence. % 47.07/47.27 exact (zenon_H3ba zenon_H102). % 47.07/47.27 apply zenon_H3b6. apply refl_equal. % 47.07/47.27 apply zenon_H3b6. apply refl_equal. % 47.07/47.27 apply zenon_H15. apply sym_equal. exact zenon_H14. % 47.07/47.27 apply zenon_H3b6. apply refl_equal. % 47.07/47.27 apply zenon_H3b6. apply refl_equal. % 47.07/47.27 (* end of lemma zenon_L406_ *) % 47.07/47.27 assert (zenon_L407_ : ((op2 (e23) (e22)) = (e20)) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((h2 (e12)) = (op2 (e21) (e21))) -> ((e22) = (op2 (e21) (e21))) -> ((h2 (e10)) = (op2 (op2 (e21) (e21)) (e21))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((op1 (e13) (e12)) = (e10)) -> (~((h2 (op1 (e13) (e12))) = (op2 (h2 (e13)) (h2 (e12))))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H260 zenon_H368 zenon_H194 zenon_H32a zenon_H183 zenon_H13 zenon_H14 zenon_H102 zenon_H3bb. % 47.07/47.27 elim (classic ((op2 (h2 (e13)) (h2 (e12))) = (op2 (h2 (e13)) (h2 (e12))))); [ zenon_intro zenon_H3bc | zenon_intro zenon_H3bd ]. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e12))) = (op2 (h2 (e13)) (h2 (e12)))) = ((h2 (op1 (e13) (e12))) = (op2 (h2 (e13)) (h2 (e12))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3bb. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H3bc. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e12))) = (op2 (h2 (e13)) (h2 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3bd]. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e12))) = (h2 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3be]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op2 (e23) (e22)) = (e20)) = ((op2 (h2 (e13)) (h2 (e12))) = (h2 (op1 (e13) (e12))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3be. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H260. % 47.07/47.27 cut (((e20) = (h2 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3b4]. % 47.07/47.27 cut (((op2 (e23) (e22)) = (op2 (h2 (e13)) (h2 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3bf]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((op2 (h2 (e13)) (h2 (e12))) = (op2 (h2 (e13)) (h2 (e12))))); [ zenon_intro zenon_H3bc | zenon_intro zenon_H3bd ]. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e12))) = (op2 (h2 (e13)) (h2 (e12)))) = ((op2 (e23) (e22)) = (op2 (h2 (e13)) (h2 (e12))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3bf. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H3bc. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e12))) = (op2 (h2 (e13)) (h2 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3bd]. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e12))) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3c0]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((h2 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H329]. % 47.07/47.27 cut (((h2 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H367]. % 47.07/47.27 congruence. % 47.07/47.27 apply (zenon_L391_); trivial. % 47.07/47.27 apply (zenon_L325_); trivial. % 47.07/47.27 apply zenon_H3bd. apply refl_equal. % 47.07/47.27 apply zenon_H3bd. apply refl_equal. % 47.07/47.27 apply (zenon_L406_); trivial. % 47.07/47.27 apply zenon_H3bd. apply refl_equal. % 47.07/47.27 apply zenon_H3bd. apply refl_equal. % 47.07/47.27 (* end of lemma zenon_L407_ *) % 47.07/47.27 assert (zenon_L408_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e12) = (e13))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((h2 (op1 (e13) (e12))) = (op2 (h2 (e13)) (h2 (e12))))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((h2 (e10)) = (op2 (op2 (e21) (e21)) (e21))) -> ((e22) = (op2 (e21) (e21))) -> ((h2 (e12)) = (op2 (e21) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((op2 (e23) (e22)) = (e20)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> False). % 47.07/47.27 do 0 intro. intros zenon_H339 zenon_Hd8 zenon_H34 zenon_H2b zenon_H8f zenon_Hd7 zenon_Hb5 zenon_Hc5 zenon_Hf9 zenon_H125 zenon_H11b zenon_H11f zenon_Hb0 zenon_H115 zenon_H101 zenon_H10d zenon_H5c zenon_H116 zenon_Hd4 zenon_Hb4 zenon_H56 zenon_H1b zenon_Hd0 zenon_Hfd zenon_Hed zenon_H63 zenon_H110 zenon_H2c zenon_H3b zenon_Hac zenon_He6 zenon_H119 zenon_H12d zenon_Hf1 zenon_H51 zenon_H130 zenon_H6a zenon_H19 zenon_H1c zenon_H3bb zenon_H14 zenon_H13 zenon_H183 zenon_H32a zenon_H194 zenon_H368 zenon_H260 zenon_H338 zenon_H172. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.27 apply (zenon_L90_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.27 apply (zenon_L19_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.27 apply (zenon_L407_); trivial. % 47.07/47.27 apply (zenon_L332_); trivial. % 47.07/47.27 (* end of lemma zenon_L408_ *) % 47.07/47.27 assert (zenon_L409_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e11)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e12) (e12)) = (e13)) -> ((op1 (e12) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> False). % 47.07/47.27 do 0 intro. intros zenon_H364 zenon_H42 zenon_H2c zenon_H119 zenon_H5b zenon_H338 zenon_H175 zenon_H306 zenon_Hdf zenon_H10d zenon_H34 zenon_H30a zenon_H2b zenon_H8b zenon_Hb8 zenon_Hc5 zenon_Hf9 zenon_Hf7 zenon_H19 zenon_Hb0 zenon_Hb4 zenon_Hd3 zenon_H1c zenon_H6a zenon_Hd0 zenon_H8f zenon_Hd7. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H364); [ zenon_intro zenon_H41 | zenon_intro zenon_H365 ]. % 47.07/47.27 apply (zenon_L11_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H365); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H366 ]. % 47.07/47.27 apply (zenon_L384_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H366); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H152 ]. % 47.07/47.27 apply (zenon_L386_); trivial. % 47.07/47.27 apply (zenon_L111_); trivial. % 47.07/47.27 (* end of lemma zenon_L409_ *) % 47.07/47.27 assert (zenon_L410_ : (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op2 (e23) (e22)) = (e20)) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((h2 (e12)) = (op2 (e21) (e21))) -> ((e22) = (op2 (e21) (e21))) -> ((h2 (e10)) = (op2 (op2 (e21) (e21)) (e21))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((h2 (op1 (e13) (e12))) = (op2 (h2 (e13)) (h2 (e12))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((op1 (e13) (e11)) = (e13)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e12)) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (e11) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H17b zenon_H260 zenon_H368 zenon_H194 zenon_H32a zenon_H183 zenon_H13 zenon_H14 zenon_H3bb zenon_H130 zenon_H51 zenon_Hf1 zenon_H12d zenon_He6 zenon_Hac zenon_H3b zenon_H110 zenon_H63 zenon_Hed zenon_Hfd zenon_H1b zenon_H56 zenon_Hd4 zenon_H116 zenon_H5c zenon_H101 zenon_H115 zenon_H11f zenon_H11b zenon_H125 zenon_Hb5 zenon_Hd8 zenon_H339 zenon_Hd7 zenon_H8f zenon_Hd0 zenon_H6a zenon_Hd3 zenon_Hb4 zenon_Hb0 zenon_Hf7 zenon_Hf9 zenon_Hc5 zenon_Hb8 zenon_H8b zenon_H2b zenon_H30a zenon_H34 zenon_H10d zenon_Hdf zenon_H306 zenon_H338 zenon_H5b zenon_H119 zenon_H42 zenon_H364 zenon_H177 zenon_H19 zenon_H2c zenon_H1c zenon_H137. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H17b); [ zenon_intro zenon_H172 | zenon_intro zenon_H17c ]. % 47.07/47.27 apply (zenon_L408_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H17c); [ zenon_intro zenon_H175 | zenon_intro zenon_H17d ]. % 47.07/47.27 apply (zenon_L409_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H176 | zenon_intro zenon_H136 ]. % 47.07/47.27 apply (zenon_L132_); trivial. % 47.07/47.27 apply (zenon_L92_); trivial. % 47.07/47.27 (* end of lemma zenon_L410_ *) % 47.07/47.27 assert (zenon_L411_ : ((op1 (e10) (e12)) = (e12)) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op2 (e23) (e22)) = (e20)) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((h2 (e12)) = (op2 (e21) (e21))) -> ((e22) = (op2 (e21) (e21))) -> ((h2 (e10)) = (op2 (op2 (e21) (e21)) (e21))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> (~((h2 (op1 (e13) (e12))) = (op2 (h2 (e13)) (h2 (e12))))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e12) = (e13))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H5b zenon_H172 zenon_H338 zenon_H260 zenon_H368 zenon_H194 zenon_H32a zenon_H183 zenon_H13 zenon_H14 zenon_H3bb zenon_H1c zenon_H19 zenon_H6a zenon_H157 zenon_H12d zenon_He6 zenon_H11f zenon_H11b zenon_H125 zenon_H137 zenon_H154 zenon_H14c zenon_H13e zenon_H142 zenon_H119 zenon_H9c zenon_H42 zenon_H3b zenon_H149 zenon_H150 zenon_H4b zenon_Hac zenon_H5f zenon_H48 zenon_Hb7 zenon_H116 zenon_H5c zenon_H110 zenon_H63 zenon_Hed zenon_Hfd zenon_H10d zenon_H101 zenon_H115 zenon_Hb0 zenon_H34 zenon_H2b zenon_Hc5 zenon_Hf9 zenon_Hf1 zenon_H51 zenon_H130 zenon_Hd4 zenon_Hb4 zenon_H56 zenon_H1b zenon_Hd0 zenon_H2c zenon_H129 zenon_H104 zenon_H133 zenon_H8f zenon_H339 zenon_Hd8. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.27 apply (zenon_L50_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.27 apply (zenon_L51_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.27 apply (zenon_L137_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.27 apply (zenon_L10_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.27 apply (zenon_L17_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.27 apply (zenon_L113_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.27 apply (zenon_L19_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.27 apply (zenon_L407_); trivial. % 47.07/47.27 apply (zenon_L332_); trivial. % 47.07/47.27 apply (zenon_L84_); trivial. % 47.07/47.27 (* end of lemma zenon_L411_ *) % 47.07/47.27 assert (zenon_L412_ : (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((h2 (op1 (e13) (e12))) = (op2 (h2 (e13)) (h2 (e12))))) -> ((e20) = (op2 (op2 (e21) (e21)) (e21))) -> ((h2 (e10)) = (op2 (op2 (e21) (e21)) (e21))) -> ((e22) = (op2 (e21) (e21))) -> ((h2 (e12)) = (op2 (e21) (e21))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((op2 (e23) (e22)) = (e20)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e10) (e11)) = (e11)) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H6a zenon_H19 zenon_H133 zenon_H104 zenon_Hb7 zenon_H48 zenon_H4b zenon_H150 zenon_H149 zenon_H9c zenon_H142 zenon_H13e zenon_H14c zenon_H154 zenon_H137 zenon_H157 zenon_H5b zenon_H129 zenon_H35 zenon_H339 zenon_Hd8 zenon_H2b zenon_H8f zenon_Hd7 zenon_Hc5 zenon_Hf9 zenon_H125 zenon_H11b zenon_H11f zenon_Hb0 zenon_H115 zenon_H101 zenon_H10d zenon_H5c zenon_H116 zenon_Hd4 zenon_Hb4 zenon_H56 zenon_H1b zenon_Hd0 zenon_Hfd zenon_Hed zenon_H63 zenon_H110 zenon_Hac zenon_He6 zenon_H119 zenon_H12d zenon_Hf1 zenon_H51 zenon_H130 zenon_H3bb zenon_H14 zenon_H13 zenon_H183 zenon_H32a zenon_H194 zenon_H368 zenon_H260 zenon_H338 zenon_H344 zenon_H17b zenon_Hd3 zenon_Hf7 zenon_H306 zenon_H364 zenon_H177 zenon_H345 zenon_H3b zenon_H2c zenon_H1c zenon_H42. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.27 apply (zenon_L7_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H33 | zenon_intro zenon_H347 ]. % 47.07/47.27 apply (zenon_L9_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H32c | zenon_intro zenon_H348 ]. % 47.07/47.27 apply (zenon_L326_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H348); [ zenon_intro zenon_Hdf | zenon_intro zenon_H172 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.27 apply (zenon_L4_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.27 apply (zenon_L326_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H5f | zenon_intro zenon_H134 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.27 apply (zenon_L50_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.27 apply (zenon_L51_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.27 apply (zenon_L137_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.27 apply (zenon_L10_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.27 apply (zenon_L327_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.27 apply (zenon_L113_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.27 apply (zenon_L19_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.27 apply (zenon_L288_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H364); [ zenon_intro zenon_H41 | zenon_intro zenon_H365 ]. % 47.07/47.27 apply (zenon_L11_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H365); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H366 ]. % 47.07/47.27 apply (zenon_L410_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H366); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H152 ]. % 47.07/47.27 apply (zenon_L386_); trivial. % 47.07/47.27 apply (zenon_L111_); trivial. % 47.07/47.27 apply (zenon_L84_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H128 | zenon_intro zenon_H135 ]. % 47.07/47.27 apply (zenon_L87_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H60 | zenon_intro zenon_Hb5 ]. % 47.07/47.27 apply (zenon_L327_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.27 apply (zenon_L50_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.27 apply (zenon_L51_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.27 apply (zenon_L137_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.27 apply (zenon_L10_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.27 apply (zenon_L327_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.27 apply (zenon_L71_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.27 apply (zenon_L19_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.27 apply (zenon_L407_); trivial. % 47.07/47.27 apply (zenon_L410_); trivial. % 47.07/47.27 apply (zenon_L84_); trivial. % 47.07/47.27 apply (zenon_L19_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.27 apply (zenon_L4_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.27 apply (zenon_L326_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H5f | zenon_intro zenon_H134 ]. % 47.07/47.27 apply (zenon_L411_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H128 | zenon_intro zenon_H135 ]. % 47.07/47.27 apply (zenon_L87_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H60 | zenon_intro zenon_Hb5 ]. % 47.07/47.27 apply (zenon_L327_); trivial. % 47.07/47.27 apply (zenon_L408_); trivial. % 47.07/47.27 apply (zenon_L19_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.27 apply (zenon_L10_); trivial. % 47.07/47.27 apply (zenon_L11_); trivial. % 47.07/47.27 (* end of lemma zenon_L412_ *) % 47.07/47.27 assert (zenon_L413_ : (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((op1 (e11) (e13)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e12)) = (e13)) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e13)) = (e12)) -> False). % 47.07/47.27 do 0 intro. intros zenon_H110 zenon_H63 zenon_H1c zenon_H175 zenon_H174 zenon_H8b zenon_H19 zenon_Hb0 zenon_H5c zenon_H116 zenon_H10d zenon_H101 zenon_H104 zenon_H5b zenon_H119 zenon_H34 zenon_H71 zenon_H2b zenon_H56 zenon_H5f zenon_H7d zenon_Hc5 zenon_Hf9 zenon_Hff. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H62 | zenon_intro zenon_H111 ]. % 47.07/47.27 apply (zenon_L18_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H112 ]. % 47.07/47.27 apply (zenon_L127_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Ha8 ]. % 47.07/47.27 apply (zenon_L99_); trivial. % 47.07/47.27 apply (zenon_L128_); trivial. % 47.07/47.27 (* end of lemma zenon_L413_ *) % 47.07/47.27 assert (zenon_L414_ : (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e13)) = (e12)) -> ((op1 (e12) (e13)) = (e13)) -> False). % 47.07/47.27 do 0 intro. intros zenon_Hd0 zenon_H6a zenon_Hf9 zenon_H5f zenon_H56 zenon_H119 zenon_H5b zenon_H104 zenon_H101 zenon_H10d zenon_H116 zenon_H5c zenon_H8b zenon_H174 zenon_H175 zenon_H1c zenon_H63 zenon_H110 zenon_H19 zenon_H34 zenon_H71 zenon_H2b zenon_Hc5 zenon_H105 zenon_Hb0 zenon_H115 zenon_Hff zenon_Ha8. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.07/47.27 apply (zenon_L19_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.07/47.27 apply (zenon_L413_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.07/47.27 apply (zenon_L28_); trivial. % 47.07/47.27 apply (zenon_L65_); trivial. % 47.07/47.27 (* end of lemma zenon_L414_ *) % 47.07/47.27 assert (zenon_L415_ : (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((op1 (e12) (e12)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e11)) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> ((e12) = (op1 (e11) (e11))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_Hd0 zenon_H6a zenon_Hf9 zenon_H5f zenon_H56 zenon_H119 zenon_H5b zenon_H104 zenon_H101 zenon_H10d zenon_H116 zenon_H5c zenon_H8b zenon_H174 zenon_H175 zenon_H1c zenon_H63 zenon_H110 zenon_H19 zenon_H34 zenon_H71 zenon_H2b zenon_Hc5 zenon_H105 zenon_Hb0 zenon_H115. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.07/47.27 apply (zenon_L52_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.07/47.27 apply (zenon_L28_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.07/47.27 apply (zenon_L70_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H62 | zenon_intro zenon_H111 ]. % 47.07/47.27 apply (zenon_L18_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H112 ]. % 47.07/47.27 apply (zenon_L127_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Ha8 ]. % 47.07/47.27 apply (zenon_L55_); trivial. % 47.07/47.27 apply (zenon_L414_); trivial. % 47.07/47.27 (* end of lemma zenon_L415_ *) % 47.07/47.27 assert (zenon_L416_ : ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e12))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((e10) = (e11))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H5b zenon_H119 zenon_H110 zenon_H63 zenon_H175 zenon_H174 zenon_H116 zenon_H51 zenon_H1c zenon_H19 zenon_H6a zenon_H15b zenon_H339 zenon_H10d zenon_Hdf zenon_H306 zenon_H34 zenon_H30a zenon_H2b zenon_H115 zenon_H15a zenon_Hb0 zenon_Hb5 zenon_Hc5 zenon_Hf9. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H117 ]. % 47.07/47.27 apply (zenon_L328_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Haf | zenon_intro zenon_H118 ]. % 47.07/47.27 apply (zenon_L28_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hff ]. % 47.07/47.27 apply (zenon_L70_); trivial. % 47.07/47.27 apply (zenon_L338_); trivial. % 47.07/47.27 (* end of lemma zenon_L416_ *) % 47.07/47.27 assert (zenon_L417_ : ((op2 (e23) (e23)) = (e21)) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> (~((e21) = (op2 (h2 (e13)) (h2 (e13))))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H243 zenon_H368 zenon_H194 zenon_H3c1. % 47.07/47.27 elim (classic ((op2 (h2 (e13)) (h2 (e13))) = (op2 (h2 (e13)) (h2 (e13))))); [ zenon_intro zenon_H3c2 | zenon_intro zenon_H3c3 ]. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e13))) = (op2 (h2 (e13)) (h2 (e13)))) = ((e21) = (op2 (h2 (e13)) (h2 (e13))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3c1. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H3c2. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e13))) = (op2 (h2 (e13)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H3c3]. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e13))) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H3c4]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op2 (e23) (e23)) = (e21)) = ((op2 (h2 (e13)) (h2 (e13))) = (e21))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3c4. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H243. % 47.07/47.27 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.07/47.27 cut (((op2 (e23) (e23)) = (op2 (h2 (e13)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H3c5]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((op2 (h2 (e13)) (h2 (e13))) = (op2 (h2 (e13)) (h2 (e13))))); [ zenon_intro zenon_H3c2 | zenon_intro zenon_H3c3 ]. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e13))) = (op2 (h2 (e13)) (h2 (e13)))) = ((op2 (e23) (e23)) = (op2 (h2 (e13)) (h2 (e13))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3c5. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H3c2. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e13))) = (op2 (h2 (e13)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H3c3]. % 47.07/47.27 cut (((op2 (h2 (e13)) (h2 (e13))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3c6]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((h2 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H367]. % 47.07/47.27 cut (((h2 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H367]. % 47.07/47.27 congruence. % 47.07/47.27 apply (zenon_L391_); trivial. % 47.07/47.27 apply (zenon_L391_); trivial. % 47.07/47.27 apply zenon_H3c3. apply refl_equal. % 47.07/47.27 apply zenon_H3c3. apply refl_equal. % 47.07/47.27 apply zenon_H181. apply refl_equal. % 47.07/47.27 apply zenon_H3c3. apply refl_equal. % 47.07/47.27 apply zenon_H3c3. apply refl_equal. % 47.07/47.27 (* end of lemma zenon_L417_ *) % 47.07/47.27 assert (zenon_L418_ : (~((h2 (op1 (e13) (e13))) = (op2 (h2 (e13)) (h2 (e13))))) -> ((h2 (e11)) = (e21)) -> ((op1 (e13) (e13)) = (e11)) -> ((op2 (e23) (e23)) = (e21)) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H3c7 zenon_H37b zenon_H342 zenon_H243 zenon_H368 zenon_H194. % 47.07/47.27 cut (((h2 (e11)) = (e21)) = ((h2 (op1 (e13) (e13))) = (op2 (h2 (e13)) (h2 (e13))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3c7. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H37b. % 47.07/47.27 cut (((e21) = (op2 (h2 (e13)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H3c1]. % 47.07/47.27 cut (((h2 (e11)) = (h2 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H3c8]. % 47.07/47.27 congruence. % 47.07/47.27 elim (classic ((h2 (op1 (e13) (e13))) = (h2 (op1 (e13) (e13))))); [ zenon_intro zenon_H3c9 | zenon_intro zenon_H3ca ]. % 47.07/47.27 cut (((h2 (op1 (e13) (e13))) = (h2 (op1 (e13) (e13)))) = ((h2 (e11)) = (h2 (op1 (e13) (e13))))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H3c8. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H3c9. % 47.07/47.27 cut (((h2 (op1 (e13) (e13))) = (h2 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H3ca]. % 47.07/47.27 cut (((h2 (op1 (e13) (e13))) = (h2 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H3cb]. % 47.07/47.27 congruence. % 47.07/47.27 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3cc]. % 47.07/47.27 congruence. % 47.07/47.27 exact (zenon_H3cc zenon_H342). % 47.07/47.27 apply zenon_H3ca. apply refl_equal. % 47.07/47.27 apply zenon_H3ca. apply refl_equal. % 47.07/47.27 apply (zenon_L417_); trivial. % 47.07/47.27 (* end of lemma zenon_L418_ *) % 47.07/47.27 assert (zenon_L419_ : (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((h2 (op1 (e13) (e13))) = (op2 (h2 (e13)) (h2 (e13))))) -> ((h2 (e11)) = (e21)) -> ((op2 (e23) (e23)) = (e21)) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H34f zenon_Hf9 zenon_Hc5 zenon_H115 zenon_H306 zenon_Hdf zenon_H10d zenon_H339 zenon_H15b zenon_H6a zenon_H51 zenon_H116 zenon_H174 zenon_H63 zenon_H110 zenon_H119 zenon_H5b zenon_Hb4 zenon_H56 zenon_H19 zenon_H1b zenon_H1c zenon_Hd4 zenon_H34 zenon_H30a zenon_H2b zenon_Hb0 zenon_Hb5 zenon_Hd7 zenon_H8f zenon_H175 zenon_H338 zenon_H3c7 zenon_H37b zenon_H243 zenon_H368 zenon_H194. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H34f); [ zenon_intro zenon_H15a | zenon_intro zenon_H350 ]. % 47.07/47.27 apply (zenon_L416_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H350); [ zenon_intro zenon_H7d | zenon_intro zenon_H351 ]. % 47.07/47.27 apply (zenon_L344_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H351); [ zenon_intro zenon_H105 | zenon_intro zenon_H342 ]. % 47.07/47.27 apply (zenon_L382_); trivial. % 47.07/47.27 apply (zenon_L418_); trivial. % 47.07/47.27 (* end of lemma zenon_L419_ *) % 47.07/47.27 assert (zenon_L420_ : (~((e12) = (e13))) -> ((op1 (e12) (e13)) = (e12)) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((h2 (op1 (e13) (e13))) = (op2 (h2 (e13)) (h2 (e13))))) -> ((h2 (e11)) = (e21)) -> ((op2 (e23) (e23)) = (e21)) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_Hd8 zenon_Hb8 zenon_H125 zenon_H11b zenon_H11f zenon_H101 zenon_H5c zenon_Hd0 zenon_Hfd zenon_Hed zenon_H2c zenon_H3b zenon_Hac zenon_He6 zenon_H12d zenon_H34f zenon_Hf9 zenon_Hc5 zenon_H115 zenon_H306 zenon_Hdf zenon_H10d zenon_H339 zenon_H15b zenon_H6a zenon_H51 zenon_H116 zenon_H174 zenon_H63 zenon_H110 zenon_H119 zenon_H5b zenon_Hb4 zenon_H56 zenon_H19 zenon_H1b zenon_H1c zenon_Hd4 zenon_H34 zenon_H2b zenon_Hb0 zenon_Hb5 zenon_Hd7 zenon_H8f zenon_H175 zenon_H338 zenon_H3c7 zenon_H37b zenon_H243 zenon_H368 zenon_H194. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.27 apply (zenon_L89_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.27 apply (zenon_L19_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.27 apply (zenon_L288_); trivial. % 47.07/47.27 apply (zenon_L419_); trivial. % 47.07/47.27 (* end of lemma zenon_L420_ *) % 47.07/47.27 assert (zenon_L421_ : ((op1 (e13) (e12)) = (e11)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e12) = (e13))) -> ((op1 (e12) (e13)) = (e12)) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((h2 (op1 (e13) (e13))) = (op2 (h2 (e13)) (h2 (e13))))) -> ((h2 (e11)) = (e21)) -> ((op2 (e23) (e23)) = (e21)) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H105 zenon_H104 zenon_Hd8 zenon_Hb8 zenon_H125 zenon_H11b zenon_H11f zenon_H101 zenon_H5c zenon_Hd0 zenon_Hfd zenon_Hed zenon_H2c zenon_H3b zenon_Hac zenon_He6 zenon_H12d zenon_H34f zenon_Hf9 zenon_Hc5 zenon_H115 zenon_H306 zenon_Hdf zenon_H10d zenon_H339 zenon_H15b zenon_H6a zenon_H51 zenon_H116 zenon_H174 zenon_H63 zenon_H110 zenon_H119 zenon_H5b zenon_Hb4 zenon_H56 zenon_H19 zenon_H1b zenon_H1c zenon_Hd4 zenon_H34 zenon_H2b zenon_Hb0 zenon_Hd7 zenon_H8f zenon_H175 zenon_H338 zenon_H3c7 zenon_H37b zenon_H243 zenon_H368 zenon_H194. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.07/47.27 apply (zenon_L19_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.07/47.27 apply (zenon_L57_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.07/47.27 apply (zenon_L28_); trivial. % 47.07/47.27 apply (zenon_L420_); trivial. % 47.07/47.27 (* end of lemma zenon_L421_ *) % 47.07/47.27 assert (zenon_L422_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((op2 (e23) (e23)) = (e21)) -> ((h2 (e11)) = (e21)) -> (~((h2 (op1 (e13) (e13))) = (op2 (h2 (e13)) (h2 (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((e10) = (e11))) -> ((op1 (e10) (e13)) = (e13)) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> False). % 47.07/47.27 do 0 intro. intros zenon_H48 zenon_H194 zenon_H368 zenon_H243 zenon_H37b zenon_H3c7 zenon_Hfd zenon_Hed zenon_H15b zenon_Hd7 zenon_Ha9 zenon_H33e zenon_H344 zenon_H34f zenon_Hf9 zenon_Hc5 zenon_H115 zenon_H306 zenon_H10d zenon_H339 zenon_H51 zenon_H116 zenon_H174 zenon_H63 zenon_H110 zenon_H119 zenon_H5b zenon_Hb4 zenon_H56 zenon_H1b zenon_Hd4 zenon_H2b zenon_Hb0 zenon_H8f zenon_H338 zenon_Hd3 zenon_H150 zenon_H130 zenon_Hf1 zenon_H12d zenon_He6 zenon_Hac zenon_Hd0 zenon_H5c zenon_H101 zenon_H11f zenon_H11b zenon_H125 zenon_Hd8 zenon_H35 zenon_H129 zenon_H9c zenon_H314 zenon_H104 zenon_H133 zenon_H19 zenon_H6a zenon_H345 zenon_H3b zenon_H2c zenon_H1c zenon_H42. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.27 apply (zenon_L7_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H33 | zenon_intro zenon_H347 ]. % 47.07/47.27 apply (zenon_L9_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H32c | zenon_intro zenon_H348 ]. % 47.07/47.27 apply (zenon_L326_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H348); [ zenon_intro zenon_Hdf | zenon_intro zenon_H172 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.27 apply (zenon_L4_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.27 apply (zenon_L326_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H5f | zenon_intro zenon_H134 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.27 apply (zenon_L50_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.27 apply (zenon_L51_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.27 apply (zenon_L137_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H34f); [ zenon_intro zenon_H15a | zenon_intro zenon_H350 ]. % 47.07/47.27 apply (zenon_L297_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H350); [ zenon_intro zenon_H7d | zenon_intro zenon_H351 ]. % 47.07/47.27 apply (zenon_L40_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H351); [ zenon_intro zenon_H105 | zenon_intro zenon_H342 ]. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H14f | zenon_intro zenon_H340 ]. % 47.07/47.27 apply (zenon_L123_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H175 | zenon_intro zenon_H341 ]. % 47.07/47.27 apply (zenon_L421_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H342 ]. % 47.07/47.27 apply (zenon_L54_); trivial. % 47.07/47.27 apply (zenon_L418_); trivial. % 47.07/47.27 apply (zenon_L418_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H128 | zenon_intro zenon_H135 ]. % 47.07/47.27 apply (zenon_L87_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H60 | zenon_intro zenon_Hb5 ]. % 47.07/47.27 apply (zenon_L327_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.27 apply (zenon_L90_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.27 apply (zenon_L19_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.27 apply (zenon_L288_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H14f | zenon_intro zenon_H340 ]. % 47.07/47.27 apply (zenon_L105_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H175 | zenon_intro zenon_H341 ]. % 47.07/47.27 apply (zenon_L419_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H342 ]. % 47.07/47.27 apply (zenon_L54_); trivial. % 47.07/47.27 apply (zenon_L418_); trivial. % 47.07/47.27 apply (zenon_L19_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H14f | zenon_intro zenon_H340 ]. % 47.07/47.27 apply (zenon_L123_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H175 | zenon_intro zenon_H341 ]. % 47.07/47.27 apply (zenon_L287_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H342 ]. % 47.07/47.27 apply (zenon_L54_); trivial. % 47.07/47.27 apply (zenon_L418_); trivial. % 47.07/47.27 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.27 apply (zenon_L10_); trivial. % 47.07/47.27 apply (zenon_L11_); trivial. % 47.07/47.27 (* end of lemma zenon_L422_ *) % 47.07/47.27 assert (zenon_L423_ : (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e13)) = (e11)) -> ((op1 (e11) (e13)) = (e11)) -> False). % 47.07/47.27 do 0 intro. intros zenon_H171 zenon_H14f zenon_H175. % 47.07/47.27 cut (((op1 (e10) (e13)) = (e11)) = ((op1 (e10) (e13)) = (op1 (e11) (e13)))). % 47.07/47.27 intro zenon_D_pnotp. % 47.07/47.27 apply zenon_H171. % 47.07/47.27 rewrite <- zenon_D_pnotp. % 47.07/47.27 exact zenon_H14f. % 47.07/47.27 cut (((e11) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 47.07/47.27 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 47.07/47.27 congruence. % 47.07/47.27 apply zenon_Hba. apply refl_equal. % 47.07/47.27 apply zenon_H17e. apply sym_equal. exact zenon_H175. % 47.07/47.27 (* end of lemma zenon_L423_ *) % 47.07/47.27 assert (zenon_L424_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e11) (e13)) = (e11)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((e11) = (e13))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((e10) = (e13))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e13)) = (e13)) -> False). % 47.07/47.27 do 0 intro. intros zenon_H154 zenon_H30a zenon_H175 zenon_H171 zenon_H42 zenon_H1c zenon_H2c zenon_H3b zenon_H34f zenon_Hd8 zenon_H12d zenon_H129 zenon_H314 zenon_H133 zenon_Hd4 zenon_H163 zenon_H17b zenon_H177 zenon_H137 zenon_H335 zenon_H164 zenon_H345 zenon_H346 zenon_H33f zenon_H11b zenon_H48 zenon_H344 zenon_H1b zenon_Hb7 zenon_H339 zenon_H101 zenon_Hfd zenon_H104 zenon_H5c zenon_H116 zenon_Hb0 zenon_H2b zenon_Hc5 zenon_H115 zenon_Hf7 zenon_Hb4 zenon_Hd3 zenon_Hd0 zenon_Ha9 zenon_H15b zenon_H150 zenon_H33e zenon_H9c zenon_H35 zenon_Hac zenon_H30e zenon_H149 zenon_H142 zenon_H4b zenon_H130 zenon_H51 zenon_Hed zenon_Hf1 zenon_Hbe zenon_He6 zenon_Hde zenon_H110 zenon_H63 zenon_H174 zenon_H10d zenon_H306 zenon_H119 zenon_Hf9 zenon_H56 zenon_H5f zenon_Hea zenon_H23 zenon_H16f zenon_H30f zenon_H24 zenon_H14c zenon_H338 zenon_H19 zenon_H6a zenon_H8f zenon_H152. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H13d | zenon_intro zenon_H155 ]. % 47.07/47.28 apply (zenon_L387_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H14f | zenon_intro zenon_H156 ]. % 47.07/47.28 apply (zenon_L423_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H8e | zenon_intro zenon_Hd7 ]. % 47.07/47.28 apply (zenon_L358_); trivial. % 47.07/47.28 apply (zenon_L111_); trivial. % 47.07/47.28 (* end of lemma zenon_L424_ *) % 47.07/47.28 assert (zenon_L425_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e12)) -> (~((h2 (op1 (e13) (e13))) = (op2 (h2 (e13)) (h2 (e13))))) -> ((h2 (e11)) = (e21)) -> ((op2 (e23) (e23)) = (e21)) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((op1 (e12) (e13)) = (e12)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e11) (e13)) = (e11)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((e11) = (e13))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((e10) = (e13))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 47.07/47.28 do 0 intro. intros zenon_H157 zenon_H125 zenon_H11f zenon_H5b zenon_H3c7 zenon_H37b zenon_H243 zenon_H368 zenon_H194 zenon_Hb8 zenon_H154 zenon_H30a zenon_H175 zenon_H171 zenon_H42 zenon_H1c zenon_H2c zenon_H3b zenon_H34f zenon_Hd8 zenon_H12d zenon_H129 zenon_H314 zenon_H133 zenon_Hd4 zenon_H163 zenon_H17b zenon_H177 zenon_H137 zenon_H335 zenon_H164 zenon_H345 zenon_H346 zenon_H33f zenon_H11b zenon_H48 zenon_H344 zenon_H1b zenon_Hb7 zenon_H339 zenon_H101 zenon_Hfd zenon_H104 zenon_H5c zenon_H116 zenon_Hb0 zenon_H2b zenon_Hc5 zenon_H115 zenon_Hf7 zenon_Hb4 zenon_Hd3 zenon_Hd0 zenon_Ha9 zenon_H15b zenon_H150 zenon_H33e zenon_H9c zenon_H35 zenon_Hac zenon_H30e zenon_H149 zenon_H142 zenon_H4b zenon_H130 zenon_H51 zenon_Hed zenon_Hf1 zenon_Hbe zenon_He6 zenon_Hde zenon_H110 zenon_H63 zenon_H174 zenon_H10d zenon_H306 zenon_H119 zenon_Hf9 zenon_H56 zenon_H5f zenon_Hea zenon_H23 zenon_H16f zenon_H30f zenon_H24 zenon_H14c zenon_H338 zenon_H19 zenon_H6a zenon_H8f. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H158 ]. % 47.07/47.28 apply (zenon_L422_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H136 | zenon_intro zenon_H159 ]. % 47.07/47.28 apply (zenon_L92_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H152 ]. % 47.07/47.28 apply (zenon_L84_); trivial. % 47.07/47.28 apply (zenon_L424_); trivial. % 47.07/47.28 (* end of lemma zenon_L425_ *) % 47.07/47.28 assert (zenon_L426_ : ((op1 (e12) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e13))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e13)) = (e11)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((op2 (e23) (e23)) = (e21)) -> ((h2 (e11)) = (e21)) -> (~((h2 (op1 (e13) (e13))) = (op2 (h2 (e13)) (h2 (e13))))) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e13) (e12)) = (e11)) -> (~((e12) = (e13))) -> False). % 47.07/47.28 do 0 intro. intros zenon_H32e zenon_H8f zenon_H6a zenon_H19 zenon_H338 zenon_H14c zenon_H24 zenon_H30f zenon_H16f zenon_H23 zenon_Hea zenon_H5f zenon_H56 zenon_Hf9 zenon_H119 zenon_H306 zenon_H10d zenon_H174 zenon_H63 zenon_H110 zenon_Hde zenon_He6 zenon_Hbe zenon_Hf1 zenon_Hed zenon_H51 zenon_H130 zenon_H4b zenon_H142 zenon_H149 zenon_H30e zenon_Hac zenon_H35 zenon_H9c zenon_H33e zenon_H150 zenon_H15b zenon_Ha9 zenon_Hd0 zenon_Hd3 zenon_Hb4 zenon_Hf7 zenon_H115 zenon_Hc5 zenon_H2b zenon_Hb0 zenon_H116 zenon_H5c zenon_H104 zenon_Hfd zenon_H101 zenon_H339 zenon_Hb7 zenon_H1b zenon_H344 zenon_H48 zenon_H11b zenon_H33f zenon_H346 zenon_H345 zenon_H164 zenon_H335 zenon_H137 zenon_H177 zenon_H17b zenon_H163 zenon_Hd4 zenon_H133 zenon_H314 zenon_H129 zenon_H12d zenon_H34f zenon_H3b zenon_H2c zenon_H1c zenon_H42 zenon_H171 zenon_H175 zenon_H154 zenon_H194 zenon_H368 zenon_H243 zenon_H37b zenon_H3c7 zenon_H5b zenon_H11f zenon_H125 zenon_H157 zenon_Hdf zenon_H34 zenon_H105 zenon_Hd8. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.28 apply (zenon_L50_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.28 apply (zenon_L51_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.28 apply (zenon_L137_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.28 apply (zenon_L10_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.28 apply (zenon_L327_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.28 apply (zenon_L415_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.28 apply (zenon_L19_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.28 apply (zenon_L288_); trivial. % 47.07/47.28 apply (zenon_L425_); trivial. % 47.07/47.28 apply (zenon_L84_); trivial. % 47.07/47.28 (* end of lemma zenon_L426_ *) % 47.07/47.28 assert (zenon_L427_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> ((e23) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) -> ((op2 (e23) (e23)) = (e21)) -> ((h2 (e11)) = (e21)) -> (~((h2 (op1 (e13) (e13))) = (op2 (h2 (e13)) (h2 (e13))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e11) (e11)) (e11))) -> ((e13) = (op1 (e11) (op1 (op1 (e11) (e11)) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e11) (e11))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e11) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> False). % 47.07/47.28 do 0 intro. intros zenon_H3cd zenon_H314 zenon_H30f zenon_H306 zenon_H30e zenon_H315 zenon_H34f zenon_H194 zenon_H368 zenon_H243 zenon_H37b zenon_H3c7 zenon_H344 zenon_H338 zenon_H335 zenon_H345 zenon_H339 zenon_H346 zenon_H33f zenon_H33e zenon_H150 zenon_H133 zenon_H129 zenon_H12d zenon_He6 zenon_Hd4 zenon_Hea zenon_Hde zenon_Hbe zenon_H8f zenon_H157 zenon_H154 zenon_Hb7 zenon_Hcb zenon_H160 zenon_H16f zenon_H161 zenon_H104 zenon_H174 zenon_H163 zenon_H14c zenon_H13e zenon_H125 zenon_H11b zenon_H11f zenon_H9c zenon_H115 zenon_Hb4 zenon_H6a zenon_Hd0 zenon_Hdb zenon_H164 zenon_H42 zenon_H1c zenon_H2c zenon_H3b zenon_H149 zenon_H142 zenon_H4b zenon_H130 zenon_H51 zenon_Hf1 zenon_H119 zenon_H101 zenon_H10d zenon_Hfd zenon_H63 zenon_H110 zenon_Hac zenon_H1b zenon_Hc5 zenon_H2b zenon_H56 zenon_Hf9 zenon_H19 zenon_Hb0 zenon_H5c zenon_H116 zenon_Hd8 zenon_H48 zenon_Ha9 zenon_H35 zenon_H17b zenon_H171 zenon_H177 zenon_H137 zenon_H24 zenon_H162 zenon_H15b. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cd); [ zenon_intro zenon_H23 | zenon_intro zenon_H3ce ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H4f | zenon_intro zenon_H167 ]. % 47.07/47.28 apply (zenon_L280_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H16c ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.07/47.28 apply (zenon_L280_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.07/47.28 apply (zenon_L282_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H50 | zenon_intro zenon_H168 ]. % 47.07/47.28 apply (zenon_L283_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H57 | zenon_intro zenon_H169 ]. % 47.07/47.28 apply (zenon_L15_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H5b | zenon_intro zenon_H8e ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H50 | zenon_intro zenon_H316 ]. % 47.07/47.28 apply (zenon_L283_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H316); [ zenon_intro zenon_H301 | zenon_intro zenon_H317 ]. % 47.07/47.28 apply (zenon_L285_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H317); [ zenon_intro zenon_Hee | zenon_intro zenon_Hf7 ]. % 47.07/47.28 apply (zenon_L50_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.07/47.28 apply (zenon_L7_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.28 apply (zenon_L7_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H33 | zenon_intro zenon_H347 ]. % 47.07/47.28 apply (zenon_L9_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H32c | zenon_intro zenon_H348 ]. % 47.07/47.28 apply (zenon_L326_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H348); [ zenon_intro zenon_Hdf | zenon_intro zenon_H172 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.28 apply (zenon_L326_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H34f); [ zenon_intro zenon_H15a | zenon_intro zenon_H350 ]. % 47.07/47.28 apply (zenon_L343_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H350); [ zenon_intro zenon_H7d | zenon_intro zenon_H351 ]. % 47.07/47.28 apply (zenon_L40_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H351); [ zenon_intro zenon_H105 | zenon_intro zenon_H342 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H14f | zenon_intro zenon_H340 ]. % 47.07/47.28 apply (zenon_L303_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H175 | zenon_intro zenon_H341 ]. % 47.07/47.28 apply (zenon_L426_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H342 ]. % 47.07/47.28 apply (zenon_L54_); trivial. % 47.07/47.28 apply (zenon_L418_); trivial. % 47.07/47.28 apply (zenon_L418_); trivial. % 47.07/47.28 apply (zenon_L19_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H14f | zenon_intro zenon_H340 ]. % 47.07/47.28 apply (zenon_L303_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H175 | zenon_intro zenon_H341 ]. % 47.07/47.28 apply (zenon_L287_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H342 ]. % 47.07/47.28 apply (zenon_L54_); trivial. % 47.07/47.28 apply (zenon_L418_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.28 apply (zenon_L10_); trivial. % 47.07/47.28 apply (zenon_L11_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.07/47.28 apply (zenon_L133_); trivial. % 47.07/47.28 apply (zenon_L422_); trivial. % 47.07/47.28 apply (zenon_L361_); trivial. % 47.07/47.28 apply (zenon_L343_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H141 | zenon_intro zenon_H14f ]. % 47.07/47.28 apply (zenon_L298_); trivial. % 47.07/47.28 apply (zenon_L306_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H1d | zenon_intro zenon_H3cf ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cf); [ zenon_intro zenon_H22 | zenon_intro zenon_H13d ]. % 47.07/47.28 apply (zenon_L124_); trivial. % 47.07/47.28 apply (zenon_L142_); trivial. % 47.07/47.28 (* end of lemma zenon_L427_ *) % 47.07/47.28 apply NNPP. intro zenon_G. % 47.07/47.28 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H3d1. zenon_intro zenon_H3d0. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3d0). zenon_intro zenon_Hd4. zenon_intro zenon_H3d2. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3d2). zenon_intro zenon_H14c. zenon_intro zenon_H3d3. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3d3). zenon_intro zenon_H154. zenon_intro zenon_H3d4. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3d4). zenon_intro zenon_H3d6. zenon_intro zenon_H3d5. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3d5). zenon_intro zenon_H3d8. zenon_intro zenon_H3d7. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3d7). zenon_intro zenon_Hea. zenon_intro zenon_H3d9. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3d9). zenon_intro zenon_H17b. zenon_intro zenon_H3da. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3da). zenon_intro zenon_H3dc. zenon_intro zenon_H3db. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3db). zenon_intro zenon_H3de. zenon_intro zenon_H3dd. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H125. zenon_intro zenon_H3df. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3df). zenon_intro zenon_H110. zenon_intro zenon_H3e0. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3e0). zenon_intro zenon_H3e2. zenon_intro zenon_H3e1. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3e1). zenon_intro zenon_Hd0. zenon_intro zenon_H3e3. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3e3). zenon_intro zenon_H10d. zenon_intro zenon_H3e4. % 47.07/47.28 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H3cd. zenon_intro zenon_H3e5. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3e5). zenon_intro zenon_H160. zenon_intro zenon_H3e6. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3e6). zenon_intro zenon_H161. zenon_intro zenon_H3e7. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3e7). zenon_intro zenon_H162. zenon_intro zenon_H3e8. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3e8). zenon_intro zenon_H163. zenon_intro zenon_H3e9. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3e9). zenon_intro zenon_H315. zenon_intro zenon_H3ea. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_H164. zenon_intro zenon_H3eb. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3eb). zenon_intro zenon_H48. zenon_intro zenon_H3ec. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3ec). zenon_intro zenon_H345. zenon_intro zenon_H3ed. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3ed). zenon_intro zenon_H344. zenon_intro zenon_H3ee. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3ee). zenon_intro zenon_H30e. zenon_intro zenon_H3ef. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3ef). zenon_intro zenon_H149. zenon_intro zenon_H3f0. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3f0). zenon_intro zenon_H3f2. zenon_intro zenon_H3f1. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3f1). zenon_intro zenon_H3f4. zenon_intro zenon_H3f3. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3f3). zenon_intro zenon_H3f6. zenon_intro zenon_H3f5. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3f5). zenon_intro zenon_H133. zenon_intro zenon_H3f7. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3f7). zenon_intro zenon_H346. zenon_intro zenon_H3f8. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3f8). zenon_intro zenon_H3fa. zenon_intro zenon_H3f9. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3f9). zenon_intro zenon_H3fc. zenon_intro zenon_H3fb. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3fb). zenon_intro zenon_H3fe. zenon_intro zenon_H3fd. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3fd). zenon_intro zenon_H130. zenon_intro zenon_H3ff. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H3ff). zenon_intro zenon_H12d. zenon_intro zenon_H400. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H400). zenon_intro zenon_Hac. zenon_intro zenon_H401. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H401). zenon_intro zenon_Hcb. zenon_intro zenon_H402. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H402). zenon_intro zenon_H339. zenon_intro zenon_H403. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H403). zenon_intro zenon_H30f. zenon_intro zenon_H404. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H404). zenon_intro zenon_H34f. zenon_intro zenon_H405. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H405). zenon_intro zenon_H33e. zenon_intro zenon_H406. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H406). zenon_intro zenon_H116. zenon_intro zenon_H407. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H407). zenon_intro zenon_H409. zenon_intro zenon_H408. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H408). zenon_intro zenon_H364. zenon_intro zenon_H157. % 47.07/47.28 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H40b. zenon_intro zenon_H40a. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H40a). zenon_intro zenon_H40d. zenon_intro zenon_H40c. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H40c). zenon_intro zenon_H40f. zenon_intro zenon_H40e. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H40e). zenon_intro zenon_H411. zenon_intro zenon_H410. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H410). zenon_intro zenon_H413. zenon_intro zenon_H412. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H412). zenon_intro zenon_H415. zenon_intro zenon_H414. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H414). zenon_intro zenon_H417. zenon_intro zenon_H416. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H416). zenon_intro zenon_H2ee. zenon_intro zenon_H418. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H418). zenon_intro zenon_H2b5. zenon_intro zenon_H419. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H419). zenon_intro zenon_H41b. zenon_intro zenon_H41a. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H41a). zenon_intro zenon_H29c. zenon_intro zenon_H41c. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H41c). zenon_intro zenon_H24b. zenon_intro zenon_H41d. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H41d). zenon_intro zenon_H41f. zenon_intro zenon_H41e. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H41e). zenon_intro zenon_H230. zenon_intro zenon_H420. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H420). zenon_intro zenon_H271. zenon_intro zenon_H421. % 47.07/47.28 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H423. zenon_intro zenon_H422. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H422). zenon_intro zenon_H2d1. zenon_intro zenon_H424. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H424). zenon_intro zenon_H2d2. zenon_intro zenon_H425. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H425). zenon_intro zenon_H2ba. zenon_intro zenon_H426. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H426). zenon_intro zenon_H27a. zenon_intro zenon_H427. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H427). zenon_intro zenon_H27d. zenon_intro zenon_H428. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H428). zenon_intro zenon_H27b. zenon_intro zenon_H429. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H429). zenon_intro zenon_H1b0. zenon_intro zenon_H42a. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H42a). zenon_intro zenon_H2d7. zenon_intro zenon_H42b. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H42b). zenon_intro zenon_H2bd. zenon_intro zenon_H42c. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H42c). zenon_intro zenon_H2d3. zenon_intro zenon_H42d. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H42d). zenon_intro zenon_H2bb. zenon_intro zenon_H42e. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H42e). zenon_intro zenon_H430. zenon_intro zenon_H42f. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H42f). zenon_intro zenon_H432. zenon_intro zenon_H431. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H431). zenon_intro zenon_H434. zenon_intro zenon_H433. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H433). zenon_intro zenon_H2d4. zenon_intro zenon_H435. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H435). zenon_intro zenon_H437. zenon_intro zenon_H436. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H436). zenon_intro zenon_H355. zenon_intro zenon_H438. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H438). zenon_intro zenon_H360. zenon_intro zenon_H439. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H439). zenon_intro zenon_H2fc. zenon_intro zenon_H43a. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H43a). zenon_intro zenon_H2bc. zenon_intro zenon_H43b. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H43b). zenon_intro zenon_H2d6. zenon_intro zenon_H43c. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H43c). zenon_intro zenon_H225. zenon_intro zenon_H43d. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H43d). zenon_intro zenon_H2d5. zenon_intro zenon_H43e. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H43e). zenon_intro zenon_H354. zenon_intro zenon_H43f. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H43f). zenon_intro zenon_H322. zenon_intro zenon_H440. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H440). zenon_intro zenon_H442. zenon_intro zenon_H441. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H441). zenon_intro zenon_H2c7. zenon_intro zenon_H443. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H443). zenon_intro zenon_H27c. zenon_intro zenon_H444. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H444). zenon_intro zenon_H28d. zenon_intro zenon_H445. % 47.07/47.28 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H2b. zenon_intro zenon_H446. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H446). zenon_intro zenon_H448. zenon_intro zenon_H447. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H447). zenon_intro zenon_H335. zenon_intro zenon_H449. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H449). zenon_intro zenon_H3b. zenon_intro zenon_H44a. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H44a). zenon_intro zenon_H42. zenon_intro zenon_H44b. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H44b). zenon_intro zenon_H44d. zenon_intro zenon_H44c. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H44c). zenon_intro zenon_H56. zenon_intro zenon_H44e. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H44e). zenon_intro zenon_H1b. zenon_intro zenon_H44f. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H44f). zenon_intro zenon_Hb4. zenon_intro zenon_H450. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H450). zenon_intro zenon_Hf1. zenon_intro zenon_H451. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H451). zenon_intro zenon_Hb0. zenon_intro zenon_H452. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H452). zenon_intro zenon_H6a. zenon_intro zenon_H453. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H453). zenon_intro zenon_Hde. zenon_intro zenon_H454. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H454). zenon_intro zenon_H9c. zenon_intro zenon_H455. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H455). zenon_intro zenon_H119. zenon_intro zenon_H456. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H456). zenon_intro zenon_H458. zenon_intro zenon_H457. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H457). zenon_intro zenon_H306. zenon_intro zenon_H459. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H459). zenon_intro zenon_Hf9. zenon_intro zenon_H45a. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H45a). zenon_intro zenon_H171. zenon_intro zenon_H45b. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H45b). zenon_intro zenon_Hb7. zenon_intro zenon_H45c. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H45c). zenon_intro zenon_H8f. zenon_intro zenon_H45d. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H45d). zenon_intro zenon_H174. zenon_intro zenon_H45e. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H45e). zenon_intro zenon_H338. zenon_intro zenon_H45f. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H45f). zenon_intro zenon_Hc5. zenon_intro zenon_H460. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H460). zenon_intro zenon_Hdb. zenon_intro zenon_H461. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H461). zenon_intro zenon_H24. zenon_intro zenon_H462. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H462). zenon_intro zenon_H16f. zenon_intro zenon_H463. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H463). zenon_intro zenon_H142. zenon_intro zenon_H464. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H464). zenon_intro zenon_H150. zenon_intro zenon_H465. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H465). zenon_intro zenon_H13e. zenon_intro zenon_H466. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H466). zenon_intro zenon_H129. zenon_intro zenon_H467. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H467). zenon_intro zenon_Hbe. zenon_intro zenon_H468. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H468). zenon_intro zenon_H137. zenon_intro zenon_H469. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H469). zenon_intro zenon_He6. zenon_intro zenon_H46a. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H46a). zenon_intro zenon_H177. zenon_intro zenon_H46b. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H46b). zenon_intro zenon_H46d. zenon_intro zenon_H46c. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H46c). zenon_intro zenon_H4b. zenon_intro zenon_H46e. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H46e). zenon_intro zenon_H11f. zenon_intro zenon_H46f. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H46f). zenon_intro zenon_Hfd. zenon_intro zenon_H470. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H470). zenon_intro zenon_H11b. zenon_intro zenon_H471. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H471). zenon_intro zenon_H63. zenon_intro zenon_H472. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H472). zenon_intro zenon_H115. zenon_intro zenon_H473. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H473). zenon_intro zenon_H314. zenon_intro zenon_H474. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H474). zenon_intro zenon_H101. zenon_intro zenon_H475. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H475). zenon_intro zenon_H33f. zenon_intro zenon_H476. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H476). zenon_intro zenon_H104. zenon_intro zenon_H477. % 47.07/47.28 apply (zenon_and_s _ _ ax6). zenon_intro zenon_H193. zenon_intro zenon_H478. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H478). zenon_intro zenon_H47a. zenon_intro zenon_H479. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H479). zenon_intro zenon_H35d. zenon_intro zenon_H47b. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H47b). zenon_intro zenon_H1a3. zenon_intro zenon_H47c. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H47c). zenon_intro zenon_H1aa. zenon_intro zenon_H47d. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H47d). zenon_intro zenon_H47f. zenon_intro zenon_H47e. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H47e). zenon_intro zenon_H1be. zenon_intro zenon_H480. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H480). zenon_intro zenon_H185. zenon_intro zenon_H481. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H481). zenon_intro zenon_H22d. zenon_intro zenon_H482. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H482). zenon_intro zenon_H2ab. zenon_intro zenon_H483. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H483). zenon_intro zenon_H229. zenon_intro zenon_H484. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H484). zenon_intro zenon_H1e4. zenon_intro zenon_H485. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H485). zenon_intro zenon_H1cf. zenon_intro zenon_H486. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H486). zenon_intro zenon_H216. zenon_intro zenon_H487. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H487). zenon_intro zenon_H259. zenon_intro zenon_H488. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H488). zenon_intro zenon_H295. zenon_intro zenon_H489. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H489). zenon_intro zenon_H48b. zenon_intro zenon_H48a. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H48a). zenon_intro zenon_H270. zenon_intro zenon_H48c. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H48c). zenon_intro zenon_H2ec. zenon_intro zenon_H48d. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H48d). zenon_intro zenon_H25c. zenon_intro zenon_H48e. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H48e). zenon_intro zenon_H20a. zenon_intro zenon_H48f. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H48f). zenon_intro zenon_H2eb. zenon_intro zenon_H490. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H490). zenon_intro zenon_H378. zenon_intro zenon_H491. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H491). zenon_intro zenon_H23f. zenon_intro zenon_H492. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H492). zenon_intro zenon_H2a0. zenon_intro zenon_H493. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H493). zenon_intro zenon_H18d. zenon_intro zenon_H494. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H494). zenon_intro zenon_H2e7. zenon_intro zenon_H495. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H495). zenon_intro zenon_H2f7. zenon_intro zenon_H496. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H496). zenon_intro zenon_H498. zenon_intro zenon_H497. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H497). zenon_intro zenon_H49a. zenon_intro zenon_H499. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H499). zenon_intro zenon_H1c7. zenon_intro zenon_H49b. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H49b). zenon_intro zenon_H251. zenon_intro zenon_H49c. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H49c). zenon_intro zenon_H2ef. zenon_intro zenon_H49d. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H49d). zenon_intro zenon_H2cb. zenon_intro zenon_H49e. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H49e). zenon_intro zenon_H287. zenon_intro zenon_H49f. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H49f). zenon_intro zenon_H4a1. zenon_intro zenon_H4a0. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4a0). zenon_intro zenon_H1b3. zenon_intro zenon_H4a2. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4a2). zenon_intro zenon_H299. zenon_intro zenon_H4a3. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4a3). zenon_intro zenon_H23a. zenon_intro zenon_H4a4. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4a4). zenon_intro zenon_H291. zenon_intro zenon_H4a5. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4a5). zenon_intro zenon_H234. zenon_intro zenon_H4a6. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4a6). zenon_intro zenon_H265. zenon_intro zenon_H4a7. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4a7). zenon_intro zenon_H325. zenon_intro zenon_H4a8. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4a8). zenon_intro zenon_H25f. zenon_intro zenon_H4a9. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4a9). zenon_intro zenon_H4ab. zenon_intro zenon_H4aa. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4aa). zenon_intro zenon_H262. zenon_intro zenon_H4ac. % 47.07/47.28 apply (zenon_and_s _ _ ax7). zenon_intro zenon_H15b. zenon_intro zenon_H4ad. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4ad). zenon_intro zenon_H5c. zenon_intro zenon_H4ae. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4ae). zenon_intro zenon_H35. zenon_intro zenon_H4af. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4af). zenon_intro zenon_H51. zenon_intro zenon_H4b0. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4b0). zenon_intro zenon_Ha9. zenon_intro zenon_Hd8. % 47.07/47.28 apply (zenon_and_s _ _ ax8). zenon_intro zenon_H1df. zenon_intro zenon_H4b1. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4b1). zenon_intro zenon_H1c4. zenon_intro zenon_H4b2. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4b2). zenon_intro zenon_H19d. zenon_intro zenon_H4b3. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4b3). zenon_intro zenon_H1b9. zenon_intro zenon_H4b4. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4b4). zenon_intro zenon_H1d3. zenon_intro zenon_H276. % 47.07/47.28 apply (zenon_and_s _ _ ax12). zenon_intro zenon_H1c. zenon_intro zenon_H4b5. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4b5). zenon_intro zenon_H19. zenon_intro zenon_H2c. % 47.07/47.28 apply (zenon_and_s _ _ ax13). zenon_intro zenon_H14. zenon_intro zenon_H4b6. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4b6). zenon_intro zenon_H183. zenon_intro zenon_H194. % 47.07/47.28 apply (zenon_and_s _ _ ax15). zenon_intro zenon_H37b. zenon_intro zenon_H4b7. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4b7). zenon_intro zenon_H13. zenon_intro zenon_H4b8. % 47.07/47.28 apply (zenon_and_s _ _ zenon_H4b8). zenon_intro zenon_H32a. zenon_intro zenon_H368. % 47.07/47.28 apply (zenon_notor_s _ _ zenon_G). zenon_intro zenon_H4ba. zenon_intro zenon_H4b9. % 47.07/47.28 apply (zenon_notor_s _ _ zenon_H4b9). zenon_intro zenon_H4bc. zenon_intro zenon_H4bb. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H4bc); [ zenon_intro zenon_H4be | zenon_intro zenon_H4bd ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H423); [ zenon_intro zenon_H18c | zenon_intro zenon_H4bf ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cd); [ zenon_intro zenon_H23 | zenon_intro zenon_H3ce ]. % 47.07/47.28 cut (((h2 (e10)) = (op2 (op2 (e21) (e21)) (e21))) = ((h2 (op1 (e10) (e10))) = (op2 (h2 (e10)) (h2 (e10))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4be. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H13. % 47.07/47.28 cut (((op2 (op2 (e21) (e21)) (e21)) = (op2 (h2 (e10)) (h2 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H4c0]. % 47.07/47.28 cut (((h2 (e10)) = (h2 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H4c1]. % 47.07/47.28 congruence. % 47.07/47.28 elim (classic ((h2 (op1 (e10) (e10))) = (h2 (op1 (e10) (e10))))); [ zenon_intro zenon_H4c2 | zenon_intro zenon_H4c3 ]. % 47.07/47.28 cut (((h2 (op1 (e10) (e10))) = (h2 (op1 (e10) (e10)))) = ((h2 (e10)) = (h2 (op1 (e10) (e10))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4c1. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H4c2. % 47.07/47.28 cut (((h2 (op1 (e10) (e10))) = (h2 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H4c3]. % 47.07/47.28 cut (((h2 (op1 (e10) (e10))) = (h2 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H4c4]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((op1 (e10) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H4c5]. % 47.07/47.28 congruence. % 47.07/47.28 exact (zenon_H4c5 zenon_H23). % 47.07/47.28 apply zenon_H4c3. apply refl_equal. % 47.07/47.28 apply zenon_H4c3. apply refl_equal. % 47.07/47.28 elim (classic ((op2 (h2 (e10)) (h2 (e10))) = (op2 (h2 (e10)) (h2 (e10))))); [ zenon_intro zenon_H4c6 | zenon_intro zenon_H4c7 ]. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e10))) = (op2 (h2 (e10)) (h2 (e10)))) = ((op2 (op2 (e21) (e21)) (e21)) = (op2 (h2 (e10)) (h2 (e10))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4c0. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H4c6. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e10))) = (op2 (h2 (e10)) (h2 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H4c7]. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e10))) = (op2 (op2 (e21) (e21)) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H4c8]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((op2 (e20) (e20)) = (e20)) = ((op2 (h2 (e10)) (h2 (e10))) = (op2 (op2 (e21) (e21)) (e21)))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4c8. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H18c. % 47.07/47.28 cut (((e20) = (op2 (op2 (e21) (e21)) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H393]. % 47.07/47.28 cut (((op2 (e20) (e20)) = (op2 (h2 (e10)) (h2 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H4c9]. % 47.07/47.28 congruence. % 47.07/47.28 elim (classic ((op2 (h2 (e10)) (h2 (e10))) = (op2 (h2 (e10)) (h2 (e10))))); [ zenon_intro zenon_H4c6 | zenon_intro zenon_H4c7 ]. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e10))) = (op2 (h2 (e10)) (h2 (e10)))) = ((op2 (e20) (e20)) = (op2 (h2 (e10)) (h2 (e10))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4c9. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H4c6. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e10))) = (op2 (h2 (e10)) (h2 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H4c7]. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e10))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H4ca]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((h2 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 47.07/47.28 cut (((h2 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 47.07/47.28 congruence. % 47.07/47.28 apply (zenon_L1_); trivial. % 47.07/47.28 apply (zenon_L1_); trivial. % 47.07/47.28 apply zenon_H4c7. apply refl_equal. % 47.07/47.28 apply zenon_H4c7. apply refl_equal. % 47.07/47.28 exact (zenon_H393 zenon_H14). % 47.07/47.28 apply zenon_H4c7. apply refl_equal. % 47.07/47.28 apply zenon_H4c7. apply refl_equal. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H1d | zenon_intro zenon_H3cf ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cf); [ zenon_intro zenon_H22 | zenon_intro zenon_H13d ]. % 47.07/47.28 apply (zenon_L124_); trivial. % 47.07/47.28 apply (zenon_L142_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4bf); [ zenon_intro zenon_H186 | zenon_intro zenon_H4cb ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4cb); [ zenon_intro zenon_H18b | zenon_intro zenon_H2e6 ]. % 47.07/47.28 apply (zenon_L251_); trivial. % 47.07/47.28 apply (zenon_L278_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H4bd); [ zenon_intro zenon_H4cd | zenon_intro zenon_H4cc ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H423); [ zenon_intro zenon_H18c | zenon_intro zenon_H4bf ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2da ]. % 47.07/47.28 apply (zenon_L279_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H29f | zenon_intro zenon_H2e1 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cd); [ zenon_intro zenon_H23 | zenon_intro zenon_H3ce ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H4f | zenon_intro zenon_H167 ]. % 47.07/47.28 apply (zenon_L280_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H16c ]. % 47.07/47.28 cut (((h2 (e11)) = (e21)) = ((h2 (op1 (e10) (e11))) = (op2 (h2 (e10)) (h2 (e11))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4cd. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H37b. % 47.07/47.28 cut (((e21) = (op2 (h2 (e10)) (h2 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H4ce]. % 47.07/47.28 cut (((h2 (e11)) = (h2 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H4cf]. % 47.07/47.28 congruence. % 47.07/47.28 elim (classic ((h2 (op1 (e10) (e11))) = (h2 (op1 (e10) (e11))))); [ zenon_intro zenon_H4d0 | zenon_intro zenon_H4d1 ]. % 47.07/47.28 cut (((h2 (op1 (e10) (e11))) = (h2 (op1 (e10) (e11)))) = ((h2 (e11)) = (h2 (op1 (e10) (e11))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4cf. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H4d0. % 47.07/47.28 cut (((h2 (op1 (e10) (e11))) = (h2 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H4d1]. % 47.07/47.28 cut (((h2 (op1 (e10) (e11))) = (h2 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H4d2]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((op1 (e10) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H4d3]. % 47.07/47.28 congruence. % 47.07/47.28 exact (zenon_H4d3 zenon_Hd3). % 47.07/47.28 apply zenon_H4d1. apply refl_equal. % 47.07/47.28 apply zenon_H4d1. apply refl_equal. % 47.07/47.28 elim (classic ((op2 (h2 (e10)) (h2 (e11))) = (op2 (h2 (e10)) (h2 (e11))))); [ zenon_intro zenon_H4d4 | zenon_intro zenon_H4d5 ]. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e11))) = (op2 (h2 (e10)) (h2 (e11)))) = ((e21) = (op2 (h2 (e10)) (h2 (e11))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4ce. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H4d4. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e11))) = (op2 (h2 (e10)) (h2 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H4d5]. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e11))) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H4d6]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((op2 (e20) (e21)) = (e21)) = ((op2 (h2 (e10)) (h2 (e11))) = (e21))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4d6. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H29f. % 47.07/47.28 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.07/47.28 cut (((op2 (e20) (e21)) = (op2 (h2 (e10)) (h2 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H4d7]. % 47.07/47.28 congruence. % 47.07/47.28 elim (classic ((op2 (h2 (e10)) (h2 (e11))) = (op2 (h2 (e10)) (h2 (e11))))); [ zenon_intro zenon_H4d4 | zenon_intro zenon_H4d5 ]. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e11))) = (op2 (h2 (e10)) (h2 (e11)))) = ((op2 (e20) (e21)) = (op2 (h2 (e10)) (h2 (e11))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4d7. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H4d4. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e11))) = (op2 (h2 (e10)) (h2 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H4d5]. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e11))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H4d8]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((h2 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H388]. % 47.07/47.28 cut (((h2 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 47.07/47.28 congruence. % 47.07/47.28 apply (zenon_L1_); trivial. % 47.07/47.28 exact (zenon_H388 zenon_H37b). % 47.07/47.28 apply zenon_H4d5. apply refl_equal. % 47.07/47.28 apply zenon_H4d5. apply refl_equal. % 47.07/47.28 apply zenon_H181. apply refl_equal. % 47.07/47.28 apply zenon_H4d5. apply refl_equal. % 47.07/47.28 apply zenon_H4d5. apply refl_equal. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H141 | zenon_intro zenon_H14f ]. % 47.07/47.28 apply (zenon_L298_); trivial. % 47.07/47.28 apply (zenon_L306_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H1d | zenon_intro zenon_H3cf ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cf); [ zenon_intro zenon_H22 | zenon_intro zenon_H13d ]. % 47.07/47.28 apply (zenon_L124_); trivial. % 47.07/47.28 apply (zenon_L142_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2cf | zenon_intro zenon_H1da ]. % 47.07/47.28 apply (zenon_L320_); trivial. % 47.07/47.28 apply (zenon_L324_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4bf); [ zenon_intro zenon_H186 | zenon_intro zenon_H4cb ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4cb); [ zenon_intro zenon_H18b | zenon_intro zenon_H2e6 ]. % 47.07/47.28 apply (zenon_L251_); trivial. % 47.07/47.28 apply (zenon_L278_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H4cc); [ zenon_intro zenon_H4da | zenon_intro zenon_H4d9 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H423); [ zenon_intro zenon_H18c | zenon_intro zenon_H4bf ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2da ]. % 47.07/47.28 apply (zenon_L279_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H29f | zenon_intro zenon_H2e1 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.07/47.28 apply (zenon_L218_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.07/47.28 apply (zenon_L219_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.07/47.28 apply (zenon_L307_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.07/47.28 apply (zenon_L156_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cd); [ zenon_intro zenon_H23 | zenon_intro zenon_H3ce ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H4f | zenon_intro zenon_H167 ]. % 47.07/47.28 apply (zenon_L280_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H16c ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.07/47.28 apply (zenon_L45_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.07/47.28 apply (zenon_L282_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H50 | zenon_intro zenon_H168 ]. % 47.07/47.28 apply (zenon_L283_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H57 | zenon_intro zenon_H169 ]. % 47.07/47.28 apply (zenon_L15_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H5b | zenon_intro zenon_H8e ]. % 47.07/47.28 cut (((h2 (e12)) = (op2 (e21) (e21))) = ((h2 (op1 (e10) (e12))) = (op2 (h2 (e10)) (h2 (e12))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4da. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H32a. % 47.07/47.28 cut (((op2 (e21) (e21)) = (op2 (h2 (e10)) (h2 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4db]. % 47.07/47.28 cut (((h2 (e12)) = (h2 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4dc]. % 47.07/47.28 congruence. % 47.07/47.28 elim (classic ((h2 (op1 (e10) (e12))) = (h2 (op1 (e10) (e12))))); [ zenon_intro zenon_H4dd | zenon_intro zenon_H4de ]. % 47.07/47.28 cut (((h2 (op1 (e10) (e12))) = (h2 (op1 (e10) (e12)))) = ((h2 (e12)) = (h2 (op1 (e10) (e12))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4dc. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H4dd. % 47.07/47.28 cut (((h2 (op1 (e10) (e12))) = (h2 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4de]. % 47.07/47.28 cut (((h2 (op1 (e10) (e12))) = (h2 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H4df]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((op1 (e10) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 47.07/47.28 congruence. % 47.07/47.28 exact (zenon_H5e zenon_H5b). % 47.07/47.28 apply zenon_H4de. apply refl_equal. % 47.07/47.28 apply zenon_H4de. apply refl_equal. % 47.07/47.28 elim (classic ((op2 (h2 (e10)) (h2 (e12))) = (op2 (h2 (e10)) (h2 (e12))))); [ zenon_intro zenon_H4e0 | zenon_intro zenon_H4e1 ]. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e12))) = (op2 (h2 (e10)) (h2 (e12)))) = ((op2 (e21) (e21)) = (op2 (h2 (e10)) (h2 (e12))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4db. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H4e0. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e12))) = (op2 (h2 (e10)) (h2 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4e1]. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e12))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H4e2]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((op2 (e20) (e22)) = (e22)) = ((op2 (h2 (e10)) (h2 (e12))) = (op2 (e21) (e21)))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4e2. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H1c3. % 47.07/47.28 cut (((e22) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H4e3]. % 47.07/47.28 cut (((op2 (e20) (e22)) = (op2 (h2 (e10)) (h2 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4e4]. % 47.07/47.28 congruence. % 47.07/47.28 elim (classic ((op2 (h2 (e10)) (h2 (e12))) = (op2 (h2 (e10)) (h2 (e12))))); [ zenon_intro zenon_H4e0 | zenon_intro zenon_H4e1 ]. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e12))) = (op2 (h2 (e10)) (h2 (e12)))) = ((op2 (e20) (e22)) = (op2 (h2 (e10)) (h2 (e12))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4e4. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H4e0. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e12))) = (op2 (h2 (e10)) (h2 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4e1]. % 47.07/47.28 cut (((op2 (h2 (e10)) (h2 (e12))) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H4e5]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((h2 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H329]. % 47.07/47.28 cut (((h2 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 47.07/47.28 congruence. % 47.07/47.28 apply (zenon_L1_); trivial. % 47.07/47.28 apply (zenon_L325_); trivial. % 47.07/47.28 apply zenon_H4e1. apply refl_equal. % 47.07/47.28 apply zenon_H4e1. apply refl_equal. % 47.07/47.28 exact (zenon_H4e3 zenon_H183). % 47.07/47.28 apply zenon_H4e1. apply refl_equal. % 47.07/47.28 apply zenon_H4e1. apply refl_equal. % 47.07/47.28 apply (zenon_L361_); trivial. % 47.07/47.28 apply (zenon_L343_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H141 | zenon_intro zenon_H14f ]. % 47.07/47.28 apply (zenon_L298_); trivial. % 47.07/47.28 apply (zenon_L306_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H1d | zenon_intro zenon_H3cf ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cf); [ zenon_intro zenon_H22 | zenon_intro zenon_H13d ]. % 47.07/47.28 apply (zenon_L124_); trivial. % 47.07/47.28 apply (zenon_L142_); trivial. % 47.07/47.28 apply (zenon_L366_); trivial. % 47.07/47.28 apply (zenon_L381_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2cf | zenon_intro zenon_H1da ]. % 47.07/47.28 apply (zenon_L320_); trivial. % 47.07/47.28 apply (zenon_L324_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4bf); [ zenon_intro zenon_H186 | zenon_intro zenon_H4cb ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4cb); [ zenon_intro zenon_H18b | zenon_intro zenon_H2e6 ]. % 47.07/47.28 apply (zenon_L251_); trivial. % 47.07/47.28 apply (zenon_L278_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H4d9); [ zenon_intro zenon_H36b | zenon_intro zenon_H4e6 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H423); [ zenon_intro zenon_H18c | zenon_intro zenon_H4bf ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2da ]. % 47.07/47.28 apply (zenon_L279_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H29f | zenon_intro zenon_H2e1 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.07/47.28 apply (zenon_L218_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.07/47.28 apply (zenon_L219_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.07/47.28 apply (zenon_L307_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.07/47.28 apply (zenon_L156_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.28 apply (zenon_L148_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.28 apply (zenon_L220_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.28 apply (zenon_L206_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cd); [ zenon_intro zenon_H23 | zenon_intro zenon_H3ce ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H4f | zenon_intro zenon_H167 ]. % 47.07/47.28 apply (zenon_L280_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H16c ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.07/47.28 apply (zenon_L45_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.07/47.28 apply (zenon_L282_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H50 | zenon_intro zenon_H168 ]. % 47.07/47.28 apply (zenon_L283_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H57 | zenon_intro zenon_H169 ]. % 47.07/47.28 apply (zenon_L15_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H5b | zenon_intro zenon_H8e ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H50 | zenon_intro zenon_H316 ]. % 47.07/47.28 apply (zenon_L283_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H316); [ zenon_intro zenon_H301 | zenon_intro zenon_H317 ]. % 47.07/47.28 apply (zenon_L285_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H317); [ zenon_intro zenon_Hee | zenon_intro zenon_Hf7 ]. % 47.07/47.28 apply (zenon_L50_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.07/47.28 apply (zenon_L7_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.28 apply (zenon_L7_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H33 | zenon_intro zenon_H347 ]. % 47.07/47.28 apply (zenon_L9_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H32c | zenon_intro zenon_H348 ]. % 47.07/47.28 apply (zenon_L326_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H348); [ zenon_intro zenon_Hdf | zenon_intro zenon_H172 ]. % 47.07/47.28 apply (zenon_L390_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.28 apply (zenon_L326_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3fa); [ zenon_intro zenon_H22 | zenon_intro zenon_H4e7 ]. % 47.07/47.28 apply (zenon_L16_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4e7); [ zenon_intro zenon_Hdf | zenon_intro zenon_H4e8 ]. % 47.07/47.28 apply (zenon_L390_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4e8); [ zenon_intro zenon_H11a | zenon_intro zenon_H102 ]. % 47.07/47.28 apply (zenon_L72_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H14f | zenon_intro zenon_H340 ]. % 47.07/47.28 apply (zenon_L306_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H175 | zenon_intro zenon_H341 ]. % 47.07/47.28 apply (zenon_L287_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H342 ]. % 47.07/47.28 apply (zenon_L54_); trivial. % 47.07/47.28 apply (zenon_L395_); trivial. % 47.07/47.28 apply (zenon_L19_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.28 apply (zenon_L10_); trivial. % 47.07/47.28 apply (zenon_L11_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.07/47.28 apply (zenon_L133_); trivial. % 47.07/47.28 apply (zenon_L392_); trivial. % 47.07/47.28 apply (zenon_L361_); trivial. % 47.07/47.28 apply (zenon_L343_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H141 | zenon_intro zenon_H14f ]. % 47.07/47.28 apply (zenon_L298_); trivial. % 47.07/47.28 apply (zenon_L306_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H1d | zenon_intro zenon_H3cf ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cf); [ zenon_intro zenon_H22 | zenon_intro zenon_H13d ]. % 47.07/47.28 apply (zenon_L124_); trivial. % 47.07/47.28 apply (zenon_L142_); trivial. % 47.07/47.28 apply (zenon_L366_); trivial. % 47.07/47.28 apply (zenon_L381_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2cf | zenon_intro zenon_H1da ]. % 47.07/47.28 apply (zenon_L320_); trivial. % 47.07/47.28 apply (zenon_L324_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4bf); [ zenon_intro zenon_H186 | zenon_intro zenon_H4cb ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4cb); [ zenon_intro zenon_H18b | zenon_intro zenon_H2e6 ]. % 47.07/47.28 apply (zenon_L251_); trivial. % 47.07/47.28 apply (zenon_L278_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H4e6); [ zenon_intro zenon_H4ea | zenon_intro zenon_H4e9 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.28 apply (zenon_L7_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.28 cut (((h2 (e13)) = (op2 (e21) (op2 (op2 (e21) (e21)) (e21)))) = ((h2 (op1 (e11) (e10))) = (op2 (h2 (e11)) (h2 (e10))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4ea. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H368. % 47.07/47.28 cut (((op2 (e21) (op2 (op2 (e21) (e21)) (e21))) = (op2 (h2 (e11)) (h2 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H4eb]. % 47.07/47.28 cut (((h2 (e13)) = (h2 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H4ec]. % 47.07/47.28 congruence. % 47.07/47.28 elim (classic ((h2 (op1 (e11) (e10))) = (h2 (op1 (e11) (e10))))); [ zenon_intro zenon_H4ed | zenon_intro zenon_H4ee ]. % 47.07/47.28 cut (((h2 (op1 (e11) (e10))) = (h2 (op1 (e11) (e10)))) = ((h2 (e13)) = (h2 (op1 (e11) (e10))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4ec. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H4ed. % 47.07/47.28 cut (((h2 (op1 (e11) (e10))) = (h2 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H4ee]. % 47.07/47.28 cut (((h2 (op1 (e11) (e10))) = (h2 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H4ef]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((op1 (e11) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 47.07/47.28 congruence. % 47.07/47.28 exact (zenon_H39 zenon_H34). % 47.07/47.28 apply zenon_H4ee. apply refl_equal. % 47.07/47.28 apply zenon_H4ee. apply refl_equal. % 47.07/47.28 cut (((op2 (op2 (e21) (e21)) (e21)) = (h2 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H4f0]. % 47.07/47.28 cut (((e21) = (h2 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H4f1]. % 47.07/47.28 congruence. % 47.07/47.28 apply zenon_H4f1. apply sym_equal. exact zenon_H37b. % 47.07/47.28 apply zenon_H4f0. apply sym_equal. exact zenon_H13. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.28 apply (zenon_L10_); trivial. % 47.07/47.28 apply (zenon_L11_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H4e9); [ zenon_intro zenon_H4f3 | zenon_intro zenon_H4f2 ]. % 47.07/47.28 cut (((h2 (e12)) = (op2 (e21) (e21))) = ((h2 (op1 (e11) (e11))) = (op2 (h2 (e11)) (h2 (e11))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4f3. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H32a. % 47.07/47.28 cut (((op2 (e21) (e21)) = (op2 (h2 (e11)) (h2 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H4f4]. % 47.07/47.28 cut (((h2 (e12)) = (h2 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H4f5]. % 47.07/47.28 congruence. % 47.07/47.28 elim (classic ((h2 (op1 (e11) (e11))) = (h2 (op1 (e11) (e11))))); [ zenon_intro zenon_H4f6 | zenon_intro zenon_H4f7 ]. % 47.07/47.28 cut (((h2 (op1 (e11) (e11))) = (h2 (op1 (e11) (e11)))) = ((h2 (e12)) = (h2 (op1 (e11) (e11))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4f5. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H4f6. % 47.07/47.28 cut (((h2 (op1 (e11) (e11))) = (h2 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H4f7]. % 47.07/47.28 cut (((h2 (op1 (e11) (e11))) = (h2 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H4f8]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((op1 (e11) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 47.07/47.28 congruence. % 47.07/47.28 apply zenon_H1a. apply sym_equal. exact zenon_H19. % 47.07/47.28 apply zenon_H4f7. apply refl_equal. % 47.07/47.28 apply zenon_H4f7. apply refl_equal. % 47.07/47.28 cut (((e21) = (h2 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H4f1]. % 47.07/47.28 cut (((e21) = (h2 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H4f1]. % 47.07/47.28 congruence. % 47.07/47.28 apply zenon_H4f1. apply sym_equal. exact zenon_H37b. % 47.07/47.28 apply zenon_H4f1. apply sym_equal. exact zenon_H37b. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H4f2); [ zenon_intro zenon_H37c | zenon_intro zenon_H4f9 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H423); [ zenon_intro zenon_H18c | zenon_intro zenon_H4bf ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2da ]. % 47.07/47.28 apply (zenon_L279_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H29f | zenon_intro zenon_H2e1 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.07/47.28 apply (zenon_L218_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.07/47.28 apply (zenon_L219_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.07/47.28 apply (zenon_L307_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.07/47.28 apply (zenon_L156_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.28 apply (zenon_L148_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.28 apply (zenon_L220_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.28 apply (zenon_L206_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.07/47.28 apply (zenon_L148_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H19b | zenon_intro zenon_H2db ]. % 47.07/47.28 apply (zenon_L150_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2dc ]. % 47.07/47.28 apply (zenon_L160_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H1dd ]. % 47.07/47.28 apply (zenon_L399_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2dd ]. % 47.07/47.28 apply (zenon_L162_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2de ]. % 47.07/47.28 apply (zenon_L163_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2de); [ zenon_intro zenon_H296 | zenon_intro zenon_H1de ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cd); [ zenon_intro zenon_H23 | zenon_intro zenon_H3ce ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H4f | zenon_intro zenon_H167 ]. % 47.07/47.28 apply (zenon_L280_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H16c ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.07/47.28 apply (zenon_L45_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.07/47.28 apply (zenon_L282_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H50 | zenon_intro zenon_H168 ]. % 47.07/47.28 apply (zenon_L283_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H57 | zenon_intro zenon_H169 ]. % 47.07/47.28 apply (zenon_L15_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H5b | zenon_intro zenon_H8e ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H50 | zenon_intro zenon_H316 ]. % 47.07/47.28 apply (zenon_L283_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H316); [ zenon_intro zenon_H301 | zenon_intro zenon_H317 ]. % 47.07/47.28 apply (zenon_L285_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H317); [ zenon_intro zenon_Hee | zenon_intro zenon_Hf7 ]. % 47.07/47.28 apply (zenon_L50_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.07/47.28 apply (zenon_L7_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.28 apply (zenon_L7_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H33 | zenon_intro zenon_H347 ]. % 47.07/47.28 apply (zenon_L9_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H32c | zenon_intro zenon_H348 ]. % 47.07/47.28 apply (zenon_L326_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H348); [ zenon_intro zenon_Hdf | zenon_intro zenon_H172 ]. % 47.07/47.28 apply (zenon_L390_); trivial. % 47.07/47.28 apply (zenon_L400_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.28 apply (zenon_L10_); trivial. % 47.07/47.28 apply (zenon_L11_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.07/47.28 apply (zenon_L133_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.28 apply (zenon_L7_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H33 | zenon_intro zenon_H347 ]. % 47.07/47.28 apply (zenon_L9_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H32c | zenon_intro zenon_H348 ]. % 47.07/47.28 apply (zenon_L326_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H348); [ zenon_intro zenon_Hdf | zenon_intro zenon_H172 ]. % 47.07/47.28 apply (zenon_L401_); trivial. % 47.07/47.28 apply (zenon_L400_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.28 apply (zenon_L10_); trivial. % 47.07/47.28 apply (zenon_L11_); trivial. % 47.07/47.28 apply (zenon_L361_); trivial. % 47.07/47.28 apply (zenon_L343_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H141 | zenon_intro zenon_H14f ]. % 47.07/47.28 apply (zenon_L298_); trivial. % 47.07/47.28 apply (zenon_L306_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H1d | zenon_intro zenon_H3cf ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cf); [ zenon_intro zenon_H22 | zenon_intro zenon_H13d ]. % 47.07/47.28 apply (zenon_L124_); trivial. % 47.07/47.28 apply (zenon_L142_); trivial. % 47.07/47.28 apply (zenon_L166_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.07/47.28 apply (zenon_L151_); trivial. % 47.07/47.28 apply (zenon_L152_); trivial. % 47.07/47.28 apply (zenon_L366_); trivial. % 47.07/47.28 apply (zenon_L381_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2cf | zenon_intro zenon_H1da ]. % 47.07/47.28 apply (zenon_L320_); trivial. % 47.07/47.28 apply (zenon_L324_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4bf); [ zenon_intro zenon_H186 | zenon_intro zenon_H4cb ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4cb); [ zenon_intro zenon_H18b | zenon_intro zenon_H2e6 ]. % 47.07/47.28 apply (zenon_L251_); trivial. % 47.07/47.28 apply (zenon_L278_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H4f9); [ zenon_intro zenon_H389 | zenon_intro zenon_H4fa ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H423); [ zenon_intro zenon_H18c | zenon_intro zenon_H4bf ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2da ]. % 47.07/47.28 apply (zenon_L279_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H29f | zenon_intro zenon_H2e1 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.07/47.28 apply (zenon_L218_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.07/47.28 apply (zenon_L219_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.07/47.28 apply (zenon_L307_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.07/47.28 apply (zenon_L156_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.28 apply (zenon_L148_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.28 apply (zenon_L220_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.28 apply (zenon_L206_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.07/47.28 apply (zenon_L148_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H19b | zenon_intro zenon_H2db ]. % 47.07/47.28 apply (zenon_L150_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2dc ]. % 47.07/47.28 apply (zenon_L160_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H1dd ]. % 47.07/47.28 apply (zenon_L399_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cd); [ zenon_intro zenon_H23 | zenon_intro zenon_H3ce ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H4f | zenon_intro zenon_H167 ]. % 47.07/47.28 apply (zenon_L280_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H16c ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.07/47.28 apply (zenon_L45_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.07/47.28 apply (zenon_L282_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H50 | zenon_intro zenon_H168 ]. % 47.07/47.28 apply (zenon_L283_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H57 | zenon_intro zenon_H169 ]. % 47.07/47.28 apply (zenon_L15_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H5b | zenon_intro zenon_H8e ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H50 | zenon_intro zenon_H316 ]. % 47.07/47.28 apply (zenon_L283_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H316); [ zenon_intro zenon_H301 | zenon_intro zenon_H317 ]. % 47.07/47.28 apply (zenon_L285_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H317); [ zenon_intro zenon_Hee | zenon_intro zenon_Hf7 ]. % 47.07/47.28 apply (zenon_L50_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.07/47.28 apply (zenon_L7_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.28 apply (zenon_L7_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H33 | zenon_intro zenon_H347 ]. % 47.07/47.28 apply (zenon_L9_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H32c | zenon_intro zenon_H348 ]. % 47.07/47.28 apply (zenon_L326_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H348); [ zenon_intro zenon_Hdf | zenon_intro zenon_H172 ]. % 47.07/47.28 apply (zenon_L390_); trivial. % 47.07/47.28 apply (zenon_L402_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.28 apply (zenon_L10_); trivial. % 47.07/47.28 apply (zenon_L11_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.07/47.28 apply (zenon_L133_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.28 apply (zenon_L7_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H33 | zenon_intro zenon_H347 ]. % 47.07/47.28 apply (zenon_L9_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H32c | zenon_intro zenon_H348 ]. % 47.07/47.28 apply (zenon_L326_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H348); [ zenon_intro zenon_Hdf | zenon_intro zenon_H172 ]. % 47.07/47.28 apply (zenon_L401_); trivial. % 47.07/47.28 apply (zenon_L402_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.28 apply (zenon_L10_); trivial. % 47.07/47.28 apply (zenon_L11_); trivial. % 47.07/47.28 apply (zenon_L361_); trivial. % 47.07/47.28 apply (zenon_L343_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H141 | zenon_intro zenon_H14f ]. % 47.07/47.28 apply (zenon_L298_); trivial. % 47.07/47.28 apply (zenon_L306_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H1d | zenon_intro zenon_H3cf ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cf); [ zenon_intro zenon_H22 | zenon_intro zenon_H13d ]. % 47.07/47.28 apply (zenon_L124_); trivial. % 47.07/47.28 apply (zenon_L142_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.07/47.28 apply (zenon_L151_); trivial. % 47.07/47.28 apply (zenon_L152_); trivial. % 47.07/47.28 apply (zenon_L366_); trivial. % 47.07/47.28 apply (zenon_L381_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2cf | zenon_intro zenon_H1da ]. % 47.07/47.28 apply (zenon_L320_); trivial. % 47.07/47.28 apply (zenon_L324_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4bf); [ zenon_intro zenon_H186 | zenon_intro zenon_H4cb ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4cb); [ zenon_intro zenon_H18b | zenon_intro zenon_H2e6 ]. % 47.07/47.28 apply (zenon_L251_); trivial. % 47.07/47.28 apply (zenon_L278_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H4fa); [ zenon_intro zenon_H4fc | zenon_intro zenon_H4fb ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H423); [ zenon_intro zenon_H18c | zenon_intro zenon_H4bf ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2da ]. % 47.07/47.28 apply (zenon_L279_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H29f | zenon_intro zenon_H2e1 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.07/47.28 apply (zenon_L218_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.07/47.28 apply (zenon_L219_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cd); [ zenon_intro zenon_H23 | zenon_intro zenon_H3ce ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H4f | zenon_intro zenon_H167 ]. % 47.07/47.28 apply (zenon_L280_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H16c ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.07/47.28 apply (zenon_L45_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.07/47.28 apply (zenon_L282_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.07/47.28 cut (((h2 (e11)) = (e21)) = ((h2 (op1 (e12) (e10))) = (op2 (h2 (e12)) (h2 (e10))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4fc. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H37b. % 47.07/47.28 cut (((e21) = (op2 (h2 (e12)) (h2 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H4fd]. % 47.07/47.28 cut (((h2 (e11)) = (h2 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H4fe]. % 47.07/47.28 congruence. % 47.07/47.28 elim (classic ((h2 (op1 (e12) (e10))) = (h2 (op1 (e12) (e10))))); [ zenon_intro zenon_H4ff | zenon_intro zenon_H500 ]. % 47.07/47.28 cut (((h2 (op1 (e12) (e10))) = (h2 (op1 (e12) (e10)))) = ((h2 (e11)) = (h2 (op1 (e12) (e10))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4fe. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H4ff. % 47.07/47.28 cut (((h2 (op1 (e12) (e10))) = (h2 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H500]. % 47.07/47.28 cut (((h2 (op1 (e12) (e10))) = (h2 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H501]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((op1 (e12) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H502]. % 47.07/47.28 congruence. % 47.07/47.28 exact (zenon_H502 zenon_Hed). % 47.07/47.28 apply zenon_H500. apply refl_equal. % 47.07/47.28 apply zenon_H500. apply refl_equal. % 47.07/47.28 elim (classic ((op2 (h2 (e12)) (h2 (e10))) = (op2 (h2 (e12)) (h2 (e10))))); [ zenon_intro zenon_H503 | zenon_intro zenon_H504 ]. % 47.07/47.28 cut (((op2 (h2 (e12)) (h2 (e10))) = (op2 (h2 (e12)) (h2 (e10)))) = ((e21) = (op2 (h2 (e12)) (h2 (e10))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H4fd. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H503. % 47.07/47.28 cut (((op2 (h2 (e12)) (h2 (e10))) = (op2 (h2 (e12)) (h2 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H504]. % 47.07/47.28 cut (((op2 (h2 (e12)) (h2 (e10))) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H505]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((op2 (e22) (e20)) = (e21)) = ((op2 (h2 (e12)) (h2 (e10))) = (e21))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H505. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H2a8. % 47.07/47.28 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 47.07/47.28 cut (((op2 (e22) (e20)) = (op2 (h2 (e12)) (h2 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H506]. % 47.07/47.28 congruence. % 47.07/47.28 elim (classic ((op2 (h2 (e12)) (h2 (e10))) = (op2 (h2 (e12)) (h2 (e10))))); [ zenon_intro zenon_H503 | zenon_intro zenon_H504 ]. % 47.07/47.28 cut (((op2 (h2 (e12)) (h2 (e10))) = (op2 (h2 (e12)) (h2 (e10)))) = ((op2 (e22) (e20)) = (op2 (h2 (e12)) (h2 (e10))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H506. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H503. % 47.07/47.28 cut (((op2 (h2 (e12)) (h2 (e10))) = (op2 (h2 (e12)) (h2 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H504]. % 47.07/47.28 cut (((op2 (h2 (e12)) (h2 (e10))) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H507]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((h2 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 47.07/47.28 cut (((h2 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H329]. % 47.07/47.28 congruence. % 47.07/47.28 apply (zenon_L325_); trivial. % 47.07/47.28 apply (zenon_L1_); trivial. % 47.07/47.28 apply zenon_H504. apply refl_equal. % 47.07/47.28 apply zenon_H504. apply refl_equal. % 47.07/47.28 apply zenon_H181. apply refl_equal. % 47.07/47.28 apply zenon_H504. apply refl_equal. % 47.07/47.28 apply zenon_H504. apply refl_equal. % 47.07/47.28 apply (zenon_L343_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H141 | zenon_intro zenon_H14f ]. % 47.07/47.28 apply (zenon_L298_); trivial. % 47.07/47.28 apply (zenon_L306_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H1d | zenon_intro zenon_H3cf ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cf); [ zenon_intro zenon_H22 | zenon_intro zenon_H13d ]. % 47.07/47.28 apply (zenon_L124_); trivial. % 47.07/47.28 apply (zenon_L142_); trivial. % 47.07/47.28 apply (zenon_L381_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2cf | zenon_intro zenon_H1da ]. % 47.07/47.28 apply (zenon_L320_); trivial. % 47.07/47.28 apply (zenon_L324_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4bf); [ zenon_intro zenon_H186 | zenon_intro zenon_H4cb ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4cb); [ zenon_intro zenon_H18b | zenon_intro zenon_H2e6 ]. % 47.07/47.28 apply (zenon_L251_); trivial. % 47.07/47.28 apply (zenon_L278_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H4fb); [ zenon_intro zenon_H509 | zenon_intro zenon_H508 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.28 apply (zenon_L326_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.28 cut (((h2 (e10)) = (op2 (op2 (e21) (e21)) (e21))) = ((h2 (op1 (e12) (e11))) = (op2 (h2 (e12)) (h2 (e11))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H509. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H13. % 47.07/47.28 cut (((op2 (op2 (e21) (e21)) (e21)) = (op2 (h2 (e12)) (h2 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H50a]. % 47.07/47.28 cut (((h2 (e10)) = (h2 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H50b]. % 47.07/47.28 congruence. % 47.07/47.28 elim (classic ((h2 (op1 (e12) (e11))) = (h2 (op1 (e12) (e11))))); [ zenon_intro zenon_H50c | zenon_intro zenon_H50d ]. % 47.07/47.28 cut (((h2 (op1 (e12) (e11))) = (h2 (op1 (e12) (e11)))) = ((h2 (e10)) = (h2 (op1 (e12) (e11))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H50b. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H50c. % 47.07/47.28 cut (((h2 (op1 (e12) (e11))) = (h2 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H50d]. % 47.07/47.28 cut (((h2 (op1 (e12) (e11))) = (h2 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H50e]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((op1 (e12) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H50f]. % 47.07/47.28 congruence. % 47.07/47.28 exact (zenon_H50f zenon_H32e). % 47.07/47.28 apply zenon_H50d. apply refl_equal. % 47.07/47.28 apply zenon_H50d. apply refl_equal. % 47.07/47.28 cut (((e21) = (h2 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H4f1]. % 47.07/47.28 cut (((op2 (e21) (e21)) = (h2 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H510]. % 47.07/47.28 congruence. % 47.07/47.28 apply zenon_H510. apply sym_equal. exact zenon_H32a. % 47.07/47.28 apply zenon_H4f1. apply sym_equal. exact zenon_H37b. % 47.07/47.28 apply (zenon_L19_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H508); [ zenon_intro zenon_H396 | zenon_intro zenon_H511 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H423); [ zenon_intro zenon_H18c | zenon_intro zenon_H4bf ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2da ]. % 47.07/47.28 apply (zenon_L279_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H29f | zenon_intro zenon_H2e1 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.07/47.28 apply (zenon_L218_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.07/47.28 apply (zenon_L219_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.07/47.28 apply (zenon_L307_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.07/47.28 apply (zenon_L156_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.07/47.28 apply (zenon_L160_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2bc); [ zenon_intro zenon_H23b | zenon_intro zenon_H2c4 ]. % 47.07/47.28 apply (zenon_L222_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_H2aa | zenon_intro zenon_H2c5 ]. % 47.07/47.28 apply (zenon_L223_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H29a | zenon_intro zenon_H23c ]. % 47.07/47.28 apply (zenon_L321_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H226 ]. % 47.07/47.28 apply (zenon_L151_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H227 ]. % 47.07/47.28 apply (zenon_L168_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H207 | zenon_intro zenon_H223 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cd); [ zenon_intro zenon_H23 | zenon_intro zenon_H3ce ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H4f | zenon_intro zenon_H167 ]. % 47.07/47.28 apply (zenon_L280_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H16c ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.07/47.28 apply (zenon_L45_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.07/47.28 apply (zenon_L282_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H50 | zenon_intro zenon_H168 ]. % 47.07/47.28 apply (zenon_L283_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H57 | zenon_intro zenon_H169 ]. % 47.07/47.28 apply (zenon_L15_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H5b | zenon_intro zenon_H8e ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.28 apply (zenon_L326_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.28 apply (zenon_L50_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.28 apply (zenon_L51_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.28 apply (zenon_L137_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.28 apply (zenon_L10_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.28 apply (zenon_L327_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.28 apply (zenon_L403_); trivial. % 47.07/47.28 apply (zenon_L84_); trivial. % 47.07/47.28 apply (zenon_L19_); trivial. % 47.07/47.28 apply (zenon_L361_); trivial. % 47.07/47.28 apply (zenon_L343_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H141 | zenon_intro zenon_H14f ]. % 47.07/47.28 apply (zenon_L298_); trivial. % 47.07/47.28 apply (zenon_L306_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H1d | zenon_intro zenon_H3cf ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cf); [ zenon_intro zenon_H22 | zenon_intro zenon_H13d ]. % 47.07/47.28 apply (zenon_L124_); trivial. % 47.07/47.28 apply (zenon_L142_); trivial. % 47.07/47.28 apply (zenon_L210_); trivial. % 47.07/47.28 apply (zenon_L167_); trivial. % 47.07/47.28 apply (zenon_L366_); trivial. % 47.07/47.28 apply (zenon_L381_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2cf | zenon_intro zenon_H1da ]. % 47.07/47.28 apply (zenon_L320_); trivial. % 47.07/47.28 apply (zenon_L324_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4bf); [ zenon_intro zenon_H186 | zenon_intro zenon_H4cb ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4cb); [ zenon_intro zenon_H18b | zenon_intro zenon_H2e6 ]. % 47.07/47.28 apply (zenon_L251_); trivial. % 47.07/47.28 apply (zenon_L278_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H511); [ zenon_intro zenon_H513 | zenon_intro zenon_H512 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H423); [ zenon_intro zenon_H18c | zenon_intro zenon_H4bf ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2da ]. % 47.07/47.28 apply (zenon_L279_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H29f | zenon_intro zenon_H2e1 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.07/47.28 apply (zenon_L218_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.07/47.28 apply (zenon_L219_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.07/47.28 apply (zenon_L307_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.07/47.28 apply (zenon_L156_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2bc); [ zenon_intro zenon_H23b | zenon_intro zenon_H2c4 ]. % 47.07/47.28 apply (zenon_L222_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_H2aa | zenon_intro zenon_H2c5 ]. % 47.07/47.28 apply (zenon_L223_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H29a | zenon_intro zenon_H23c ]. % 47.07/47.28 apply (zenon_L321_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cd); [ zenon_intro zenon_H23 | zenon_intro zenon_H3ce ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H4f | zenon_intro zenon_H167 ]. % 47.07/47.28 apply (zenon_L280_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H16c ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.07/47.28 apply (zenon_L45_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.07/47.28 apply (zenon_L282_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H50 | zenon_intro zenon_H168 ]. % 47.07/47.28 apply (zenon_L283_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H57 | zenon_intro zenon_H169 ]. % 47.07/47.28 apply (zenon_L15_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H5b | zenon_intro zenon_H8e ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.28 apply (zenon_L50_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.28 apply (zenon_L51_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.28 apply (zenon_L137_); trivial. % 47.07/47.28 cut (((h2 (e12)) = (op2 (e21) (e21))) = ((h2 (op1 (e12) (e13))) = (op2 (h2 (e12)) (h2 (e13))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H513. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H32a. % 47.07/47.28 cut (((op2 (e21) (e21)) = (op2 (h2 (e12)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H514]. % 47.07/47.28 cut (((h2 (e12)) = (h2 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H515]. % 47.07/47.28 congruence. % 47.07/47.28 elim (classic ((h2 (op1 (e12) (e13))) = (h2 (op1 (e12) (e13))))); [ zenon_intro zenon_H516 | zenon_intro zenon_H517 ]. % 47.07/47.28 cut (((h2 (op1 (e12) (e13))) = (h2 (op1 (e12) (e13)))) = ((h2 (e12)) = (h2 (op1 (e12) (e13))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H515. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H516. % 47.07/47.28 cut (((h2 (op1 (e12) (e13))) = (h2 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H517]. % 47.07/47.28 cut (((h2 (op1 (e12) (e13))) = (h2 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H518]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((op1 (e12) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H519]. % 47.07/47.28 congruence. % 47.07/47.28 exact (zenon_H519 zenon_Hb8). % 47.07/47.28 apply zenon_H517. apply refl_equal. % 47.07/47.28 apply zenon_H517. apply refl_equal. % 47.07/47.28 elim (classic ((op2 (h2 (e12)) (h2 (e13))) = (op2 (h2 (e12)) (h2 (e13))))); [ zenon_intro zenon_H51a | zenon_intro zenon_H51b ]. % 47.07/47.28 cut (((op2 (h2 (e12)) (h2 (e13))) = (op2 (h2 (e12)) (h2 (e13)))) = ((op2 (e21) (e21)) = (op2 (h2 (e12)) (h2 (e13))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H514. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H51a. % 47.07/47.28 cut (((op2 (h2 (e12)) (h2 (e13))) = (op2 (h2 (e12)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H51b]. % 47.07/47.28 cut (((op2 (h2 (e12)) (h2 (e13))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H51c]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((op2 (e22) (e23)) = (e22)) = ((op2 (h2 (e12)) (h2 (e13))) = (op2 (e21) (e21)))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H51c. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H23c. % 47.07/47.28 cut (((e22) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H4e3]. % 47.07/47.28 cut (((op2 (e22) (e23)) = (op2 (h2 (e12)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H51d]. % 47.07/47.28 congruence. % 47.07/47.28 elim (classic ((op2 (h2 (e12)) (h2 (e13))) = (op2 (h2 (e12)) (h2 (e13))))); [ zenon_intro zenon_H51a | zenon_intro zenon_H51b ]. % 47.07/47.28 cut (((op2 (h2 (e12)) (h2 (e13))) = (op2 (h2 (e12)) (h2 (e13)))) = ((op2 (e22) (e23)) = (op2 (h2 (e12)) (h2 (e13))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H51d. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H51a. % 47.07/47.28 cut (((op2 (h2 (e12)) (h2 (e13))) = (op2 (h2 (e12)) (h2 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H51b]. % 47.07/47.28 cut (((op2 (h2 (e12)) (h2 (e13))) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H51e]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((h2 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H367]. % 47.07/47.28 cut (((h2 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H329]. % 47.07/47.28 congruence. % 47.07/47.28 apply (zenon_L325_); trivial. % 47.07/47.28 apply (zenon_L391_); trivial. % 47.07/47.28 apply zenon_H51b. apply refl_equal. % 47.07/47.28 apply zenon_H51b. apply refl_equal. % 47.07/47.28 exact (zenon_H4e3 zenon_H183). % 47.07/47.28 apply zenon_H51b. apply refl_equal. % 47.07/47.28 apply zenon_H51b. apply refl_equal. % 47.07/47.28 apply (zenon_L361_); trivial. % 47.07/47.28 apply (zenon_L343_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H141 | zenon_intro zenon_H14f ]. % 47.07/47.28 apply (zenon_L298_); trivial. % 47.07/47.28 apply (zenon_L306_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H1d | zenon_intro zenon_H3cf ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cf); [ zenon_intro zenon_H22 | zenon_intro zenon_H13d ]. % 47.07/47.28 apply (zenon_L124_); trivial. % 47.07/47.28 apply (zenon_L142_); trivial. % 47.07/47.28 apply (zenon_L366_); trivial. % 47.07/47.28 apply (zenon_L381_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2cf | zenon_intro zenon_H1da ]. % 47.07/47.28 apply (zenon_L320_); trivial. % 47.07/47.28 apply (zenon_L324_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4bf); [ zenon_intro zenon_H186 | zenon_intro zenon_H4cb ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4cb); [ zenon_intro zenon_H18b | zenon_intro zenon_H2e6 ]. % 47.07/47.28 apply (zenon_L251_); trivial. % 47.07/47.28 apply (zenon_L278_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H512); [ zenon_intro zenon_H520 | zenon_intro zenon_H51f ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H423); [ zenon_intro zenon_H18c | zenon_intro zenon_H4bf ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2da ]. % 47.07/47.28 apply (zenon_L279_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H29f | zenon_intro zenon_H2e1 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.07/47.28 apply (zenon_L218_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.07/47.28 apply (zenon_L219_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27d); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H280 ]. % 47.07/47.28 apply (zenon_L307_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H281 ]. % 47.07/47.28 apply (zenon_L158_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H23b | zenon_intro zenon_H257 ]. % 47.07/47.28 apply (zenon_L222_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cd); [ zenon_intro zenon_H23 | zenon_intro zenon_H3ce ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H4f | zenon_intro zenon_H167 ]. % 47.07/47.28 apply (zenon_L280_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H16c ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.07/47.28 apply (zenon_L45_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.07/47.28 apply (zenon_L282_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H50 | zenon_intro zenon_H316 ]. % 47.07/47.28 apply (zenon_L283_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H316); [ zenon_intro zenon_H301 | zenon_intro zenon_H317 ]. % 47.07/47.28 apply (zenon_L285_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H317); [ zenon_intro zenon_Hee | zenon_intro zenon_Hf7 ]. % 47.07/47.28 apply (zenon_L50_); trivial. % 47.07/47.28 elim (classic ((op2 (h2 (e13)) (h2 (e10))) = (op2 (h2 (e13)) (h2 (e10))))); [ zenon_intro zenon_H521 | zenon_intro zenon_H522 ]. % 47.07/47.28 cut (((op2 (h2 (e13)) (h2 (e10))) = (op2 (h2 (e13)) (h2 (e10)))) = ((h2 (op1 (e13) (e10))) = (op2 (h2 (e13)) (h2 (e10))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H520. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H521. % 47.07/47.28 cut (((op2 (h2 (e13)) (h2 (e10))) = (op2 (h2 (e13)) (h2 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H522]. % 47.07/47.28 cut (((op2 (h2 (e13)) (h2 (e10))) = (h2 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H523]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((op2 (e23) (e20)) = (e22)) = ((op2 (h2 (e13)) (h2 (e10))) = (h2 (op1 (e13) (e10))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H523. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H257. % 47.07/47.28 cut (((e22) = (h2 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3a2]. % 47.07/47.28 cut (((op2 (e23) (e20)) = (op2 (h2 (e13)) (h2 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H524]. % 47.07/47.28 congruence. % 47.07/47.28 elim (classic ((op2 (h2 (e13)) (h2 (e10))) = (op2 (h2 (e13)) (h2 (e10))))); [ zenon_intro zenon_H521 | zenon_intro zenon_H522 ]. % 47.07/47.28 cut (((op2 (h2 (e13)) (h2 (e10))) = (op2 (h2 (e13)) (h2 (e10)))) = ((op2 (e23) (e20)) = (op2 (h2 (e13)) (h2 (e10))))). % 47.07/47.28 intro zenon_D_pnotp. % 47.07/47.28 apply zenon_H524. % 47.07/47.28 rewrite <- zenon_D_pnotp. % 47.07/47.28 exact zenon_H521. % 47.07/47.28 cut (((op2 (h2 (e13)) (h2 (e10))) = (op2 (h2 (e13)) (h2 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H522]. % 47.07/47.28 cut (((op2 (h2 (e13)) (h2 (e10))) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H525]. % 47.07/47.28 congruence. % 47.07/47.28 cut (((h2 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 47.07/47.28 cut (((h2 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H367]. % 47.07/47.28 congruence. % 47.07/47.28 apply (zenon_L391_); trivial. % 47.07/47.28 apply (zenon_L1_); trivial. % 47.07/47.28 apply zenon_H522. apply refl_equal. % 47.07/47.28 apply zenon_H522. apply refl_equal. % 47.07/47.28 apply (zenon_L404_); trivial. % 47.07/47.28 apply zenon_H522. apply refl_equal. % 47.07/47.28 apply zenon_H522. apply refl_equal. % 47.07/47.28 apply (zenon_L343_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H141 | zenon_intro zenon_H14f ]. % 47.07/47.28 apply (zenon_L298_); trivial. % 47.07/47.28 apply (zenon_L306_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H1d | zenon_intro zenon_H3cf ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cf); [ zenon_intro zenon_H22 | zenon_intro zenon_H13d ]. % 47.07/47.28 apply (zenon_L124_); trivial. % 47.07/47.28 apply (zenon_L142_); trivial. % 47.07/47.28 apply (zenon_L381_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2cf | zenon_intro zenon_H1da ]. % 47.07/47.28 apply (zenon_L320_); trivial. % 47.07/47.28 apply (zenon_L324_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4bf); [ zenon_intro zenon_H186 | zenon_intro zenon_H4cb ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4cb); [ zenon_intro zenon_H18b | zenon_intro zenon_H2e6 ]. % 47.07/47.28 apply (zenon_L251_); trivial. % 47.07/47.28 apply (zenon_L278_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H51f); [ zenon_intro zenon_H3a8 | zenon_intro zenon_H526 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H423); [ zenon_intro zenon_H18c | zenon_intro zenon_H4bf ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2da ]. % 47.07/47.28 apply (zenon_L279_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H29f | zenon_intro zenon_H2e1 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.07/47.28 apply (zenon_L160_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H2e2 ]. % 47.07/47.28 apply (zenon_L220_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2a4 | zenon_intro zenon_H2e3 ]. % 47.07/47.28 apply (zenon_L221_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H22e ]. % 47.07/47.28 apply (zenon_L168_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cd); [ zenon_intro zenon_H23 | zenon_intro zenon_H3ce ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H4f | zenon_intro zenon_H167 ]. % 47.07/47.28 apply (zenon_L280_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H16c ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H69 | zenon_intro zenon_Hd1 ]. % 47.07/47.28 apply (zenon_L19_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H7d | zenon_intro zenon_Hd2 ]. % 47.07/47.28 apply (zenon_L40_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Haf | zenon_intro zenon_Hb5 ]. % 47.07/47.28 apply (zenon_L28_); trivial. % 47.07/47.28 apply (zenon_L405_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H141 | zenon_intro zenon_H14f ]. % 47.07/47.28 apply (zenon_L298_); trivial. % 47.07/47.28 apply (zenon_L306_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H1d | zenon_intro zenon_H3cf ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cf); [ zenon_intro zenon_H22 | zenon_intro zenon_H13d ]. % 47.07/47.28 apply (zenon_L124_); trivial. % 47.07/47.28 apply (zenon_L142_); trivial. % 47.07/47.28 apply (zenon_L167_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2cf | zenon_intro zenon_H1da ]. % 47.07/47.28 apply (zenon_L320_); trivial. % 47.07/47.28 apply (zenon_L324_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4bf); [ zenon_intro zenon_H186 | zenon_intro zenon_H4cb ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4cb); [ zenon_intro zenon_H18b | zenon_intro zenon_H2e6 ]. % 47.07/47.28 apply (zenon_L251_); trivial. % 47.07/47.28 apply (zenon_L278_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H526); [ zenon_intro zenon_H3bb | zenon_intro zenon_H527 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H423); [ zenon_intro zenon_H18c | zenon_intro zenon_H4bf ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2da ]. % 47.07/47.28 apply (zenon_L279_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H29f | zenon_intro zenon_H2e1 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.07/47.28 apply (zenon_L218_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.07/47.28 apply (zenon_L219_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.07/47.28 apply (zenon_L307_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.07/47.28 apply (zenon_L156_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.28 apply (zenon_L148_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.28 apply (zenon_L220_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.28 apply (zenon_L206_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.07/47.28 apply (zenon_L148_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H186 | zenon_intro zenon_H2c0 ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2c1 ]. % 47.07/47.28 apply (zenon_L160_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e3 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H355); [ zenon_intro zenon_H18b | zenon_intro zenon_H358 ]. % 47.07/47.28 apply (zenon_L157_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H358); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H359 ]. % 47.07/47.28 apply (zenon_L398_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H359); [ zenon_intro zenon_H290 | zenon_intro zenon_H260 ]. % 47.07/47.28 apply (zenon_L213_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cd); [ zenon_intro zenon_H23 | zenon_intro zenon_H3ce ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H4f | zenon_intro zenon_H167 ]. % 47.07/47.28 apply (zenon_L280_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H16c ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H4f | zenon_intro zenon_H16d ]. % 47.07/47.28 apply (zenon_L45_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_He1 | zenon_intro zenon_H16e ]. % 47.07/47.28 apply (zenon_L282_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_Hed | zenon_intro zenon_H15a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H50 | zenon_intro zenon_H168 ]. % 47.07/47.28 apply (zenon_L283_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H57 | zenon_intro zenon_H169 ]. % 47.07/47.28 apply (zenon_L15_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H5b | zenon_intro zenon_H8e ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H50 | zenon_intro zenon_H316 ]. % 47.07/47.28 apply (zenon_L283_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H316); [ zenon_intro zenon_H301 | zenon_intro zenon_H317 ]. % 47.07/47.28 apply (zenon_L285_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H317); [ zenon_intro zenon_Hee | zenon_intro zenon_Hf7 ]. % 47.07/47.28 apply (zenon_L50_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H2d | zenon_intro zenon_H16a ]. % 47.07/47.28 apply (zenon_L7_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H5f | zenon_intro zenon_H16b ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H2d | zenon_intro zenon_H49 ]. % 47.07/47.28 apply (zenon_L7_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H33 | zenon_intro zenon_H347 ]. % 47.07/47.28 apply (zenon_L9_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H32c | zenon_intro zenon_H348 ]. % 47.07/47.28 apply (zenon_L326_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H348); [ zenon_intro zenon_Hdf | zenon_intro zenon_H172 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H1d | zenon_intro zenon_H349 ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H349); [ zenon_intro zenon_H32c | zenon_intro zenon_H34a ]. % 47.07/47.28 apply (zenon_L326_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H34a); [ zenon_intro zenon_H32e | zenon_intro zenon_H69 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_Hee | zenon_intro zenon_H131 ]. % 47.07/47.28 apply (zenon_L50_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H132 ]. % 47.07/47.28 apply (zenon_L51_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hb8 ]. % 47.07/47.28 apply (zenon_L137_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H3a | zenon_intro zenon_Had ]. % 47.07/47.28 apply (zenon_L10_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H60 | zenon_intro zenon_Hae ]. % 47.07/47.28 apply (zenon_L327_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H71 | zenon_intro zenon_H33a ]. % 47.07/47.28 apply (zenon_L113_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H69 | zenon_intro zenon_H33b ]. % 47.07/47.28 apply (zenon_L19_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H33b); [ zenon_intro zenon_H102 | zenon_intro zenon_H30a ]. % 47.07/47.28 apply (zenon_L288_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H158 ]. % 47.07/47.28 apply (zenon_L412_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H136 | zenon_intro zenon_H159 ]. % 47.07/47.28 apply (zenon_L92_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H152 ]. % 47.07/47.28 apply (zenon_L84_); trivial. % 47.07/47.28 apply (zenon_L388_); trivial. % 47.07/47.28 apply (zenon_L84_); trivial. % 47.07/47.28 apply (zenon_L19_); trivial. % 47.07/47.28 apply (zenon_L411_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H41 ]. % 47.07/47.28 apply (zenon_L10_); trivial. % 47.07/47.28 apply (zenon_L11_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd7 ]. % 47.07/47.28 apply (zenon_L133_); trivial. % 47.07/47.28 apply (zenon_L412_); trivial. % 47.07/47.28 apply (zenon_L361_); trivial. % 47.07/47.28 apply (zenon_L343_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H141 | zenon_intro zenon_H14f ]. % 47.07/47.28 apply (zenon_L298_); trivial. % 47.07/47.28 apply (zenon_L306_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H1d | zenon_intro zenon_H3cf ]. % 47.07/47.28 apply (zenon_L4_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H3cf); [ zenon_intro zenon_H22 | zenon_intro zenon_H13d ]. % 47.07/47.28 apply (zenon_L124_); trivial. % 47.07/47.28 apply (zenon_L142_); trivial. % 47.07/47.28 apply (zenon_L167_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.07/47.28 apply (zenon_L151_); trivial. % 47.07/47.28 apply (zenon_L152_); trivial. % 47.07/47.28 apply (zenon_L366_); trivial. % 47.07/47.28 apply (zenon_L381_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2cf | zenon_intro zenon_H1da ]. % 47.07/47.28 apply (zenon_L320_); trivial. % 47.07/47.28 apply (zenon_L324_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4bf); [ zenon_intro zenon_H186 | zenon_intro zenon_H4cb ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4cb); [ zenon_intro zenon_H18b | zenon_intro zenon_H2e6 ]. % 47.07/47.28 apply (zenon_L251_); trivial. % 47.07/47.28 apply (zenon_L278_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H527); [ zenon_intro zenon_H3c7 | zenon_intro zenon_H528 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H423); [ zenon_intro zenon_H18c | zenon_intro zenon_H4bf ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2da ]. % 47.07/47.28 apply (zenon_L279_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H29f | zenon_intro zenon_H2e1 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2be ]. % 47.07/47.28 apply (zenon_L279_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H2bf ]. % 47.07/47.28 apply (zenon_L219_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2b8 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H27e ]. % 47.07/47.28 apply (zenon_L307_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1bf | zenon_intro zenon_H27f ]. % 47.07/47.28 apply (zenon_L156_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1db ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H195 | zenon_intro zenon_H282 ]. % 47.07/47.28 apply (zenon_L148_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H283 ]. % 47.07/47.28 apply (zenon_L220_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H24e | zenon_intro zenon_H278 ]. % 47.07/47.28 apply (zenon_L206_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b1 ]. % 47.07/47.28 apply (zenon_L148_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H19c | zenon_intro zenon_H1b2 ]. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H19b | zenon_intro zenon_H2db ]. % 47.07/47.28 apply (zenon_L150_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H1cd | zenon_intro zenon_H2dc ]. % 47.07/47.28 apply (zenon_L160_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H1dd ]. % 47.07/47.28 apply (zenon_L399_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_H1da | zenon_intro zenon_H2c8 ]. % 47.07/47.28 apply (zenon_L207_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2c8); [ zenon_intro zenon_H1de | zenon_intro zenon_H2c9 ]. % 47.07/47.28 apply (zenon_L166_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2c9); [ zenon_intro zenon_H222 | zenon_intro zenon_H243 ]. % 47.07/47.28 apply (zenon_L233_); trivial. % 47.07/47.28 apply (zenon_L427_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1a9 ]. % 47.07/47.28 apply (zenon_L151_); trivial. % 47.07/47.28 apply (zenon_L152_); trivial. % 47.07/47.28 apply (zenon_L366_); trivial. % 47.07/47.28 apply (zenon_L381_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2cf | zenon_intro zenon_H1da ]. % 47.07/47.28 apply (zenon_L320_); trivial. % 47.07/47.28 apply (zenon_L324_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4bf); [ zenon_intro zenon_H186 | zenon_intro zenon_H4cb ]. % 47.07/47.28 apply (zenon_L145_); trivial. % 47.07/47.28 apply (zenon_or_s _ _ zenon_H4cb); [ zenon_intro zenon_H18b | zenon_intro zenon_H2e6 ]. % 47.07/47.28 apply (zenon_L251_); trivial. % 47.07/47.28 apply (zenon_L278_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H528); [ zenon_intro zenon_H52a | zenon_intro zenon_H529 ]. % 47.07/47.28 apply (zenon_notor_s _ _ zenon_H52a). zenon_intro zenon_H12. zenon_intro zenon_H52b. % 47.07/47.28 apply (zenon_L1_); trivial. % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H529); [ zenon_intro zenon_H52d | zenon_intro zenon_H52c ]. % 47.07/47.28 apply (zenon_notor_s _ _ zenon_H52d). zenon_intro zenon_H52f. zenon_intro zenon_H52e. % 47.07/47.28 apply (zenon_notor_s _ _ zenon_H52e). zenon_intro zenon_H388. zenon_intro zenon_H530. % 47.07/47.28 exact (zenon_H388 zenon_H37b). % 47.07/47.28 apply (zenon_notand_s _ _ zenon_H52c); [ zenon_intro zenon_H532 | zenon_intro zenon_H531 ]. % 47.07/47.28 apply (zenon_notor_s _ _ zenon_H532). zenon_intro zenon_H534. zenon_intro zenon_H533. % 47.07/47.28 apply (zenon_notor_s _ _ zenon_H533). zenon_intro zenon_H536. zenon_intro zenon_H535. % 47.07/47.28 apply (zenon_notor_s _ _ zenon_H535). zenon_intro zenon_H329. zenon_intro zenon_H537. % 47.07/47.28 apply (zenon_L325_); trivial. % 47.07/47.28 apply (zenon_notor_s _ _ zenon_H531). zenon_intro zenon_H539. zenon_intro zenon_H538. % 47.07/47.28 apply (zenon_notor_s _ _ zenon_H538). zenon_intro zenon_H53b. zenon_intro zenon_H53a. % 47.07/47.28 apply (zenon_notor_s _ _ zenon_H53a). zenon_intro zenon_H53c. zenon_intro zenon_H367. % 47.07/47.28 apply (zenon_L391_); trivial. % 47.07/47.28 Qed. % 47.07/47.28 % SZS output end Proof % 47.07/47.28 (* END-PROOF *) % 47.07/47.28 nodes searched: 1993535 % 47.07/47.28 max branch formulas: 2155 % 47.07/47.28 proof nodes created: 32373 % 47.07/47.28 formulas created: 1117574 % 47.07/47.28 %------------------------------------------------------------------------------